Daily Papers

We introduce Score identity Distillation (SiD), an innovative data-free method that distills the generative capabilities of pretrained diffusion models into a single-step generator. SiD not only facilitates an exponentially fast reduction in Fr\'echet inception distance (FID) during distillation but also approaches or even exceeds the FID performance of the original teacher diffusion models. By reformulating forward diffusion processes as semi-implicit distributions, we leverage three score-related identities to create an innovative loss mechanism. This mechanism achieves rapid FID reduction by training the generator using its own synthesized images, eliminating the need for real data or reverse-diffusion-based generation, all accomplished within significantly shortened generation time. Upon evaluation across four benchmark datasets, the SiD algorithm demonstrates high iteration efficiency during distillation and surpasses competing distillation approaches, whether they are one-step or few-step, data-free, or dependent on training data, in terms of generation quality. This achievement not only redefines the benchmarks for efficiency and effectiveness in diffusion distillation but also in the broader field of diffusion-based generation. The PyTorch implementation is available at https://github.com/mingyuanzhou/SiD

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we propose an innovative second-order algorithm that employs a Newton-type method with hard thresholding. This algorithm overcomes the linear convergence limitations of first-order methods while preserving their hallmark per-iteration computational efficiency. We provide theoretical guarantees that our algorithm converges to the s-sparse ground truth signal x^{natural} in R^n (up to a global sign) at a quadratic convergence rate after at most O(log (Vertx^{natural} Vert /x_{min}^{natural})) iterations, using Omega(s^2log n) Gaussian random samples. Numerical experiments show that our algorithm achieves a significantly faster convergence rate than state-of-the-art methods.

Continuous chain-of-thought has been shown to be effective in saving reasoning tokens for large language models. By reasoning with continuous latent thought tokens, continuous CoT is able to perform implicit reasoning in a compact manner. However, the sequential dependencies between latent thought tokens spoil parallel training, leading to long training time. In this paper, we propose Parallel Continuous Chain-of-Thought (PCCoT), which performs Jacobi iteration on the latent thought tokens, updating them iteratively in parallel instead of sequentially and thus improving both training and inference efficiency of continuous CoT. Experiments demonstrate that by choosing the proper number of iterations, we are able to achieve comparable or even better performance while saving nearly 50% of the training and inference time. Moreover, PCCoT shows better stability and robustness in the training process. Our code is available at https://github.com/whyNLP/PCCoT.

Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting finite-sum structure, which generically arises in empirical variants of learning problems in these contexts. Further, methods with computable approximation errors are highly desirable, as they provide verifiable exit criteria. Motivated by these applications, we study finite-sum monotone inclusion problems, which model broad classes of equilibrium problems. Our main contributions are variants of the classical Halpern iteration that employ variance reduction to obtain improved complexity guarantees in which n component operators in the finite sum are ``on average'' either cocoercive or Lipschitz continuous and monotone, with parameter L. The resulting oracle complexity of our methods, which provide guarantees for the last iterate and for a (computable) operator norm residual, is mathcal{O}( n + nLvarepsilon^{-1}), which improves upon existing methods by a factor up to n. This constitutes the first variance reduction-type result for general finite-sum monotone inclusions and for more specific problems such as convex-concave optimization when operator norm residual is the optimality measure. We further argue that, up to poly-logarithmic factors, this complexity is unimprovable in the monotone Lipschitz setting; i.e., the provided result is near-optimal.

Image generation models have achieved widespread applications. As an instance, the TarFlow model combines the transformer architecture with Normalizing Flow models, achieving state-of-the-art results on multiple benchmarks. However, due to the causal form of attention requiring sequential computation, TarFlow's sampling process is extremely slow. In this paper, we demonstrate that through a series of optimization strategies, TarFlow sampling can be greatly accelerated by using the Gauss-Seidel-Jacobi (abbreviated as GS-Jacobi) iteration method. Specifically, we find that blocks in the TarFlow model have varying importance: a small number of blocks play a major role in image generation tasks, while other blocks contribute relatively little; some blocks are sensitive to initial values and prone to numerical overflow, while others are relatively robust. Based on these two characteristics, we propose the Convergence Ranking Metric (CRM) and the Initial Guessing Metric (IGM): CRM is used to identify whether a TarFlow block is "simple" (converges in few iterations) or "tough" (requires more iterations); IGM is used to evaluate whether the initial value of the iteration is good. Experiments on four TarFlow models demonstrate that GS-Jacobi sampling can significantly enhance sampling efficiency while maintaining the quality of generated images (measured by FID), achieving speed-ups of 4.53x in Img128cond, 5.32x in AFHQ, 2.96x in Img64uncond, and 2.51x in Img64cond without degrading FID scores or sample quality. Code and checkpoints are accessible on https://github.com/encoreus/GS-Jacobi_for_TarFlow

Normalizing flows (NFs) are end-to-end likelihood-based generative models for continuous data, and have recently regained attention with encouraging progress on image generation. Yet in the video generation domain, where spatiotemporal complexity and computational cost are substantially higher, state-of-the-art systems almost exclusively rely on diffusion-based models. In this work, we revisit this design space by presenting STARFlow-V, a normalizing flow-based video generator with substantial benefits such as end-to-end learning, robust causal prediction, and native likelihood estimation. Building upon the recently proposed STARFlow, STARFlow-V operates in the spatiotemporal latent space with a global-local architecture which restricts causal dependencies to a global latent space while preserving rich local within-frame interactions. This eases error accumulation over time, a common pitfall of standard autoregressive diffusion model generation. Additionally, we propose flow-score matching, which equips the model with a light-weight causal denoiser to improve the video generation consistency in an autoregressive fashion. To improve the sampling efficiency, STARFlow-V employs a video-aware Jacobi iteration scheme that recasts inner updates as parallelizable iterations without breaking causality. Thanks to the invertible structure, the same model can natively support text-to-video, image-to-video as well as video-to-video generation tasks. Empirically, STARFlow-V achieves strong visual fidelity and temporal consistency with practical sampling throughput relative to diffusion-based baselines. These results present the first evidence, to our knowledge, that NFs are capable of high-quality autoregressive video generation, establishing them as a promising research direction for building world models. Code and generated samples are available at https://github.com/apple/ml-starflow.

Humans can learn incrementally, whereas neural networks forget previously acquired information catastrophically. Continual Learning (CL) approaches seek to bridge this gap by facilitating the transfer of knowledge to both previous tasks (backward transfer) and future ones (forward transfer) during training. Recent research has shown that self-supervision can produce versatile models that can generalize well to diverse downstream tasks. However, contrastive self-supervised learning (CSSL), a popular self-supervision technique, has limited effectiveness in online CL (OCL). OCL only permits one iteration of the input dataset, and CSSL's low sample efficiency hinders its use on the input data-stream. In this work, we propose Continual Learning via Equivariant Regularization (CLER), an OCL approach that leverages equivariant tasks for self-supervision, avoiding CSSL's limitations. Our method represents the first attempt at combining equivariant knowledge with CL and can be easily integrated with existing OCL methods. Extensive ablations shed light on how equivariant pretext tasks affect the network's information flow and its impact on CL dynamics.

Open-source reinforcement learning (RL) environments have played a crucial role in driving progress in the development of AI algorithms. In modern RL research, there is a need for simulated environments that are performant, scalable, and modular to enable their utilization in a wider range of potential real-world applications. Therefore, we present Jumanji, a suite of diverse RL environments specifically designed to be fast, flexible, and scalable. Jumanji provides a suite of environments focusing on combinatorial problems frequently encountered in industry, as well as challenging general decision-making tasks. By leveraging the efficiency of JAX and hardware accelerators like GPUs and TPUs, Jumanji enables rapid iteration of research ideas and large-scale experimentation, ultimately empowering more capable agents. Unlike existing RL environment suites, Jumanji is highly customizable, allowing users to tailor the initial state distribution and problem complexity to their needs. Furthermore, we provide actor-critic baselines for each environment, accompanied by preliminary findings on scaling and generalization scenarios. Jumanji aims to set a new standard for speed, adaptability, and scalability of RL environments.

Text-to-image generation has advanced rapidly, yet aligning complex textual prompts with generated visuals remains challenging, especially with intricate object relationships and fine-grained details. This paper introduces Fast Prompt Alignment (FPA), a prompt optimization framework that leverages a one-pass approach, enhancing text-to-image alignment efficiency without the iterative overhead typical of current methods like OPT2I. FPA uses large language models (LLMs) for single-iteration prompt paraphrasing, followed by fine-tuning or in-context learning with optimized prompts to enable real-time inference, reducing computational demands while preserving alignment fidelity. Extensive evaluations on the COCO Captions and PartiPrompts datasets demonstrate that FPA achieves competitive text-image alignment scores at a fraction of the processing time, as validated through both automated metrics (TIFA, VQA) and human evaluation. A human study with expert annotators further reveals a strong correlation between human alignment judgments and automated scores, underscoring the robustness of FPA's improvements. The proposed method showcases a scalable, efficient alternative to iterative prompt optimization, enabling broader applicability in real-time, high-demand settings. The codebase is provided to facilitate further research: https://github.com/tiktok/fast_prompt_alignment

A rising interest in the modality extension of foundation language models warrants discussion on the most effective, and efficient, multimodal training approach. This work focuses on neural machine translation (NMT) and proposes a joint multimodal training regime of Speech-LLM to include automatic speech translation (AST). We investigate two different foundation model architectures, decoder-only GPT and encoder-decoder T5, extended with Canary-1B's speech encoder. To handle joint multimodal training, we propose a novel training framework called EMMeTT. EMMeTT improves training efficiency with the following: balanced sampling across languages, datasets, and modalities; efficient sequential data iteration; and a novel 2D bucketing scheme for multimodal data, complemented by a batch size optimizer (OOMptimizer). We show that a multimodal training consistently helps with both architectures. Moreover, SALM-T5 trained with EMMeTT retains the original NMT capability while outperforming AST baselines on four-language subsets of FLORES and FLEURS. The resultant Multimodal Translation Model produces strong text and speech translation results at the same time.

Slot filling and intent detection are two main tasks in spoken language understanding (SLU) system. In this paper, we propose a novel non-autoregressive model named SlotRefine for joint intent detection and slot filling. Besides, we design a novel two-pass iteration mechanism to handle the uncoordinated slots problem caused by conditional independence of non-autoregressive model. Experiments demonstrate that our model significantly outperforms previous models in slot filling task, while considerably speeding up the decoding (up to X 10.77). In-depth analyses show that 1) pretraining schemes could further enhance our model; 2) two-pass mechanism indeed remedy the uncoordinated slots.

Recent works in volume rendering, e.g. NeRF and 3D Gaussian Splatting (3DGS), significantly advance the rendering quality and efficiency with the help of the learned implicit neural radiance field or 3D Gaussians. Rendering on top of an explicit representation, the vanilla 3DGS and its variants deliver real-time efficiency by optimizing the parametric model with single-view supervision per iteration during training which is adopted from NeRF. Consequently, certain views are overfitted, leading to unsatisfying appearance in novel-view synthesis and imprecise 3D geometries. To solve aforementioned problems, we propose a new 3DGS optimization method embodying four key novel contributions: 1) We transform the conventional single-view training paradigm into a multi-view training strategy. With our proposed multi-view regulation, 3D Gaussian attributes are further optimized without overfitting certain training views. As a general solution, we improve the overall accuracy in a variety of scenarios and different Gaussian variants. 2) Inspired by the benefit introduced by additional views, we further propose a cross-intrinsic guidance scheme, leading to a coarse-to-fine training procedure concerning different resolutions. 3) Built on top of our multi-view regulated training, we further propose a cross-ray densification strategy, densifying more Gaussian kernels in the ray-intersect regions from a selection of views. 4) By further investigating the densification strategy, we found that the effect of densification should be enhanced when certain views are distinct dramatically. As a solution, we propose a novel multi-view augmented densification strategy, where 3D Gaussians are encouraged to get densified to a sufficient number accordingly, resulting in improved reconstruction accuracy.

Freely Long-Thinking Transformer (FraiLT) is an improved transformer model designed to enhance processing capabilities without scaling up size. It utilizes a recursive approach, iterating over a subset of layers multiple times, and introduces iteration encodings to maintain awareness across these cycles. Iteration encoding allows FraiLT to achieve the interpretive depth of larger models in a compact form. When evaluated on a synthetic story dataset, FraiLT outperformed larger models, showcasing its ability to deliver high-quality performance while reducing memory demands. This model represents a step forward towards more efficient and accessible language models.

To address the challenges of limited Battery Swap Stations datasets, high operational costs, and fluctuating user charging demand, this research proposes a probability estimation model based on charging pile data and constructs nine scenario-specific battery swap demand datasets. In addition, this study combines Least Recently Used strategy with Genetic Algorithm and incorporates a guided search mechanism, which effectively enhances the global optimization capability. Thus, a dual-factor decision-making based charging schedule optimization system is constructed. Experimental results show that the constructed datasets exhibit stable trend characteristics, adhering to 24-hour and 168-hour periodicity patterns, with outlier ratios consistently below 3.26%, confirming data validity. Compared to baseline, the improved algorithm achieves better fitness individuals in 80% of test regions under the same iterations. When benchmarked against immediate swap-and-charge strategy, our algorithm achieves a peak cost reduction of 13.96%. Moreover, peak user satisfaction reaches 98.57%, while the average iteration time remains below 0.6 seconds, demonstrating good computational efficiency. The complete datasets and optimization algorithm are open-sourced at https://github.com/qingshufan/GA-EVLRU.

Due to the nonlinear nature of Deep Neural Networks (DNNs), one can not guarantee convergence to a unique global minimum of the loss when using optimizers relying only on local information, such as SGD. Indeed, this was a primary source of skepticism regarding the feasibility of DNNs in the early days of the field. The past decades of progress in deep learning have revealed this skepticism to be misplaced, and a large body of empirical evidence shows that sufficiently large DNNs following standard training protocols exhibit well-behaved optimization dynamics that converge to performant solutions. This success has biased the community to use convex optimization as a mental model for learning, leading to a focus on training efficiency, either in terms of required iteration, FLOPs or wall-clock time, when improving optimizers. We argue that, while this perspective has proven extremely fruitful, another perspective specific to DNNs has received considerably less attention: the optimizer not only influences the rate of convergence, but also the qualitative properties of the learned solutions. Restated, the optimizer can and will encode inductive biases and change the effective expressivity of a given class of models. Furthermore, we believe the optimizer can be an effective way of encoding desiderata in the learning process. We contend that the community should aim at understanding the biases of already existing methods, as well as aim to build new optimizers with the explicit intent of inducing certain properties of the solution, rather than solely judging them based on their convergence rates. We hope our arguments will inspire research to improve our understanding of how the learning process can impact the type of solution we converge to, and lead to a greater recognition of optimizers design as a critical lever that complements the roles of architecture and data in shaping model outcomes.

Interactive segmentation has an important role in facilitating the annotation process of future LiDAR datasets. Existing approaches sequentially segment individual objects at each LiDAR scan, repeating the process throughout the entire sequence, which is redundant and ineffective. In this work, we propose interactive 4D segmentation, a new paradigm that allows segmenting multiple objects on multiple LiDAR scans simultaneously, and Interactive4D, the first interactive 4D segmentation model that segments multiple objects on superimposed consecutive LiDAR scans in a single iteration by utilizing the sequential nature of LiDAR data. While performing interactive segmentation, our model leverages the entire space-time volume, leading to more efficient segmentation. Operating on the 4D volume, it directly provides consistent instance IDs over time and also simplifies tracking annotations. Moreover, we show that click simulations are crucial for successful model training on LiDAR point clouds. To this end, we design a click simulation strategy that is better suited for the characteristics of LiDAR data. To demonstrate its accuracy and effectiveness, we evaluate Interactive4D on multiple LiDAR datasets, where Interactive4D achieves a new state-of-the-art by a large margin. We publicly release the code and models at https://vision.rwth-aachen.de/Interactive4D.

We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced by Zermelo almost a century ago. Here we describe an alternative and similarly simple iteration that provably returns identical results but does so much faster -- over a hundred times faster in some cases. We demonstrate this algorithm with applications to a range of example data sets and derive a number of results regarding its convergence.

We introduce Differential Performance Evaluation (DPE), a framework designed to reliably evaluate Large Language Models (LLMs) for efficient code generation. Traditional coding benchmarks often fail to provide reliable insights into code efficiency, due to their reliance on simplistic test inputs and the absence of effective compound metrics. DPE addresses these issues by focusing on efficiency-demanding programming tasks and establishing an insightful compound metric for performance evaluation. DPE operates in two phases: To curate efficiency datasets, it selects efficiency-demanding tasks from existing coding benchmarks and generates computationally expensive inputs to stress the efficiency of LLM solutions. To assess the code efficiency, DPE profiles the new solution and compares it globally against a set of reference solutions that exhibit distinct efficiency levels, where the matched level defines its efficiency score. As a proof of concept, we use DPE to create EvalPerf, a benchmark with 121 performance-challenging coding tasks. Our comprehensive evaluation draws interesting findings on the efficiency impact of model sizes, instruction tuning, and prompting. For example, while the scaling law fails to account for code efficiency, general instruction tuning benefits both code correctness and efficiency. We also evaluate the evaluation by examining the effectiveness of DPE, showing that EvalPerf is reliable and convenient to use even across platforms.

As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect infeasible or misspecified problem instances, but the computational complexity of first-order methods for doing so has yet to be formally studied. In this work, we characterize the optimal accelerated rate of infeasibility detection. We show that the standard fixed-point iteration achieves a O(1/k^2) and O(1/k) rates, respectively, on the normalized iterates and the fixed-point residual converging to the infimal displacement vector, while the accelerated fixed-point iteration achieves O(1/k^2) and mathcal{O}(1/k^2) rates. We then provide a matching complexity lower bound to establish that Theta(1/k^2) is indeed the optimal accelerated rate.

The emergence of large language models (LLMs) has significantly pushed the frontiers of program synthesis. Advancement of LLM-based program synthesis calls for a thorough evaluation of LLM-generated code. Most evaluation frameworks focus on the (functional) correctness of generated code; efficiency, as an important measure of code quality, has been overlooked in existing evaluations. In this work, we develop ENAMEL (EfficeNcy AutoMatic EvaLuator), a rigorous and high-standard benchmark for evaluating the capability of LLMs in generating efficient code. Firstly, we propose a new efficiency metric called eff@k, which generalizes the pass@k metric from correctness to efficiency and appropriately handles right-censored execution time. Furthermore, we derive an unbiased and variance-reduced estimator of eff@k via Rao--Blackwellization; we also provide a numerically stable implementation for the new estimator. Secondly, to set a high-standard for efficiency evaluation, we employ a human expert to design best algorithms and implementations as our reference solutions of efficiency, many of which are much more efficient than existing canonical solutions in HumanEval and HumanEval+. Moreover, to ensure a rigorous evaluation, we employ a human expert to curate strong test case generators to filter out wrong code and differentiate suboptimal algorithms. An extensive study across 30 popular LLMs using our benchmark ENAMEL shows that LLMs still fall short of generating expert-level efficient code. Using two subsets of our problem set, we demonstrate that such deficiency is because current LLMs struggle in designing advanced algorithms and are barely aware of implementation optimization. Our benchmark is publicly available at https://github.com/q-rz/enamel .

We study multi-agent reinforcement learning in the setting of episodic Markov decision processes, where multiple agents cooperate via communication through a central server. We propose a provably efficient algorithm based on value iteration that enable asynchronous communication while ensuring the advantage of cooperation with low communication overhead. With linear function approximation, we prove that our algorithm enjoys an mathcal{O}(d^{3/2}H^2K) regret with mathcal{O}(dHM^2) communication complexity, where d is the feature dimension, H is the horizon length, M is the total number of agents, and K is the total number of episodes. We also provide a lower bound showing that a minimal Omega(dM) communication complexity is required to improve the performance through collaboration.

First-order optimization (FOO) algorithms are pivotal in numerous computational domains such as machine learning and signal denoising. However, their application to complex tasks like neural network training often entails significant inefficiencies due to the need for many sequential iterations for convergence. In response, we introduce first-order optimization expedited with approximately parallelized iterations (OptEx), the first framework that enhances the efficiency of FOO by leveraging parallel computing to mitigate its iterative bottleneck. OptEx employs kernelized gradient estimation to make use of gradient history for future gradient prediction, enabling parallelization of iterations -- a strategy once considered impractical because of the inherent iterative dependency in FOO. We provide theoretical guarantees for the reliability of our kernelized gradient estimation and the iteration complexity of SGD-based OptEx, confirming that estimation errors diminish to zero as historical gradients accumulate and that SGD-based OptEx enjoys an effective acceleration rate of Omega(N) over standard SGD given parallelism of N. We also use extensive empirical studies, including synthetic functions, reinforcement learning tasks, and neural network training across various datasets, to underscore the substantial efficiency improvements achieved by OptEx.

Large Language Models (LLMs), particularly Code LLMs, have demonstrated impressive performance in code generation. Current research primarily focuses on the correctness of generated code, while efficiency remains less explored. Recent works have focused on modifying the initial version of the code to improve its efficiency. However, such refinements are limited by the algorithmic design and overall logic of the initial code, resulting in only incremental improvements. In contrast, when human developers write high-quality code, they typically begin by designing several potential solutions at the logical level, evaluating various algorithms and their complexities, and then proceeding to implement and optimize the solution. In this study, we introduce \tool: Large Language Model for Code Efficiency, a novel framework that enables LLMs to generate code that balances both efficiency and correctness. Specifically, \tool divides the efficiency optimization process into two domains: algorithmic exploration in the logic domain and implementation optimization in the code domain. The correctness of the code is then guaranteed through a synthetic test case refinement process. This approach, which prioritizes efficiency before ensuring correctness, offers a new paradigm for efficient code generation. Experiments demonstrate that \tool consistently improves both efficiency and correctness, achieving new state-of-the-art performance in code efficiency benchmarks across various LLM backbones.

Learning rate schedules used in practice bear little resemblance to those recommended by theory. We close much of this theory/practice gap, and as a consequence are able to derive new problem-adaptive learning rate schedules. Our key technical contribution is a refined analysis of learning rate schedules for a wide class of optimization algorithms (including SGD). In contrast to most prior works that study the convergence of the average iterate, we study the last iterate, which is what most people use in practice. When considering only worst-case analysis, our theory predicts that the best choice is the linear decay schedule: a popular choice in practice that sets the stepsize proportionally to 1 - t/T, where t is the current iteration and T is the total number of steps. To go beyond this worst-case analysis, we use the observed gradient norms to derive schedules refined for any particular task. These refined schedules exhibit learning rate warm-up and rapid learning rate annealing near the end of training. Ours is the first systematic approach to automatically yield both of these properties. We perform the most comprehensive evaluation of learning rate schedules to date, evaluating across 10 diverse deep learning problems, a series of LLMs, and a suite of logistic regression problems. We validate that overall, the linear-decay schedule matches or outperforms all commonly used default schedules including cosine annealing, and that our schedule refinement method gives further improvements.

The success of deep neural networks (DNNs) is attributable to three factors: increased compute capacity, more complex models, and more data. These factors, however, are not always present, especially for edge applications such as autonomous driving, augmented reality, and internet-of-things. Training DNNs requires a large amount of data, which is difficult to obtain. Edge devices such as mobile phones have limited compute capacity, and therefore, require specialized and efficient DNNs. However, due to the enormous design space and prohibitive training costs, designing efficient DNNs for different target devices is challenging. So the question is, with limited data, compute capacity, and model complexity, can we still successfully apply deep neural networks? This dissertation focuses on the above problems and improving the efficiency of deep neural networks at four levels. Model efficiency: we designed neural networks for various computer vision tasks and achieved more than 10x faster speed and lower energy. Data efficiency: we developed an advanced tool that enables 6.2x faster annotation of a LiDAR point cloud. We also leveraged domain adaptation to utilize simulated data, bypassing the need for real data. Hardware efficiency: we co-designed neural networks and hardware accelerators and achieved 11.6x faster inference. Design efficiency: the process of finding the optimal neural networks is time-consuming. Our automated neural architecture search algorithms discovered, using 421x lower computational cost than previous search methods, models with state-of-the-art accuracy and efficiency.

Recent years have seen the remarkable capabilities of large language models (LLMs) for code generation. Different from existing work that evaluate the correctness of the code generated by LLMs, we propose to further evaluate its efficiency. More efficient code can lead to higher performance and execution efficiency of programs and software completed by LLM-assisted programming. First, we evaluate the efficiency of the code generated by LLMs on two benchmarks, HumanEval and MBPP. Then, we choose a set of programming problems from the online judge platform LeetCode to conduct a more difficult evaluation. Finally, we explore several prompts that would enable LLMs to generate more efficient code.

In this paper, we consider the problem of sleeping bandits with stochastic action sets and adversarial rewards. In this setting, in contrast to most work in bandits, the actions may not be available at all times. For instance, some products might be out of stock in item recommendation. The best existing efficient (i.e., polynomial-time) algorithms for this problem only guarantee an O(T^{2/3}) upper-bound on the regret. Yet, inefficient algorithms based on EXP4 can achieve O(T). In this paper, we provide a new computationally efficient algorithm inspired by EXP3 satisfying a regret of order O(T) when the availabilities of each action i in cA are independent. We then study the most general version of the problem where at each round available sets are generated from some unknown arbitrary distribution (i.e., without the independence assumption) and propose an efficient algorithm with O(2^K T) regret guarantee. Our theoretical results are corroborated with experimental evaluations.

Recent studies have shown that diffusion language models achieve remarkable data efficiency under limited-data constraints, yet the underlying mechanisms remain unclear. In this work, we perform extensive ablation experiments to disentangle the sources of this efficiency. Our results show that random masking of input tokens plays the dominant role. We further show that similar gains can be obtained through in MLP dropout and weight decay, indicating that stochastic regularization broadly enhances data efficiency in multi-epoch training. Our code is available at https://github.com/zitian-gao/data-efficiency.

With the advent of large language models (LLMs) like GPT-3, a natural question is the extent to which these models can be utilized for source code optimization. This paper presents methodologically stringent case studies applied to well-known open source python libraries pillow and numpy. We find that contemporary LLM ChatGPT-4 (state September and October 2023) is surprisingly adept at optimizing energy and compute efficiency. However, this is only the case in interactive use, with a human expert in the loop. Aware of experimenter bias, we document our qualitative approach in detail, and provide transcript and source code. We start by providing a detailed description of our approach in conversing with the LLM to optimize the _getextrema function in the pillow library, and a quantitative evaluation of the performance improvement. To demonstrate qualitative replicability, we report further attempts on another locus in the pillow library, and one code locus in the numpy library, to demonstrate generalization within and beyond a library. In all attempts, the performance improvement is significant (factor up to 38). We have also not omitted reporting of failed attempts (there were none). We conclude that LLMs are a promising tool for code optimization in open source libraries, but that the human expert in the loop is essential for success. Nonetheless, we were surprised by how few iterations were required to achieve substantial performance improvements that were not obvious to the expert in the loop. We would like bring attention to the qualitative nature of this study, more robust quantitative studies would need to introduce a layer of selecting experts in a representative sample -- we invite the community to collaborate.

Code generation models have increasingly become integral to aiding software development, offering assistance in tasks such as code completion, debugging, and code translation. Although current research has thoroughly examined the correctness of code produced by code generation models, a vital aspect, i.e., the efficiency of the generated code, has often been neglected. This paper presents EffiBench, a benchmark with 1,000 efficiency-critical coding problems for assessing the efficiency of code generated by code generation models. EffiBench contains a diverse set of LeetCode coding problems. Each problem is paired with an executable human-written canonical solution. With EffiBench, we empirically examine the capability of 21 Large Language Models (13 open-sourced and 8 closed-sourced) in generating efficient code. The results demonstrate that GPT-4-turbo generates the most efficient code, significantly outperforming Palm-2-chat-bison, Claude-instant-1, Gemini-pro, GPT-4, and GPT-3.5. Nevertheless, its code efficiency is still worse than the efficiency of human-written canonical solutions. In particular, the average and worst execution time of GPT-4-turbo generated code is 1.69 and 45.49 times that of the canonical solutions.

Large Language Models (LLMs) generate functionally correct solutions but often fall short in code efficiency, a critical bottleneck for real-world deployment. In this paper, we introduce a novel test-time iterative optimization framework to address this, employing a closed-loop system where LLMs iteratively refine code based on empirical performance feedback from an execution sandbox. We explore three training strategies: Supervised Fine-Tuning (SFT), Direct Preference Optimization (DPO), and Group Relative Policy Optimization~(GRPO). Experiments on our Venus dataset and the APPS benchmark show that SFT and DPO rapidly saturate in efficiency gains. In contrast, GRPO, using reinforcement learning (RL) with execution feedback, continuously optimizes code performance, significantly boosting both pass@1 (from 47% to 62%) and the likelihood of outperforming human submissions in efficiency (from 31% to 45%). Our work demonstrates effective test-time code efficiency improvement and critically reveals the power of RL in teaching LLMs to truly self-improve code efficiency.

Efficiency is a key property to foster inclusiveness and reduce environmental costs, especially in an era of LLMs. In this work, we provide a comprehensive evaluation of efficiency for MT evaluation metrics. Our approach involves replacing computation-intensive transformers with lighter alternatives and employing linear and quadratic approximations for alignment algorithms on top of LLM representations. We evaluate six (reference-free and reference-based) metrics across three MT datasets and examine 16 lightweight transformers. In addition, we look into the training efficiency of metrics like COMET by utilizing adapters. Our results indicate that (a) TinyBERT provides the optimal balance between quality and efficiency, (b) CPU speed-ups are more substantial than those on GPU; (c) WMD approximations yield no efficiency gains while reducing quality and (d) adapters enhance training efficiency (regarding backward pass speed and memory requirements) as well as, in some cases, metric quality. These findings can help to strike a balance between evaluation speed and quality, which is essential for effective NLG systems. Furthermore, our research contributes to the ongoing efforts to optimize NLG evaluation metrics with minimal impact on performance. To our knowledge, ours is the most comprehensive analysis of different aspects of efficiency for MT metrics conducted so far.

Large language models (LLMs) have shown remarkable progress in code generation, but their generated code often suffers from inefficiency, resulting in longer execution times and higher memory consumption. To address this issue, we propose EffiLearner, a self-optimization framework that utilizes execution overhead profiles to improve the efficiency of LLM-generated code. EffiLearner first generates code using an LLM, then executes it locally to capture execution time and memory usage profiles. These profiles are fed back to the LLM, which then revises the code to reduce overhead. To evaluate the effectiveness of EffiLearner, we conduct extensive experiments on the EffiBench, HumanEval, and MBPP with 16 open-source and 6 closed-source models. Our evaluation results demonstrate that through iterative self-optimization, EffiLearner significantly enhances the efficiency of LLM-generated code. For example, the execution time (ET) of StarCoder2-15B for the EffiBench decreases from 0.93 (s) to 0.12 (s) which reduces 87.1% the execution time requirement compared with the initial code. The total memory usage (TMU) of StarCoder2-15B also decreases from 22.02 (Mb*s) to 2.03 (Mb*s), which decreases 90.8% of total memory consumption during the execution process. The source code of EffiLearner was released in https://github.com/huangd1999/EffiLearner

We study compute efficiency of LLM training when using different parameterizations, i.e., rules for adjusting model and optimizer hyperparameters (HPs) as model size changes. Some parameterizations fail to transfer optimal base HPs (such as learning rate) across changes in model depth, requiring practitioners to either re-tune these HPs as they scale up (expensive), or accept sub-optimal training when re-tuning is prohibitive. Even when they achieve HP transfer, we develop theory to show parameterizations may still exist in the lazy learning regime where layers learn only features close to their linearization, preventing effective use of depth and nonlinearity. Finally, we identify and adopt the parameterization we call CompleteP that achieves both depth-wise HP transfer and non-lazy learning in all layers. CompleteP enables a wider range of model width/depth ratios to remain compute-efficient, unlocking shapes better suited for different hardware settings and operational contexts. Moreover, CompleteP enables 12-34% compute efficiency improvements over the prior state-of-the-art.

Efficiently training large language models requires parallelizing across hundreds of hardware accelerators and invoking various compute and memory optimizations. When combined, many of these strategies have complex interactions regarding the final training efficiency. Prior work tackling this problem did not have access to the latest set of optimizations, such as FlashAttention or sequence parallelism. In this work, we conduct a comprehensive ablation study of possible training configurations for large language models. We distill this large study into several key recommendations for the most efficient training. For instance, we find that using a micro-batch size of 1 usually enables the most efficient training layouts. Larger micro-batch sizes necessitate activation checkpointing or higher degrees of model parallelism and also lead to larger pipeline bubbles. Our most efficient configurations enable us to achieve state-of-the-art training efficiency results over a range of model sizes, most notably a Model FLOPs utilization of 70.5% when training a Llama 13B model.

Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration complexity, and propose a generic approach that, based on optimal first-order methods, allows to obtain in a black-box fashion new zeroth-order algorithms for non-smooth convex optimization problems. Our approach not only leads to optimal oracle complexity, but also allows to obtain iteration complexity similar to first-order methods, which, in turn, allows to exploit parallel computations to accelerate the convergence of our algorithms. We also elaborate on extensions for stochastic optimization problems, saddle-point problems, and distributed optimization.

Although large language models (LLMs) have been largely successful in generating functionally correct programs, conditioning models to produce efficient solutions while ensuring correctness remains a challenge. Further, unreliability in benchmarking code efficiency is a hurdle across varying hardware specifications for popular interpreted languages such as Python. In this paper, we present ECCO, a reproducible benchmark for evaluating program efficiency via two paradigms: natural language (NL) based code generation and history-based code editing. On ECCO, we adapt and thoroughly investigate the three most promising existing LLM-based approaches: in-context learning, iterative refinement with execution or NL feedback, and fine-tuning conditioned on execution and editing history. While most methods degrade functional correctness and moderately increase program efficiency, we find that adding execution information often helps maintain functional correctness, and NL feedback enhances more on efficiency. We release our benchmark to support future work on LLM-based generation of efficient code.

As deep learning models scale, their training cost has surged significantly. Due to both hardware advancements and limitations in current software stacks, the need for data efficiency has risen. Data efficiency refers to the effective hiding of data access latency and the avoidance of unnecessary data movements. Major challenges arise from the growing disparity between GPU memory bandwidth and computational throughput, imminent GPU memory capacity limitations, and inefficiencies in the PyTorch software stack, including a lack of device-specific PCIe transfer optimizations and high-level domain-specific abstractions. To effectively mitigate these data inefficiencies for deep learning training, this dissertation analyzes data inefficiency in representative deep training tasks, specifically in graph neural networks (GNNs) and large language models (LLMs). It then proposes novel runtime and code generation techniques to mitigate these challenges and implements these optimizations seamlessly within the PyTorch stack while maintaining strong programmability and interoperability. First, PyTorch-Direct is devised to incorporate the GPU-centric PCIe data transfer paradigm in PyTorch for GNN training. Next, Hector intermediate representation (IR) and its code generator are proposed to introduce domain-specific high-level abstraction and systematically address memory-intensive performance challenges for relational GNNs. Finally, in LLM training, the throughput has been increasingly constrained by GPU memory capacity. To mitigate this, the SSDTrain offloading framework is designed and implemented. Together, these contributions show that code generation and runtime techniques can systematically mitigate the data management bottlenecks in deep learning training, which stem from the data-intensive nature of workloads and the oversimplification inherent in the deep learning training software stack.

This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of Dimensional complexity in algorithmic efficiency and deduce that an optimally efficient algorithm has zero Time complexity, zero Space complexity, and an infinite Dimensional complexity. This algorithm is used to generate the number line.

We theoretically explore the relationship between sample-efficiency and adaptivity in reinforcement learning. An algorithm is sample-efficient if it uses a number of queries n to the environment that is polynomial in the dimension d of the problem. Adaptivity refers to the frequency at which queries are sent and feedback is processed to update the querying strategy. To investigate this interplay, we employ a learning framework that allows sending queries in K batches, with feedback being processed and queries updated after each batch. This model encompasses the whole adaptivity spectrum, ranging from non-adaptive 'offline' (K=1) to fully adaptive (K=n) scenarios, and regimes in between. For the problems of policy evaluation and best-policy identification under d-dimensional linear function approximation, we establish Omega(log log d) lower bounds on the number of batches K required for sample-efficient algorithms with n = O(poly(d)) queries. Our results show that just having adaptivity (K>1) does not necessarily guarantee sample-efficiency. Notably, the adaptivity-boundary for sample-efficiency is not between offline reinforcement learning (K=1), where sample-efficiency was known to not be possible, and adaptive settings. Instead, the boundary lies between different regimes of adaptivity and depends on the problem dimension.

The rapid growth of Large Language Models (LLMs) has been a driving force in transforming various domains, reshaping the artificial general intelligence landscape. However, the increasing computational and memory demands of these models present substantial challenges, hindering both academic research and practical applications. To address these issues, a wide array of methods, including both algorithmic and hardware solutions, have been developed to enhance the efficiency of LLMs. This survey delivers a comprehensive review of algorithmic advancements aimed at improving LLM efficiency. Unlike other surveys that typically focus on specific areas such as training or model compression, this paper examines the multi-faceted dimensions of efficiency essential for the end-to-end algorithmic development of LLMs. Specifically, it covers various topics related to efficiency, including scaling laws, data utilization, architectural innovations, training and tuning strategies, and inference techniques. This paper aims to serve as a valuable resource for researchers and practitioners, laying the groundwork for future innovations in this critical research area. Our repository of relevant references is maintained at url{https://github.com/tding1/Efficient-LLM-Survey}.

The increasing versatility of language models LMs has given rise to a new class of benchmarks that comprehensively assess a broad range of capabilities. Such benchmarks are associated with massive computational costs reaching thousands of GPU hours per model. However the efficiency aspect of these evaluation efforts had raised little discussion in the literature. In this work we present the problem of Efficient Benchmarking namely intelligently reducing the computation costs of LM evaluation without compromising reliability. Using the HELM benchmark as a test case we investigate how different benchmark design choices affect the computation-reliability tradeoff. We propose to evaluate the reliability of such decisions by using a new measure Decision Impact on Reliability DIoR for short. We find for example that the current leader on HELM may change by merely removing a low-ranked model from the benchmark and observe that a handful of examples suffice to obtain the correct benchmark ranking. Conversely a slightly different choice of HELM scenarios varies ranking widely. Based on our findings we outline a set of concrete recommendations for more efficient benchmark design and utilization practices leading to dramatic cost savings with minimal loss of benchmark reliability often reducing computation by x100 or more.

We study convergence lower bounds of without-replacement stochastic gradient descent (SGD) for solving smooth (strongly-)convex finite-sum minimization problems. Unlike most existing results focusing on final iterate lower bounds in terms of the number of components n and the number of epochs K, we seek bounds for arbitrary weighted average iterates that are tight in all factors including the condition number kappa. For SGD with Random Reshuffling, we present lower bounds that have tighter kappa dependencies than existing bounds. Our results are the first to perfectly close the gap between lower and upper bounds for weighted average iterates in both strongly-convex and convex cases. We also prove weighted average iterate lower bounds for arbitrary permutation-based SGD, which apply to all variants that carefully choose the best permutation. Our bounds improve the existing bounds in factors of n and kappa and thereby match the upper bounds shown for a recently proposed algorithm called GraB.

Large Transformer models routinely achieve state-of-the-art results on a number of tasks but training these models can be prohibitively costly, especially on long sequences. We introduce two techniques to improve the efficiency of Transformers. For one, we replace dot-product attention by one that uses locality-sensitive hashing, changing its complexity from O(L^2) to O(Llog L), where L is the length of the sequence. Furthermore, we use reversible residual layers instead of the standard residuals, which allows storing activations only once in the training process instead of N times, where N is the number of layers. The resulting model, the Reformer, performs on par with Transformer models while being much more memory-efficient and much faster on long sequences.

Since compute grows much faster than web text available for language model pre-training, we ask how one should approach pre-training under fixed data and no compute constraints. We first show that existing data-constrained approaches of increasing epoch count and parameter count eventually overfit, and we significantly improve upon such recipes by properly tuning regularization, finding that the optimal weight decay is 30times larger than standard practice. Since our regularized recipe monotonically decreases loss following a simple power law in parameter count, we estimate its best possible performance via the asymptote of its scaling law rather than the performance at a fixed compute budget. We then identify that ensembling independently trained models achieves a significantly lower loss asymptote than the regularized recipe. Our best intervention combining epoching, regularization, parameter scaling, and ensemble scaling achieves an asymptote at 200M tokens using 5.17times less data than our baseline, and our data scaling laws predict that this improvement persists at higher token budgets. We find that our data efficiency gains can be realized at much smaller parameter counts as we can distill an ensemble into a student model that is 8times smaller and retains 83% of the ensembling benefit. Finally, our interventions designed for validation loss generalize to downstream benchmarks, achieving a 9% improvement for pre-training evals and a 17.5times data efficiency improvement over continued pre-training on math mid-training data. Our results show that simple algorithmic improvements can enable significantly more data-efficient pre-training in a compute-rich future.

Recent advancements in large reasoning models (LRMs) have significantly enhanced language models' capabilities in complex problem-solving by emulating human-like deliberative thinking. However, these models often exhibit overthinking (i.e., the generation of unnecessarily verbose and redundant content), which hinders efficiency and inflates inference cost. In this work, we explore the representational and behavioral origins of this inefficiency, revealing that LRMs inherently possess the capacity for more concise reasoning. Empirical analyses show that correct reasoning paths vary significantly in length, and the shortest correct responses often suffice, indicating untapped efficiency potential. Exploiting these findings, we propose two lightweight methods to enhance LRM efficiency. First, we introduce Efficiency Steering, a training-free activation steering technique that modulates reasoning behavior via a single direction in the model's representation space. Second, we develop Self-Rewarded Efficiency RL, a reinforcement learning framework that dynamically balances task accuracy and brevity by rewarding concise correct solutions. Extensive experiments on seven LRM backbones across multiple mathematical reasoning benchmarks demonstrate that our methods significantly reduce reasoning length while preserving or improving task performance. Our results highlight that reasoning efficiency can be improved by leveraging and guiding the intrinsic capabilities of existing models in a self-guided manner.

Existing code generation benchmarks primarily evaluate functional correctness, with limited focus on code efficiency and often restricted to a single language like Python. To address this gap, we introduce EffiBench-X, the first multi-language benchmark designed to measure the efficiency of LLM-generated code. EffiBench-X supports Python, C++, Java, JavaScript, Ruby, and Golang. It comprises competitive programming tasks with human-expert solutions as efficiency baselines. Evaluating state-of-the-art LLMs on EffiBench-X reveals that while models generate functionally correct code, they consistently underperform human experts in efficiency. Even the most efficient LLM-generated solutions (Qwen3-32B) achieve only around 62\% of human efficiency on average, with significant language-specific variations. LLMs show better efficiency in Python, Ruby, and JavaScript than in Java, C++, and Golang. For instance, DeepSeek-R1's Python code is significantly more efficient than its Java code. These results highlight the critical need for research into LLM optimization techniques to improve code efficiency across diverse languages. The dataset and evaluation infrastructure are submitted and available at https://github.com/EffiBench/EffiBench-X.git and https://huggingface.co/datasets/EffiBench/effibench-x.

Language models (LMs) are being scaled and becoming powerful. Improving their efficiency is one of the core research topics in neural information processing systems. Tay et al. (2022) provided a comprehensive overview of efficient Transformers that have become an indispensable staple in the field of NLP. However, in the section of "On Evaluation", they left an open question "which fundamental efficient Transformer one should consider," answered by "still a mystery" because "many research papers select their own benchmarks." Unfortunately, there was not quantitative analysis about the performances of Transformers on any benchmarks. Moreover, state space models (SSMs) have demonstrated their abilities of modeling long-range sequences with non-attention mechanisms, which were not discussed in the prior review. This article makes a meta analysis on the results from a set of papers on efficient Transformers as well as those on SSMs. It provides a quantitative review on LM efficiency research and gives suggestions for future research.

The growing size of datasets and deep learning models has made faster and memory-efficient training crucial. Reversible transformers have recently been introduced as an exciting new method for extremely memory-efficient training, but they come with an additional computation overhead of activation re-computation in the backpropagation phase. We present PaReprop, a fast Parallelized Reversible Backpropagation algorithm that parallelizes the additional activation re-computation overhead in reversible training with the gradient computation itself in backpropagation phase. We demonstrate the effectiveness of the proposed PaReprop algorithm through extensive benchmarking across model families (ViT, MViT, Swin and RoBERTa), data modalities (Vision & NLP), model sizes (from small to giant), and training batch sizes. Our empirical results show that PaReprop achieves up to 20% higher training throughput than vanilla reversible training, largely mitigating the theoretical overhead of 25% lower throughput from activation recomputation in reversible training. Project page: https://tylerzhu.com/pareprop.

Self-attention in Transformers comes with a high computational cost because of their quadratic computational complexity, but their effectiveness in addressing problems in language and vision has sparked extensive research aimed at enhancing their efficiency. However, diverse experimental conditions, spanning multiple input domains, prevent a fair comparison based solely on reported results, posing challenges for model selection. To address this gap in comparability, we perform a large-scale benchmark of more than 45 models for image classification, evaluating key efficiency aspects, including accuracy, speed, and memory usage. Our benchmark provides a standardized baseline for efficiency-oriented transformers. We analyze the results based on the Pareto front -- the boundary of optimal models. Surprisingly, despite claims of other models being more efficient, ViT remains Pareto optimal across multiple metrics. We observe that hybrid attention-CNN models exhibit remarkable inference memory- and parameter-efficiency. Moreover, our benchmark shows that using a larger model in general is more efficient than using higher resolution images. Thanks to our holistic evaluation, we provide a centralized resource for practitioners and researchers, facilitating informed decisions when selecting or developing efficient transformers.

Recent advances in large language models (LLMs) have greatly improved their reasoning and decision-making abilities when deployed as agents. Richer reasoning, however, often comes at the cost of longer chain of thought (CoT), hampering interaction efficiency in real-world scenarios. Nevertheless, there still lacks systematic definition of LLM agent efficiency, hindering targeted improvements. To this end, we introduce dual-efficiency, comprising (i) step-level efficiency, which minimizes tokens per step, and (ii) trajectory-level efficiency, which minimizes the number of steps to complete a task. Building on this definition, we propose DEPO, a dual-efficiency preference optimization method that jointly rewards succinct responses and fewer action steps. Experiments on WebShop and BabyAI show that DEPO cuts token usage by up to 60.9% and steps by up to 26.9%, while achieving up to a 29.3% improvement in performance. DEPO also generalizes to three out-of-domain math benchmarks and retains its efficiency gains when trained on only 25% of the data. Our project page is at https://opencausalab.github.io/DEPO.

Recent work has shown that attention-based language models excel at recall, the ability to ground generations in tokens previously seen in context. However, the efficiency of attention-based models is bottle-necked during inference by the KV-cache's aggressive memory consumption. In this work, we explore whether we can improve language model efficiency (e.g. by reducing memory consumption) without compromising on recall. By applying experiments and theory to a broad set of architectures, we identify a key tradeoff between a model's state size and recall ability. We show that efficient alternatives to attention (e.g. H3, Mamba, RWKV) maintain a fixed-size recurrent state, but struggle at recall. We propose BASED a simple architecture combining linear and sliding window attention. By varying BASED window size and linear attention feature dimension, we can dial the state size and traverse the pareto frontier of the recall-memory tradeoff curve, recovering the full quality of attention on one end and the small state size of attention-alternatives on the other. We train language models up to 1.3b parameters and show that BASED matches the strongest sub-quadratic models (e.g. Mamba) in perplexity and outperforms them on real-world recall-intensive tasks by 6.22 accuracy points. Implementations of linear attention are often less efficient than optimized standard attention implementations. To make BASED competitive, we develop IO-aware algorithms that enable 24x higher throughput on language generation than FlashAttention-2, when generating 1024 tokens using 1.3b parameter models. Code for this work is provided at: https://github.com/HazyResearch/based.

Large Language Models (LLMs) have driven significant progress, yet their growing parameter counts and context windows incur prohibitive compute, energy, and monetary costs. We introduce EfficientLLM, a novel benchmark and the first comprehensive empirical study evaluating efficiency techniques for LLMs at scale. Conducted on a production-class cluster (48xGH200, 8xH200 GPUs), our study systematically explores three key axes: (1) architecture pretraining (efficient attention variants: MQA, GQA, MLA, NSA; sparse Mixture-of-Experts (MoE)), (2) fine-tuning (parameter-efficient methods: LoRA, RSLoRA, DoRA), and (3) inference (quantization methods: int4, float16). We define six fine-grained metrics (Memory Utilization, Compute Utilization, Latency, Throughput, Energy Consumption, Compression Rate) to capture hardware saturation, latency-throughput balance, and carbon cost. Evaluating over 100 model-technique pairs (0.5B-72B parameters), we derive three core insights: (i) Efficiency involves quantifiable trade-offs: no single method is universally optimal; e.g., MoE reduces FLOPs and improves accuracy but increases VRAM by 40%, while int4 quantization cuts memory/energy by up to 3.9x at a 3-5% accuracy drop. (ii) Optima are task- and scale-dependent: MQA offers optimal memory-latency trade-offs for constrained devices, MLA achieves lowest perplexity for quality-critical tasks, and RSLoRA surpasses LoRA efficiency only beyond 14B parameters. (iii) Techniques generalize across modalities: we extend evaluations to Large Vision Models (Stable Diffusion 3.5, Wan 2.1) and Vision-Language Models (Qwen2.5-VL), confirming effective transferability. By open-sourcing datasets, evaluation pipelines, and leaderboards, EfficientLLM provides essential guidance for researchers and engineers navigating the efficiency-performance landscape of next-generation foundation models.

Latency and efficiency issues are often overlooked when evaluating IR models based on Pretrained Language Models (PLMs) in reason of multiple hardware and software testing scenarios. Nevertheless, efficiency is an important part of such systems and should not be overlooked. In this paper, we focus on improving the efficiency of the SPLADE model since it has achieved state-of-the-art zero-shot performance and competitive results on TREC collections. SPLADE efficiency can be controlled via a regularization factor, but solely controlling this regularization has been shown to not be efficient enough. In order to reduce the latency gap between SPLADE and traditional retrieval systems, we propose several techniques including L1 regularization for queries, a separation of document/query encoders, a FLOPS-regularized middle-training, and the use of faster query encoders. Our benchmark demonstrates that we can drastically improve the efficiency of these models while increasing the performance metrics on in-domain data. To our knowledge, {we propose the first neural models that, under the same computing constraints, achieve similar latency (less than 4ms difference) as traditional BM25, while having similar performance (less than 10\% MRR@10 reduction) as the state-of-the-art single-stage neural rankers on in-domain data}.

The remarkable capabilities of Large Language Model (LLM)-driven agents have enabled sophisticated systems to tackle complex, multi-step tasks, but their escalating costs threaten scalability and accessibility. This work presents the first systematic study of the efficiency-effectiveness trade-off in modern agent systems, addressing the critical need for cost-effective designs without sacrificing performance. We investigate three key questions: (1) How much complexity do agentic tasks inherently require? (2) When do additional modules yield diminishing returns? (3) How much efficiency can be gained through the design of efficient agent frameworks? Through an empirical analysis on the GAIA benchmark, we evaluate the impact of LLM backbone selection, agent framework designs, and test-time scaling strategies. Using the cost-of-pass metric, we quantify the efficiency-performance trade-off across these dimensions. Our findings inform the development of Efficient Agents , a novel agent framework that has an optimal complexity to task requirements. Efficient Agents retains 96.7% of the performance of OWL, one leading open-source agent framework, while reducing operational costs from 0.398 to 0.228, resulting in a 28.4% improvement in cost-of-pass. Our work provides actionable insights for designing efficient, high-performing agent systems, advancing the accessibility and sustainability of AI-driven solutions.

The evolving sophistication and intricacies of Large Language Models (LLMs) yield unprecedented advancements, yet they simultaneously demand considerable computational resources and incur significant costs. To alleviate these challenges, this paper introduces a novel, simple, and effective method named ``\growlength'' to accelerate the pretraining process of LLMs. Our method progressively increases the training length throughout the pretraining phase, thereby mitigating computational costs and enhancing efficiency. For instance, it begins with a sequence length of 128 and progressively extends to 4096. This approach enables models to process a larger number of tokens within limited time frames, potentially boosting their performance. In other words, the efficiency gain is derived from training with shorter sequences optimizing the utilization of resources. Our extensive experiments with various state-of-the-art LLMs have revealed that models trained using our method not only converge more swiftly but also exhibit superior performance metrics compared to those trained with existing methods. Furthermore, our method for LLMs pretraining acceleration does not require any additional engineering efforts, making it a practical solution in the realm of LLMs.

Recurrent Neural Network (RNN) inference exhibits low hardware utilization due to the strict data dependencies across time-steps. Batching multiple requests can increase throughput. However, RNN batching requires a large amount of padding since the batched input sequences may largely differ in length. Schemes that dynamically update the batch every few time-steps avoid padding. However, they require executing different RNN layers in a short timespan, decreasing energy efficiency. Hence, we propose E-BATCH, a low-latency and energy-efficient batching scheme tailored to RNN accelerators. It consists of a runtime system and effective hardware support. The runtime concatenates multiple sequences to create large batches, resulting in substantial energy savings. Furthermore, the accelerator notifies it when the evaluation of a sequence is done, so that a new sequence can be immediately added to a batch, thus largely reducing the amount of padding. E-BATCH dynamically controls the number of time-steps evaluated per batch to achieve the best trade-off between latency and energy efficiency for the given hardware platform. We evaluate E-BATCH on top of E-PUR and TPU. In E-PUR, E-BATCH improves throughput by 1.8x and energy-efficiency by 3.6x, whereas in TPU, it improves throughput by 2.1x and energy-efficiency by 1.6x, over the state-of-the-art.

This study evaluates the efficiency of code generation by Large Language Models (LLMs) and measures their performance against human-crafted solutions using a dataset from Leetcode. We compare 18 LLMs, considering factors such as model temperature and success rate, and their impact on code performance. This research introduces a novel method for measuring and comparing the speed of LLM-generated code, revealing that LLMs produce code with comparable performance, irrespective of the adopted LLM. We also find that LLMs are capable of generating code that is, on average, more efficient than the code written by humans. The paper further discusses the use of Leetcode as a benchmarking dataset, the limitations imposed by potential data contamination, and the platform's measurement reliability. We believe that our findings contribute to a better understanding of LLM capabilities in code generation and set the stage for future optimizations in the field.

Deep Learning has revolutionized the fields of computer vision, natural language understanding, speech recognition, information retrieval and more. However, with the progressive improvements in deep learning models, their number of parameters, latency, resources required to train, etc. have all have increased significantly. Consequently, it has become important to pay attention to these footprint metrics of a model as well, not just its quality. We present and motivate the problem of efficiency in deep learning, followed by a thorough survey of the five core areas of model efficiency (spanning modeling techniques, infrastructure, and hardware) and the seminal work there. We also present an experiment-based guide along with code, for practitioners to optimize their model training and deployment. We believe this is the first comprehensive survey in the efficient deep learning space that covers the landscape of model efficiency from modeling techniques to hardware support. Our hope is that this survey would provide the reader with the mental model and the necessary understanding of the field to apply generic efficiency techniques to immediately get significant improvements, and also equip them with ideas for further research and experimentation to achieve additional gains.

Each LLM serving request goes through two phases. The first is prefill which processes the entire input prompt to produce one output token and the second is decode which generates the rest of output tokens, one-at-a-time. Prefill iterations have high latency but saturate GPU compute due to parallel processing of the input prompt. In contrast, decode iterations have low latency but also low compute utilization because a decode iteration processes only a single token per request. This makes batching highly effective for decodes and consequently for overall throughput. However, batching multiple requests leads to an interleaving of prefill and decode iterations which makes it challenging to achieve both high throughput and low latency. We introduce an efficient LLM inference scheduler Sarathi-Serve inspired by the techniques we originally proposed for optimizing throughput in Sarathi. Sarathi-Serve leverages chunked-prefills from Sarathi to create stall-free schedules that can add new requests in a batch without pausing ongoing decodes. Stall-free scheduling unlocks the opportunity to improve throughput with large batch sizes while minimizing the effect of batching on latency. Our evaluation shows that Sarathi-Serve improves serving throughput within desired latency SLOs of Mistral-7B by up to 2.6x on a single A100 GPU and up to 6.9x for Falcon-180B on 8 A100 GPUs over Orca and vLLM.

Attention encoder-decoder model architecture is the backbone of several recent top performing foundation speech models: Whisper, Seamless, OWSM, and Canary-1B. However, the reported data and compute requirements for their training are prohibitive for many in the research community. In this work, we focus on the efficiency angle and ask the questions of whether we are training these speech models efficiently, and what can we do to improve? We argue that a major, if not the most severe, detrimental factor for training efficiency is related to the sampling strategy of sequential data. We show that negligence in mini-batch sampling leads to more than 50% computation being spent on padding. To that end, we study, profile, and optimize Canary-1B training to show gradual improvement in GPU utilization leading up to 5x increase in average batch sizes versus its original training settings. This in turn allows us to train an equivalent model using 4x less GPUs in the same wall time, or leverage the original resources and train it in 2x shorter wall time. Finally, we observe that the major inference bottleneck lies in the autoregressive decoder steps. We find that adjusting the model architecture to transfer model parameters from the decoder to the encoder results in a 3x inference speedup as measured by inverse real-time factor (RTFx) while preserving the accuracy and compute requirements for convergence. The training code and models will be available as open-source.

As the ever-increasing token limits of large language models (LLMs) have enabled long context as input, prompting with single data samples might no longer an efficient way. A straightforward strategy improving efficiency is to batch data within the token limit (e.g., 8k for gpt-3.5-turbo; 32k for GPT-4), which we call BatchPrompt. We have two initial observations for prompting with batched data. First, we find that prompting with batched data in longer contexts will inevitably lead to worse performance, compared to single-data prompting. Second, the performance of the language model is significantly correlated with the positions and order of the batched data, due to the corresponding change in decoder context. To retain efficiency and overcome performance loss, we propose Batch Permutation and Ensembling (BPE), and a novel Self-reflection-guided EArly Stopping (SEAS) technique. Our comprehensive experimental evaluation demonstrates that BPE can boost the performance of BatchPrompt with a striking margin on a range of popular NLP tasks, including question answering (Boolq), textual entailment (RTE), and duplicate questions identification (QQP). These performances are even competitive with/higher than single-data prompting(SinglePrompt), while BatchPrompt requires much fewer LLM calls and input tokens (For SinglePrompt v.s. BatchPrompt with batch size 32, using just 9%-16% the number of LLM calls, Boolq accuracy 90.6% to 90.9% with 27.4% tokens, QQP accuracy 87.2% to 88.4% with 18.6% tokens, RTE accuracy 91.5% to 91.1% with 30.8% tokens). To the best of our knowledge, this is the first work to technically improve prompting efficiency of large language models. We hope our simple yet effective approach will shed light on the future research of large language models. The code will be released.

Self-attention is at the heart of the popular Transformer architecture, yet suffers from quadratic time and memory complexity. The breakthrough FlashAttention algorithm revealed I/O complexity as the true bottleneck in scaling Transformers. Given two levels of memory hierarchy, a fast cache (e.g. GPU on-chip SRAM) and a slow memory (e.g. GPU high-bandwidth memory), the I/O complexity measures the number of accesses to memory. FlashAttention computes attention using N^2d^2{M} I/O operations where N is the dimension of the attention matrix, d the head-dimension and M the cache size. However, is this I/O complexity optimal? The known lower bound only rules out an I/O complexity of o(Nd) when M=Theta(Nd), since the output that needs to be written to slow memory is Omega(Nd). This leads to the main question of our work: Is FlashAttention I/O optimal for all values of M? We resolve the above question in its full generality by showing an I/O complexity lower bound that matches the upper bound provided by FlashAttention for any values of M geq d^2 within any constant factors. Further, we give a better algorithm with lower I/O complexity for M < d^2, and show that it is optimal as well. Moreover, our lower bounds do not rely on using combinatorial matrix multiplication for computing the attention matrix. We show even if one uses fast matrix multiplication, the above I/O complexity bounds cannot be improved. We do so by introducing a new communication complexity protocol for matrix compression, and connecting communication complexity to I/O complexity. To the best of our knowledge, this is the first work to establish a connection between communication complexity and I/O complexity, and we believe this connection could be of independent interest and will find many more applications in proving I/O complexity lower bounds in the future.

Context-augmented generation (CAG) techniques, including RAG and ICL, require the efficient combination of multiple contexts to generate responses to user queries. Directly inputting these contexts as a sequence introduces a considerable computational burden by re-encoding the combined selection of contexts for every request. To address this, we explore the promising potential of parallel encoding to independently pre-compute and cache each context's KV states. This approach enables the direct loading of cached states during inference while accommodating more contexts through position reuse across contexts. However, due to misalignments in attention distribution, directly applying parallel encoding results in a significant performance drop. To enable effective and efficient CAG, we propose Adaptive Parallel Encoding (APE), which brings shared prefix, attention temperature, and scaling factor to align the distribution of parallel encoding with sequential encoding. Results on RAG and ICL tasks demonstrate that APE can preserve 98% and 93% sequential encoding performance using the same inputs while outperforming parallel encoding by 3.6% and 7.9%, respectively. It also scales to many-shot CAG, effectively encoding hundreds of contexts in parallel. Efficiency evaluation shows that APE can achieve an end-to-end 4.5times speedup by reducing 28times prefilling time for a 128K-length context.

Inference with transformer-based language models begins with a prompt processing step. In this step, the model generates the first output token and stores the KV cache needed for future generation steps. This prompt processing step can be computationally expensive, taking 10s of seconds or more for billion-parameter models on edge devices when prompt lengths or batch sizes rise. This degrades user experience by introducing significant latency into the model's outputs. To reduce the time spent producing the first output (known as the ``time to first token'', or TTFT) of a pretrained model, we introduce a novel method called KV Prediction. In our method, a small auxiliary model is used to process the prompt and produce an approximation of the KV cache used by a base model. This approximated KV cache is then used with the base model for autoregressive generation without the need to query the auxiliary model again. We demonstrate that our method produces a pareto-optimal efficiency-accuracy trade-off when compared to baselines. On TriviaQA, we demonstrate relative accuracy improvements in the range of 15%-50% across a range of TTFT FLOPs budgets. We also demonstrate accuracy improvements of up to 30% on HumanEval python code completion at fixed TTFT FLOPs budgets. Additionally, we benchmark models on an Apple M2 Pro CPU and demonstrate that our improvement in FLOPs translates to a TTFT speedup on hardware. We release our code at https://github.com/apple/corenet/tree/main/projects/kv-prediction .

We classify and re-examine some of the current approaches to improve the performance-computes trade-off of language models, including (1) non-causal models (such as masked language models), (2) extension of batch length with efficient attention, (3) recurrence, (4) conditional computation and (5) retrieval. We identify some limitations (1) - (4) suffer from. For example, (1) currently struggles with open-ended text generation with the output loosely constrained by the input as well as performing general textual tasks like GPT-2/3 due to its need for a specific fine-tuning dataset. (2) and (3) do not improve the prediction of the first sim 10^3 tokens. Scaling up a model size (e.g. efficiently with (4)) still results in poor performance scaling for some tasks. We argue (5) would resolve many of these limitations, and it can (a) reduce the amount of supervision and (b) efficiently extend the context over the entire training dataset and the entire past of the current sample. We speculate how to modify MARGE to perform unsupervised causal modeling that achieves (b) with the retriever jointly trained.

Reinforcement learning exhibits potential in enhancing the reasoning abilities of large language models, yet it is hard to scale for the low sample efficiency during the rollout phase. Existing methods attempt to improve efficiency by scheduling problems based on problem difficulties. However, these approaches suffer from unstable and biased estimations of problem difficulty and fail to capture the alignment between model competence and problem difficulty in RL training, leading to suboptimal results. To tackle these limitations, this paper introduces Competence-Difficulty Alignment Sampling (CDAS), which enables accurate and stable estimation of problem difficulties by aggregating historical performance discrepancies of problems. Then the model competence is quantified to adaptively select problems whose difficulty is in alignment with the model's current competence using a fixed-point system. Experimental results across a range of challenging mathematical benchmarks show that CDAS achieves great improvements in both accuracy and efficiency. CDAS attains the highest average accuracy against baselines and exhibits significant speed advantages compared to Dynamic Sampling, a competitive strategy in DAPO, which is 2.33 times slower than CDAS.

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret performance compared to existing approaches. The first algorithm, although computationally inefficient, ensures a regret of mathcal{O}left(Kright), where K is the number of episodes. This is the first result with the optimal K dependence in the considered setting. The second algorithm, which is based on the policy optimization framework, guarantees a regret of mathcal{O}left(K^{3{4}} right) and is computationally efficient. Both our results significantly improve over the state-of-the-art: a computationally inefficient algorithm by Kong et al. [2023] with mathcal{O}left(K^{4{5}}+polyleft(1{lambda_{min}}right) right) regret, for some problem-dependent constant lambda_{min} that can be arbitrarily close to zero, and a computationally efficient algorithm by Sherman et al. [2023b] with mathcal{O}left(K^{6{7}} right) regret.

The waning of Moore's Law has shifted the focus of the tech industry towards alternative methods for continued performance gains. While optimizing compilers are a standard tool to help increase program efficiency, programmers continue to shoulder much responsibility in crafting and refactoring code with better performance characteristics. In this paper, we investigate the ability of large language models (LLMs) to suggest functionally correct, performance improving code edits. We hypothesize that language models can suggest such edits in ways that would be impractical for static analysis alone. We investigate these questions by curating a large-scale dataset of Performance-Improving Edits, PIE. PIE contains trajectories of programs, where a programmer begins with an initial, slower version and iteratively makes changes to improve the program's performance. We use PIE to evaluate and improve the capacity of large language models. Specifically, use examples from PIE to fine-tune multiple variants of CODEGEN, a billion-scale Transformer-decoder model. Additionally, we use examples from PIE to prompt OpenAI's CODEX using a few-shot prompting. By leveraging PIE, we find that both CODEX and CODEGEN can generate performance-improving edits, with speedups of more than 2.5x for over 25% of the programs, for C++ and Python, even after the C++ programs were compiled using the O3 optimization level. Crucially, we show that PIE allows CODEGEN, an open-sourced and 10x smaller model than CODEX, to match the performance of CODEX on this challenging task. Overall, this work opens new doors for creating systems and methods that can help programmers write efficient code.

Neural information retrieval (IR) systems have progressed rapidly in recent years, in large part due to the release of publicly available benchmarking tasks. Unfortunately, some dimensions of this progress are illusory: the majority of the popular IR benchmarks today focus exclusively on downstream task accuracy and thus conceal the costs incurred by systems that trade away efficiency for quality. Latency, hardware cost, and other efficiency considerations are paramount to the deployment of IR systems in user-facing settings. We propose that IR benchmarks structure their evaluation methodology to include not only metrics of accuracy, but also efficiency considerations such as a query latency and the corresponding cost budget for a reproducible hardware setting. For the popular IR benchmarks MS MARCO and XOR-TyDi, we show how the best choice of IR system varies according to how these efficiency considerations are chosen and weighed. We hope that future benchmarks will adopt these guidelines toward more holistic IR evaluation.

As models become increasingly sophisticated, conventional algorithm benchmarks are increasingly saturated, underscoring the need for more challenging benchmarks to guide future improvements in algorithmic reasoning. This paper introduces OIBench, a high-quality, private, and challenging olympiad-level informatics dataset comprising 250 carefully curated original problems. We detail the construction methodology of the benchmark, ensuring a comprehensive assessment across various programming paradigms and complexities, and we demonstrate its contamination-resistant properties via experiments. We propose Time/Space Completion Curves for finer-grained efficiency analysis and enable direct human-model comparisons through high-level participant evaluations. Our experiments reveal that while open-source models lag behind closed-source counterparts, current SOTA models already outperform most human participants in both correctness and efficiency, while still being suboptimal compared to the canonical solutions. By releasing OIBench as a fully open-source resource (https://huggingface.co/datasets/AGI-Eval/OIBench), we hope this benchmark will contribute to advancing code reasoning capabilities for future LLMs.

Reinforcement learning has achieved great success in many applications. However, sample efficiency remains a key challenge, with prominent methods requiring millions (or even billions) of environment steps to train. Recently, there has been significant progress in sample efficient image-based RL algorithms; however, consistent human-level performance on the Atari game benchmark remains an elusive goal. We propose a sample efficient model-based visual RL algorithm built on MuZero, which we name EfficientZero. Our method achieves 194.3% mean human performance and 109.0% median performance on the Atari 100k benchmark with only two hours of real-time game experience and outperforms the state SAC in some tasks on the DMControl 100k benchmark. This is the first time an algorithm achieves super-human performance on Atari games with such little data. EfficientZero's performance is also close to DQN's performance at 200 million frames while we consume 500 times less data. EfficientZero's low sample complexity and high performance can bring RL closer to real-world applicability. We implement our algorithm in an easy-to-understand manner and it is available at https://github.com/YeWR/EfficientZero. We hope it will accelerate the research of MCTS-based RL algorithms in the wider community.

Large Language Models (LLMs) face efficiency bottlenecks due to the quadratic complexity of the attention mechanism when processing long contexts. Sparse attention methods offer a promising solution, but existing approaches often suffer from incomplete effective context and/or require complex implementation of pipeline. We present a comprehensive analysis of sparse attention for autoregressive LLMs from the respective of receptive field, recognize the suboptimal nature of existing methods for expanding the receptive field, and introduce PowerAttention, a novel sparse attention design that facilitates effective and complete context extension through the theoretical analysis. PowerAttention achieves exponential receptive field growth in d-layer LLMs, allowing each output token to attend to 2^d tokens, ensuring completeness and continuity of the receptive field. Experiments demonstrate that PowerAttention outperforms existing static sparse attention methods by 5sim 40%, especially on tasks demanding long-range dependencies like Passkey Retrieval and RULER, while maintaining a comparable time complexity to sliding window attention. Efficiency evaluations further highlight PowerAttention's superior speedup in both prefilling and decoding phases compared with dynamic sparse attentions and full attention (3.0times faster on 128K context), making it a highly effective and user-friendly solution for processing long sequences in LLMs.

It is common to reject undesired outputs of Large Language Models (LLMs); however, current methods to do so require an excessive amount of computation, or severely distort the distribution of outputs. We present a method to balance the distortion of the output distribution with computational efficiency, allowing for the generation of long sequences of text with difficult-to-satisfy constraints, with less amplification of low probability outputs compared to existing methods. We show through a series of experiments that the task-specific performance of our method is comparable to methods that do not distort the output distribution, while being much more computationally efficient.

While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper presents a systematic empirical investigation of scaling behaviors in RL-based post-training, with a particular focus on mathematical reasoning. Based on a set of experiments across the full Qwen2.5 dense model series (0.5B to 72B), we characterize how model scale, data volume, and computational budget interact to shape performance. Our analysis leads to four key findings: 1.Larger models consistently exhibit superior learning efficiency on both compute and data metrics. 2.The relationship between test loss, compute, and data can be modeled by a predictive power-law which is robust across both base and instruction-tuned models. 3.Although larger models exhibit higher learning efficiency, the analytical learning efficiency term k(N) in the power-law reveals a latent saturation trend in learning efficiency as model size continues to increase. 4.In data-constrained regimes, repeated reuse of high-quality data proves highly effective, as final performance is primarily governed by the total number of optimization steps rather than the uniqueness of samples. Collectively, these results provide a principled foundation and practical guidelines for efficiently scaling the reasoning capabilities of LLMs through RL post-training.

Large language models (LLMs) power many state-of-the-art systems in natural language processing. However, these models are extremely computationally expensive, even at inference time, raising the natural question: when is the extra cost of deploying a larger model worth the anticipated boost in capabilities? Better understanding this tradeoff fundamentally could benefit from an inference efficiency metric that is both (i) easily comparable across models from different providers, and (ii) representative of the true cost of running queries in an isolated performance environment. Unfortunately, access to LLMs today is largely restricted to black-box text generation APIs and raw runtimes measured through this interface do not satisfy these desiderata: model providers can apply various software and hardware optimizations orthogonal to the model, and models served on shared infrastructure are susceptible to performance contention. To circumvent these problems, we propose a new metric for comparing inference efficiency across models. This metric puts models on equal footing as though they were served (i) on uniform hardware and software, and (ii) without performance contention. We call this metric the idealized runtime, and we propose a methodology to efficiently estimate this metric for autoregressive Transformer models. We also propose cost-aware variants that incorporate the number of accelerators needed to serve the model. Using these metrics, we compare ten state-of-the-art LLMs to provide the first analysis of inference efficiency-capability tradeoffs; we make several observations from this analysis, including the fact that the superior inference runtime performance of certain APIs is often a byproduct of optimizations within the API rather than the underlying model. Our methodology also facilitates the efficient comparison of different software and hardware stacks.

Reinforcement learning (RL) has become central to training large language models (LLMs), yet the field lacks predictive scaling methodologies comparable to those established for pre-training. Despite rapidly rising compute budgets, there is no principled understanding of how to evaluate algorithmic improvements for scaling RL compute. We present the first large-scale systematic study, amounting to more than 400,000 GPU-hours, that defines a principled framework for analyzing and predicting RL scaling in LLMs. We fit sigmoidal compute-performance curves for RL training and ablate a wide range of common design choices to analyze their effects on asymptotic performance and compute efficiency. We observe: (1) Not all recipes yield similar asymptotic performance, (2) Details such as loss aggregation, normalization, curriculum, and off-policy algorithm primarily modulate compute efficiency without materially shifting the asymptote, and (3) Stable, scalable recipes follow predictable scaling trajectories, enabling extrapolation from smaller-scale runs. Combining these insights, we propose a best-practice recipe, ScaleRL, and demonstrate its effectiveness by successfully scaling and predicting validation performance on a single RL run scaled up to 100,000 GPU-hours. Our work provides both a scientific framework for analyzing scaling in RL and a practical recipe that brings RL training closer to the predictability long achieved in pre-training.

Recent years have witnessed the rapid advancements of large language models (LLMs) and their expanding applications, leading to soaring demands for computational resources. The widespread adoption of test-time scaling further aggravates the tension between model capability and resource consumption, highlighting the importance of inference efficiency. However, a unified metric that accurately reflects an LLM's efficiency across different model sizes and architectures remains absent. Motivated by the correlation between compression and intelligence, we introduce information capacity, a measure of model efficiency based on text compression performance relative to computational complexity. Larger models can predict the next token more accurately, achieving greater compression gains but at higher computational costs. Empirical evaluations on mainstream open-source models show that models of varying sizes within a series exhibit consistent information capacity. This metric enables a fair efficiency comparison across model series and accurate performance prediction within a model series. A distinctive feature of information capacity is that it incorporates tokenizer efficiency, which affects both input and output token counts but is often neglected in LLM evaluations. We assess the information capacity of 49 models on 5 heterogeneous datasets and observe consistent results on the influences of tokenizer efficiency, pretraining data, and the mixture-of-experts architecture.

In real world, large language models (LLMs) can serve as the assistant to help users accomplish their jobs, and also support the development of advanced applications. For the wide application of LLMs, the inference efficiency is an essential concern, which has been widely studied in existing work, and numerous optimization algorithms and code libraries have been proposed to improve it. Nonetheless, users still find it challenging to compare the effectiveness of all the above methods and understand the underlying mechanisms. In this work, we perform a detailed coarse-to-fine analysis of the inference performance of various code libraries. To evaluate the overall effectiveness, we examine four usage scenarios within two practical applications. We further provide both theoretical and empirical fine-grained analyses of each module in the Transformer architecture. Our experiments yield comprehensive results that are invaluable for researchers to evaluate code libraries and improve inference strategies.

We improve the efficiency of algorithms for stochastic combinatorial semi-bandits. In most interesting problems, state-of-the-art algorithms take advantage of structural properties of rewards, such as independence. However, while being optimal in terms of asymptotic regret, these algorithms are inefficient. In our paper, we first reduce their implementation to a specific submodular maximization. Then, in case of matroid constraints, we design adapted approximation routines, thereby providing the first efficient algorithms that rely on reward structure to improve regret bound. In particular, we improve the state-of-the-art efficient gap-free regret bound by a factor m/log m, where m is the maximum action size. Finally, we show how our improvement translates to more general budgeted combinatorial semi-bandits.

Code generation has largely improved development efficiency in the era of large language models (LLMs). With the ability to follow instructions, current LLMs can be prompted to generate code solutions given detailed descriptions in natural language. Many research efforts are being devoted to improving the correctness of LLM-generated code, and many benchmarks are proposed to evaluate the correctness comprehensively. Despite the focus on correctness, the time efficiency of LLM-generated code solutions is under-explored. Current correctness benchmarks are not suitable for time efficiency evaluation since their test cases cannot well distinguish the time efficiency of different code solutions. Besides, the current execution time measurement is not stable and comprehensive, threatening the validity of the time efficiency evaluation. To address the challenges in the time efficiency evaluation of code generation, we propose COFFE, a code generation benchmark for evaluating the time efficiency of LLM-generated code solutions. COFFE contains 398 and 358 problems for function-level and file-level code generation, respectively. To improve the distinguishability, we design a novel stressful test case generation approach with contracts and two new formats of test cases to improve the accuracy of generation. For the time evaluation metric, we propose efficienct@k based on CPU instruction count to ensure a stable and solid comparison between different solutions. We evaluate 14 popular LLMs on COFFE and identify four findings. Based on the findings, we draw some implications for LLM researchers and software practitioners to facilitate future research and usage of LLMs in code generation.

We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only. We also observe that when applied to a collection of formal statements of sufficiently varied difficulty, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems, without the need for associated ground-truth proofs. Finally, by applying this expert iteration to a manually curated set of problem statements, we achieve state-of-the-art on the miniF2F benchmark, automatically solving multiple challenging problems drawn from high school olympiads.

Fueled by their remarkable ability to tackle diverse tasks across multiple domains, large language models (LLMs) have grown at an unprecedented rate, with some recent models containing trillions of parameters. This growth is accompanied by substantial computational challenges, particularly regarding the memory and compute resources required for training and fine-tuning. Numerous approaches have been explored to address these issues, such as LoRA. While these methods are effective for fine-tuning, their application to pre-training is significantly more challenging due to the need to learn vast datasets. Motivated by this issue, we aim to address the following questions: Can parameter- or memory-efficient methods enhance pre-training efficiency while achieving performance comparable to full-model training? How can the performance gap be narrowed? To this end, the contributions of this work are the following. (1) We begin by conducting a comprehensive survey that summarizes state-of-the-art methods for efficient pre-training. (2) We perform a benchmark evaluation of several representative memory efficient pre-training approaches to comprehensively evaluate their performance across model sizes. We observe that with a proper choice of optimizer and hyperparameters, full-rank training delivers the best performance, as expected. We also notice that incorporating high-rank updates in low-rank approaches is the key to improving their performance. (3) Finally, we propose two practical techniques, namely weight refactorization and momentum reset, to enhance the performance of efficient pre-training methods. We observe that applying these techniques to the low-rank method (on a 1B model) can achieve a lower perplexity than popular memory efficient algorithms such as GaLore and Fira, while simultaneously using about 25% less memory.

Many real world learning tasks involve complex or hard-to-specify objectives, and using an easier-to-specify proxy can lead to poor performance or misaligned behavior. One solution is to have humans provide a training signal by demonstrating or judging performance, but this approach fails if the task is too complicated for a human to directly evaluate. We propose Iterated Amplification, an alternative training strategy which progressively builds up a training signal for difficult problems by combining solutions to easier subproblems. Iterated Amplification is closely related to Expert Iteration (Anthony et al., 2017; Silver et al., 2017), except that it uses no external reward function. We present results in algorithmic environments, showing that Iterated Amplification can efficiently learn complex behaviors.

We rethink test-time scaling laws from a practical efficiency perspective, revealing that the effectiveness of smaller models is significantly overestimated. Prior work, grounded in compute-optimality, overlooks critical memory access bottlenecks introduced by inference-time strategies (e.g., Best-of-N, long CoTs). Our holistic analysis, spanning models from 0.6B to 32B parameters, reveals a new Kinetics Scaling Law that better guides resource allocation by incorporating both computation and memory access costs. Kinetics Scaling Law suggests that test-time compute is more effective when used on models above a threshold than smaller ones. A key reason is that in TTS, attention, rather than parameter count, emerges as the dominant cost factor. Motivated by this, we propose a new scaling paradigm centered on sparse attention, which lowers per-token cost and enables longer generations and more parallel samples within the same resource budget. Empirically, we show that sparse attention models consistently outperform dense counterparts, achieving over 60 points gains in low-cost regimes and over 5 points gains in high-cost regimes for problem-solving accuracy on AIME, encompassing evaluations on state-of-the-art MoEs. These results suggest that sparse attention is essential for realizing the full potential of test-time scaling because, unlike training, where parameter scaling saturates, test-time accuracy continues to improve through increased generation. The code is available at https://github.com/Infini-AI-Lab/Kinetics.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

Orthogonality-based optimizers, such as Muon, have recently shown strong performance across large-scale training and community-driven efficiency challenges. However, these methods rely on a costly gradient orthogonalization step. Even efficient iterative approximations such as Newton-Schulz remain expensive, typically requiring dozens of matrix multiplications to converge. We introduce a preconditioning procedure that accelerates Newton-Schulz convergence and reduces its computational cost. We evaluate its impact and show that the overhead of our preconditioning can be made negligible. Furthermore, the faster convergence it enables allows us to remove one iteration out of the usual five without degrading approximation quality. Our publicly available implementation achieves up to a 2.8x speedup in the Newton-Schulz approximation. We also show that this has a direct impact on end-to-end training runtime with 5-10% improvement in realistic training scenarios across two efficiency-focused tasks. On challenging language or vision tasks, we validate that our method maintains equal or superior model performance while improving runtime. Crucially, these improvements require no hyperparameter tuning and can be adopted as a simple drop-in replacement. Our code is publicly available on github.

Existing learning rate schedules that do not require specification of the optimization stopping step T are greatly out-performed by learning rate schedules that depend on T. We propose an approach that avoids the need for this stopping time by eschewing the use of schedules entirely, while exhibiting state-of-the-art performance compared to schedules across a wide family of problems ranging from convex problems to large-scale deep learning problems. Our Schedule-Free approach introduces no additional hyper-parameters over standard optimizers with momentum. Our method is a direct consequence of a new theory we develop that unifies scheduling and iterate averaging. An open source implementation of our method is available (https://github.com/facebookresearch/schedule_free).

Large Language Models (LLMs) have emerged as powerful tools in mathematical theorem proving, particularly when utilizing formal languages such as LEAN. The major learning paradigm is expert iteration, which necessitates a pre-defined dataset comprising numerous mathematical problems. In this process, LLMs attempt to prove problems within the dataset and iteratively refine their capabilities through self-training on the proofs they discover. We propose to use large scale LEAN problem datasets Lean-workbook for expert iteration with more than 20,000 CPU days. During expert iteration, we found log-linear trends between solved problem amount with proof length and CPU usage. We train a critic model to select relatively easy problems for policy models to make trials and guide the model to search for deeper proofs. InternLM2.5-StepProver achieves open-source state-of-the-art on MiniF2F, Lean-Workbook-Plus, ProofNet, and Putnam benchmarks. Specifically, it achieves a pass of 65.9% on the MiniF2F-test and proves (or disproves) 17.0% of problems in Lean-Workbook-Plus which shows a significant improvement compared to only 9.5% of problems proved when Lean-Workbook-Plus was released. We open-source our models and searched proofs at https://github.com/InternLM/InternLM-Math and https://huggingface.co/datasets/internlm/Lean-Workbook.

Transformer models have established new benchmarks in natural language processing; however, their increasing depth results in substantial growth in parameter counts. While existing recurrent transformer methods address this issue by reprocessing layers multiple times, they often apply recurrence indiscriminately across entire blocks of layers. In this work, we investigate Intra-Layer Recurrence (ILR), a more targeted approach that applies recurrence selectively to individual layers within a single forward pass. Our experiments show that allocating more iterations to earlier layers yields optimal results. These findings suggest that ILR offers a promising direction for optimizing recurrent structures in transformer architectures.

Time-dependent data-generating distributions have proven to be difficult for gradient-based training of neural networks, as the greedy updates result in catastrophic forgetting of previously learned knowledge. Despite the progress in the field of continual learning to overcome this forgetting, we show that a set of common state-of-the-art methods still suffers from substantial forgetting upon starting to learn new tasks, except that this forgetting is temporary and followed by a phase of performance recovery. We refer to this intriguing but potentially problematic phenomenon as the stability gap. The stability gap had likely remained under the radar due to standard practice in the field of evaluating continual learning models only after each task. Instead, we establish a framework for continual evaluation that uses per-iteration evaluation and we define a new set of metrics to quantify worst-case performance. Empirically we show that experience replay, constraint-based replay, knowledge-distillation, and parameter regularization methods are all prone to the stability gap; and that the stability gap can be observed in class-, task-, and domain-incremental learning benchmarks. Additionally, a controlled experiment shows that the stability gap increases when tasks are more dissimilar. Finally, by disentangling gradients into plasticity and stability components, we propose a conceptual explanation for the stability gap.

We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies have observed that LR+GD can find a solution with arbitrarily large step sizes, defying conventional optimization theory. Our work investigates this phenomenon and makes three interconnected key observations about LR+GD with large step sizes. First, we find a remarkably simple explanation of why LR+GD with large step sizes solves the classification problem: LR+GD reduces to a batch version of the celebrated perceptron algorithm when the step size gamma to infty. Second, we observe that larger step sizes lead LR+GD to higher logistic losses when it tends to the perceptron algorithm, but larger step sizes also lead to faster convergence to a solution for the classification problem, meaning that logistic loss is an unreliable metric of the proximity to a solution. Surprisingly, high loss values can actually indicate faster convergence. Third, since the convergence rate in terms of loss function values of LR+GD is unreliable, we examine the iteration complexity required by LR+GD with large step sizes to solve the classification problem and prove that this complexity is suboptimal. To address this, we propose a new method, Normalized LR+GD - based on the connection between LR+GD and the perceptron algorithm - with much better theoretical guarantees.

Recently, diffusion models have achieved significant advances in vision, text, and robotics. However, they still face slow generation speeds due to sequential denoising processes. To address this, a parallel sampling method based on Picard iteration was introduced, effectively reducing sequential steps while ensuring exact convergence to the original output. Nonetheless, Picard iteration does not guarantee faster convergence, which can still result in slow generation in practice. In this work, we propose a new parallelization scheme, the Picard Consistency Model (PCM), which significantly reduces the number of generation steps in Picard iteration. Inspired by the consistency model, PCM is directly trained to predict the fixed-point solution, or the final output, at any stage of the convergence trajectory. Additionally, we introduce a new concept called model switching, which addresses PCM's limitations and ensures exact convergence. Extensive experiments demonstrate that PCM achieves up to a 2.71x speedup over sequential sampling and a 1.77x speedup over Picard iteration across various tasks, including image generation and robotic control.

The remarkable performance of models like the OpenAI o1 can be attributed to their ability to emulate human-like long-time thinking during inference. These models employ extended chain-of-thought (CoT) processes, exploring multiple strategies to enhance problem-solving capabilities. However, a critical question remains: How to intelligently and efficiently scale computational resources during testing. This paper presents the first comprehensive study on the prevalent issue of overthinking in these models, where excessive computational resources are allocated for simple problems with minimal benefit. We introduce novel efficiency metrics from both outcome and process perspectives to evaluate the rational use of computational resources by o1-like models. Using a self-training paradigm, we propose strategies to mitigate overthinking, streamlining reasoning processes without compromising accuracy. Experimental results show that our approach successfully reduces computational overhead while preserving model performance across a range of testsets with varying difficulty levels, such as GSM8K, MATH500, GPQA, and AIME.

In unsupervised learning, collecting more data is not always a costly process unlike the training. For example, it is not hard to enlarge the 40GB WebText used for training GPT-2 by modifying its sampling methodology considering how many webpages there are in the Internet. On the other hand, given that training on this dataset already costs tens of thousands of dollars, training on a larger dataset naively is not cost-wise feasible. In this paper, we suggest to train on a larger dataset for only one epoch unlike the current practice, in which the unsupervised models are trained for from tens to hundreds of epochs. Furthermore, we suggest to adjust the model size and the number of iterations to be performed appropriately. We show that the performance of Transformer language model becomes dramatically improved in this way, especially if the original number of epochs is greater. For example, by replacing the training for 10 epochs with the one epoch training, this translates to 1.9-3.3x speedup in wall-clock time in our settings and more if the original number of epochs is greater. Under one epoch training, no overfitting occurs, and regularization method does nothing but slows down the training. Also, the curve of test loss over iterations follows power-law extensively. We compare the wall-clock time of the training of models with different parameter budget under one epoch training, and we show that size/iteration adjustment based on our proposed heuristics leads to 1-2.7x speedup in our cases. With the two methods combined, we achieve 3.3-5.1x speedup. Finally, we speculate various implications of one epoch training and size/iteration adjustment. In particular, based on our analysis we believe that we can reduce the cost to train the state-of-the-art models as BERT and GPT-2 dramatically, maybe even by the factor of 10.

In an increasing number of domains it has been demonstrated that deep learning models can be trained using relatively large batch sizes without sacrificing data efficiency. However the limits of this massive data parallelism seem to differ from domain to domain, ranging from batches of tens of thousands in ImageNet to batches of millions in RL agents that play the game Dota 2. To our knowledge there is limited conceptual understanding of why these limits to batch size differ or how we might choose the correct batch size in a new domain. In this paper, we demonstrate that a simple and easy-to-measure statistic called the gradient noise scale predicts the largest useful batch size across many domains and applications, including a number of supervised learning datasets (MNIST, SVHN, CIFAR-10, ImageNet, Billion Word), reinforcement learning domains (Atari and Dota), and even generative model training (autoencoders on SVHN). We find that the noise scale increases as the loss decreases over a training run and depends on the model size primarily through improved model performance. Our empirically-motivated theory also describes the tradeoff between compute-efficiency and time-efficiency, and provides a rough model of the benefits of adaptive batch-size training.

Recently, the scale of transformers has grown rapidly, which introduces considerable challenges in terms of training overhead and inference efficiency in the scope of task adaptation. Existing works, namely Parameter-Efficient Fine-Tuning (PEFT) and model compression, have separately investigated the challenges. However, PEFT cannot guarantee the inference efficiency of the original backbone, especially for large-scale models. Model compression requires significant training costs for structure searching and re-training. Consequently, a simple combination of them cannot guarantee accomplishing both training efficiency and inference efficiency with minimal costs. In this paper, we propose a novel Parallel Yielding Re-Activation (PYRA) method for such a challenge of training-inference efficient task adaptation. PYRA first utilizes parallel yielding adaptive weights to comprehensively perceive the data distribution in downstream tasks. A re-activation strategy for token modulation is then applied for tokens to be merged, leading to calibrated token features. Extensive experiments demonstrate that PYRA outperforms all competing methods under both low compression rate and high compression rate, demonstrating its effectiveness and superiority in maintaining both training efficiency and inference efficiency for large-scale foundation models. Our code will be released to the public.

We introduce a novel framework for analyzing sorting algorithms in pairwise ranking prompting (PRP), re-centering the cost model around LLM inferences rather than traditional pairwise comparisons. While classical metrics based on comparison counts have traditionally been used to gauge efficiency, our analysis reveals that expensive LLM inferences overturn these predictions; accordingly, our framework encourages strategies such as batching and caching to mitigate inference costs. We show that algorithms optimal in the classical setting can lose efficiency when LLM inferences dominate the cost under certain optimizations.

Pipeline parallelism has been widely explored, but most existing schedules lack a systematic methodology. In this paper, we propose a framework to decompose pipeline schedules as repeating a building block and we show that the lifespan of the building block decides the peak activation memory of the pipeline schedule. Guided by the observations, we find that almost all existing pipeline schedules, to the best of our knowledge, are memory inefficient. To address this, we introduce a family of memory efficient building blocks with controllable activation memory, which can reduce the peak activation memory to 1/2 of 1F1B without sacrificing efficiency, and even to 1/3 with comparable throughput. We can also achieve almost zero pipeline bubbles while maintaining the same activation memory as 1F1B. Our evaluations demonstrate that in pure pipeline parallelism settings, our methods outperform 1F1B by from 7% to 55% in terms of throughput. When employing a grid search over hybrid parallelism hyperparameters in practical scenarios, our proposed methods demonstrate a 16% throughput improvement over the 1F1B baseline for large language models.

Pruning is a well-established technique for removing unnecessary structure from neural networks after training to improve the performance of inference. Several recent results have explored the possibility of pruning at initialization time to provide similar benefits during training. In particular, the "lottery ticket hypothesis" conjectures that typical neural networks contain small subnetworks that can train to similar accuracy in a commensurate number of steps. The evidence for this claim is that a procedure based on iterative magnitude pruning (IMP) reliably finds such subnetworks retroactively on small vision tasks. However, IMP fails on deeper networks, and proposed methods to prune before training or train pruned networks encounter similar scaling limitations. In this paper, we argue that these efforts have struggled on deeper networks because they have focused on pruning precisely at initialization. We modify IMP to search for subnetworks that could have been obtained by pruning early in training (0.1% to 7% through) rather than at iteration 0. With this change, it finds small subnetworks of deeper networks (e.g., 80% sparsity on Resnet-50) that can complete the training process to match the accuracy of the original network on more challenging tasks (e.g., ImageNet). In situations where IMP fails at iteration 0, the accuracy benefits of delaying pruning accrue rapidly over the earliest iterations of training. To explain these behaviors, we study subnetwork "stability," finding that - as accuracy improves in this fashion - IMP subnetworks train to parameters closer to those of the full network and do so with improved consistency in the face of gradient noise. These results offer new insights into the opportunity to prune large-scale networks early in training and the behaviors underlying the lottery ticket hypothesis

Although deep learning has made great progress in recent years, the exploding economic and environmental costs of training neural networks are becoming unsustainable. To address this problem, there has been a great deal of research on *algorithmically-efficient deep learning*, which seeks to reduce training costs not at the hardware or implementation level, but through changes in the semantics of the training program. In this paper, we present a structured and comprehensive overview of the research in this field. First, we formalize the *algorithmic speedup* problem, then we use fundamental building blocks of algorithmically efficient training to develop a taxonomy. Our taxonomy highlights commonalities of seemingly disparate methods and reveals current research gaps. Next, we present evaluation best practices to enable comprehensive, fair, and reliable comparisons of speedup techniques. To further aid research and applications, we discuss common bottlenecks in the training pipeline (illustrated via experiments) and offer taxonomic mitigation strategies for them. Finally, we highlight some unsolved research challenges and present promising future directions.

Pre-trained code language models have achieved promising performance in code generation and improved the programming efficiency of human developers. However, their self-refinement capability is typically overlooked by the existing evaluations of code LMs, which focus only on the accuracy of the one-time prediction. For the cases when code LMs fail to implement the correct program, developers actually find it hard to debug and fix the faulty prediction since it is not written by the developers themselves. Unfortunately, our study reveals that code LMs cannot efficiently self-refine their faulty generations as well. In this paper, we propose CYCLE framework, learning to self-refine the faulty generation according to the available feedback, such as the execution results reported by the test suites. We evaluate CYCLE on three popular code generation benchmarks, HumanEval, MBPP, and APPS. The results reveal that CYCLE successfully maintains, sometimes improves, the quality of one-time code generation, while significantly improving the self-refinement capability of code LMs. We implement four variants of CYCLE with varied numbers of parameters across 350M, 1B, 2B, and 3B, and the experiments show that CYCLE consistently boosts the code generation performance, by up to 63.5%, across benchmarks and varied model sizes. We also notice that CYCLE outperforms code LMs that have 3times more parameters in self-refinement.

Language model (LM) benchmarking faces several challenges: comprehensive evaluations are costly, benchmarks often fail to measure the intended capabilities, and evaluation quality can degrade due to labeling errors and benchmark saturation. Although various strategies have been proposed to mitigate these issues, they tend to address individual aspects in isolation, neglecting broader questions about overall evaluation quality. Here, we introduce Fluid Benchmarking, a new evaluation approach that advances LM benchmarking across multiple dimensions. Inspired by psychometrics, Fluid Benchmarking is based on the insight that the relative value of benchmark items depends on an LM's capability level, suggesting that evaluation should adapt to each LM. Methodologically, Fluid Benchmarking estimates an item response model based on existing LM evaluation results and uses the inferred quantities to select evaluation items dynamically, similar to computerized adaptive testing in education. In our experiments, we compare Fluid Benchmarking against the common practice of random item sampling as well as more sophisticated baselines, including alternative methods grounded in item response theory. We examine four dimensions -- efficiency, validity, variance, and saturation -- and find that Fluid Benchmarking achieves superior performance in all of them (e.g., higher validity and less variance on MMLU with fifty times fewer items). Our analysis shows that the two components of Fluid Benchmarking have distinct effects: item response theory, used to map performance into a latent ability space, increases validity, while dynamic item selection reduces variance. Overall, our results suggest that LM benchmarking can be substantially improved by moving beyond static evaluation.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm--using only the number of iterations as feedback--can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

Test-time compute scaling has emerged as a new axis along which to improve model accuracy, where additional computation is used at inference time to allow the model to think longer for more challenging problems. One promising approach for test-time compute scaling is search against a process reward model, where a model generates multiple potential candidates at each step of the search, and these partial trajectories are then scored by a separate reward model in order to guide the search process. The diversity of trajectories in the tree search process affects the accuracy of the search, since increasing diversity promotes more exploration. However, this diversity comes at a cost, as divergent trajectories have less KV sharing, which means they consume more memory and slow down the search process. Previous search methods either do not perform sufficient exploration, or else explore diverse trajectories but have high latency. We address this challenge by proposing Efficient Tree Search (ETS), which promotes KV sharing by pruning redundant trajectories while maintaining necessary diverse trajectories. ETS incorporates a linear programming cost model to promote KV cache sharing by penalizing the number of nodes retained, while incorporating a semantic coverage term into the cost model to ensure that we retain trajectories which are semantically different. We demonstrate how ETS can achieve 1.8times reduction in average KV cache size during the search process, leading to 1.4times increased throughput relative to prior state-of-the-art methods, with minimal accuracy degradation and without requiring any custom kernel implementation. Code is available at: https://github.com/SqueezeAILab/ETS.

While recent works (e.g. o1, DeepSeek R1) have demonstrated great promise of using long Chain-of-Thought (CoT) to improve reasoning capabilities of language models, scaling it up during test-time is challenging due to inefficient memory usage -- intermediate computations accumulate indefinitely in context even no longer needed for future thoughts. We propose PENCIL, which incorporates a reduction mechanism into the autoregressive generation process, allowing the model to recursively clean up intermediate thoughts based on patterns learned from training. With this reduction mechanism, PENCIL significantly reduces the maximal context length required during generation, and thus can generate longer thoughts with limited memory, solving larger-scale problems given more thinking time. For example, we demonstrate PENCIL achieves 97\% accuracy on the challenging Einstein's puzzle -- a task even large models like GPT-4 struggle with -- using only a small 25M-parameter transformer with 2048 context length. Theoretically, we prove PENCIL can perform universal space-efficient computation by simulating Turing machines with optimal time and space complexity, and thus can solve arbitrary computational tasks that would otherwise be intractable given context window constraints.

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis. By framing neural networks as operators with fixed points representing desired solutions, we develop a theoretical framework grounded in iterative methods for operator equations. Under defined conditions, we present convergence proofs based on fixed point theory. We demonstrate that popular architectures, such as diffusion models and AlphaFold, inherently employ iterative operator learning. Empirical assessments highlight that performing iterations through network operators improves performance. We also introduce an iterative graph neural network, PIGN, that further demonstrates benefits of iterations. Our work aims to enhance the understanding of deep learning by merging insights from numerical analysis, potentially guiding the design of future networks with clearer theoretical underpinnings and improved performance.

Large Language Models (LLMs) are widely adopted for assisting in software development tasks, yet their performance evaluations have narrowly focused on the functional correctness of generated code. Human programmers, however, require LLM-generated code to be not only correct but also optimally efficient. We propose PerfCodeGen, a training-free framework that enhances the performance of LLM-generated code by incorporating feedback based on runtime during test case execution into the self-refinement iterations. With PerfCodeGen, we achieve speedups for a significantly higher proportion of problems compared to using the base LLM with sophisticated prompting techniques. Applied to open language models like Phi-3-mini, PerfCodeGen achieves runtime efficiency comparable to prompting powerful closed models like GPT-4. We achieve state-of-the-art runtime efficiency on benchmarks such as HumanEval, MBPP, and APPS, frequently surpassing the ground truth reference solutions with PerfCodeGen using GPT-3.5 and GPT-4. Additionally, we demonstrate the effectiveness of our approach in enhancing code quality across a range of open LLMs of varying sizes including Phi-3-mini, Llama 3 8B, Mixtral 8x7B, Command R, and Llama 3 70B.

The advent of the transformer has sparked a quick growth in the size of language models, far outpacing hardware improvements. (Dense) transformers are expected to reach the trillion-parameter scale in the near future, for which training requires thousands or even tens of thousands of GPUs. We investigate the challenges of training at this scale and beyond on commercially available hardware. In particular, we analyse the shortest possible training time for different configurations of distributed training, leveraging empirical scaling laws for language models to estimate the optimal (critical) batch size. Contrary to popular belief, we find no evidence for a memory wall, and instead argue that the real limitation -- other than the cost -- lies in the training duration. In addition to this analysis, we introduce two new methods, layered gradient accumulation and modular pipeline parallelism, which together cut the shortest training time by half. The methods also reduce data movement, lowering the network requirement to a point where a fast InfiniBand connection is not necessary. This increased network efficiency also improve on the methods introduced with the ZeRO optimizer, reducing the memory usage to a tiny fraction of the available GPU memory.

Code optimization is a daunting task that requires a significant level of expertise from experienced programmers. This level of expertise is not sufficient when compared to the rapid development of new hardware architectures. Towards advancing the whole code optimization process, recent approaches rely on machine learning and artificial intelligence techniques. This paper introduces a new framework to decrease the complexity of code optimization. The proposed framework builds on large language models (LLMs) and reinforcement learning (RL) and enables LLMs to receive feedback from their environment (i.e., unit tests) during the fine-tuning process. We compare our framework with existing state-of-the-art models and show that it is more efficient with respect to speed and computational usage, as a result of the decrement in training steps and its applicability to models with fewer parameters. Additionally, our framework reduces the possibility of logical and syntactical errors. Toward evaluating our approach, we run several experiments on the PIE dataset using a CodeT5 language model and RRHF, a new reinforcement learning algorithm. We adopt a variety of evaluation metrics with regards to optimization quality, and speedup. The evaluation results demonstrate that the proposed framework has similar results in comparison with existing models using shorter training times and smaller pre-trained models. In particular, we accomplish an increase of 5.6% and 2.2 over the baseline models concerning the %OP T and SP metrics.

The dominant paradigm for RLHF is online and on-policy RL: synchronously generating from the large language model (LLM) policy, labelling with a reward model, and learning using feedback on the LLM's own outputs. While performant, this paradigm is computationally inefficient. Inspired by classical deep RL literature, we propose separating generation and learning in RLHF. This enables asynchronous generation of new samples while simultaneously training on old samples, leading to faster training and more compute-optimal scaling. However, asynchronous training relies on an underexplored regime, online but off-policy RLHF: learning on samples from previous iterations of our model. To understand the challenges in this regime, we investigate a fundamental question: how much off-policyness can we tolerate for asynchronous training to speed up learning but maintain performance? Among several RLHF algorithms we tested, we find that online DPO is most robust to off-policy data, and robustness increases with the scale of the policy model. We study further compute optimizations for asynchronous RLHF but find that they come at a performance cost, giving rise to a trade-off. Finally, we verify the scalability of asynchronous RLHF by training LLaMA 3.1 8B on an instruction-following task 40% faster than a synchronous run while matching final performance.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a dominant approach for aligning LLM outputs with human preferences. Inspired by the success of RLHF, we study the performance of multiple algorithms that learn from feedback (Expert Iteration, Proximal Policy Optimization (PPO), Return-Conditioned RL) on improving LLM reasoning capabilities. We investigate both sparse and dense rewards provided to the LLM both heuristically and via a learned reward model. We additionally start from multiple model sizes and initializations both with and without supervised fine-tuning (SFT) data. Overall, we find all algorithms perform comparably, with Expert Iteration performing best in most cases. Surprisingly, we find the sample complexity of Expert Iteration is similar to that of PPO, requiring at most on the order of 10^6 samples to converge from a pretrained checkpoint. We investigate why this is the case, concluding that during RL training models fail to explore significantly beyond solutions already produced by SFT models. Additionally, we discuss a trade off between maj@1 and pass@96 metric performance during SFT training and how conversely RL training improves both simultaneously. We then conclude by discussing the implications of our findings for RLHF and the future role of RL in LLM fine-tuning.

Progress in many task domains emerges from repeated revisions to previous solution attempts. Training agents that can reliably self-improve over such sequences at inference-time is a natural target for reinforcement learning (RL), yet the naive approach assumes a fixed maximum iteration depth, which can be both costly and arbitrary. We present Exploratory Iteration (ExIt), a family of autocurriculum RL methods that directly exploits the recurrent structure of self-improvement tasks to train LLMs to perform multi-step self-improvement at inference-time while only training on the most informative single-step iterations. ExIt grows a task space by selectively sampling the most informative intermediate, partial histories encountered during an episode for continued iteration, treating these starting points as new self-iteration task instances to train a self-improvement policy. ExIt can further pair with explicit exploration mechanisms to sustain greater task diversity. Across several domains, encompassing competition math, multi-turn tool-use, and machine learning engineering, we demonstrate that ExIt strategies, starting from either a single or many task instances, can produce policies exhibiting strong inference-time self-improvement on held-out task instances, and the ability to iterate towards higher performance over a step budget extending beyond the average iteration depth encountered during training.

Large Language Models (LLMs) are powerful but often too slow and costly for real-world use during inference. Looped transformers save on parameters by reusing the same weights for multiple computational steps, or "loops." However, this approach has a major flaw: the loops run one after another, causing inference latency and memory requirements to increase with each added loop. This makes them impractical for fast applications. To solve this problem, we introduce the Parallel Loop Transformer (PLT). PLT is a new architecture that delivers the performance benefits of a deep, looped model but with the low latency of a standard, non-looped model. PLT works using two key techniques. First, Cross-Loop Parallelism (CLP) breaks the sequential dependency by computing different loops for different tokens at the same time, all within a single pass. Second, to prevent memory costs from growing, we use an Efficient Representation Enhancement strategy. This method shares the memory (KV cache) from the first loop with all other loops. It then uses a Gated Sliding-Window Attention (G-SWA) to combine this shared global information with local information, maintaining high accuracy. Our experiments show that PLT achieves the high accuracy of a traditional looped model but with almost no extra latency or memory cost compared to a standard transformer.

We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven orders of magnitude. Other architectural details such as network width or depth have minimal effects within a wide range. Simple equations govern the dependence of overfitting on model/dataset size and the dependence of training speed on model size. These relationships allow us to determine the optimal allocation of a fixed compute budget. Larger models are significantly more sample-efficient, such that optimally compute-efficient training involves training very large models on a relatively modest amount of data and stopping significantly before convergence.

Pairwise re-ranking models predict which of two documents is more relevant to a query and then aggregate a final ranking from such preferences. This is often more effective than pointwise re-ranking models that directly predict a relevance value for each document. However, the high inference overhead of pairwise models limits their practical application: usually, for a set of k documents to be re-ranked, preferences for all k^2-k comparison pairs excluding self-comparisons are aggregated. We investigate whether the efficiency of pairwise re-ranking can be improved by sampling from all pairs. In an exploratory study, we evaluate three sampling methods and five preference aggregation methods. The best combination allows for an order of magnitude fewer comparisons at an acceptable loss of retrieval effectiveness, while competitive effectiveness is already achieved with about one third of the comparisons.

Training large-scale models under given resources requires careful design of parallelism strategies. In particular, the efficiency notion of critical batch size (CBS), concerning the compromise between time and compute, marks the threshold beyond which greater data parallelism leads to diminishing returns. To operationalize it, we propose a measure of CBS and pre-train a series of auto-regressive language models, ranging from 85 million to 1.2 billion parameters, on the C4 dataset. Through extensive hyper-parameter sweeps and careful control of factors such as batch size, momentum, and learning rate along with its scheduling, we systematically investigate the impact of scale on CBS. Then we fit scaling laws with respect to model and data sizes to decouple their effects. Overall, our results demonstrate that CBS scales primarily with data size rather than model size, a finding we justify theoretically through the analysis of infinite-width limits of neural networks and infinite-dimensional least squares regression. Of independent interest, we highlight the importance of common hyper-parameter choices and strategies for studying large-scale pre-training beyond fixed training durations.

Major winning Convolutional Neural Networks (CNNs), such as AlexNet, VGGNet, ResNet, GoogleNet, include tens to hundreds of millions of parameters, which impose considerable computation and memory overhead. This limits their practical use for training, optimization and memory efficiency. On the contrary, light-weight architectures, being proposed to address this issue, mainly suffer from low accuracy. These inefficiencies mostly stem from following an ad hoc procedure. We propose a simple architecture, called SimpleNet, based on a set of designing principles, with which we empirically show, a well-crafted yet simple and reasonably deep architecture can perform on par with deeper and more complex architectures. SimpleNet provides a good tradeoff between the computation/memory efficiency and the accuracy. Our simple 13-layer architecture outperforms most of the deeper and complex architectures to date such as VGGNet, ResNet, and GoogleNet on several well-known benchmarks while having 2 to 25 times fewer number of parameters and operations. This makes it very handy for embedded systems or systems with computational and memory limitations. We achieved state-of-the-art result on CIFAR10 outperforming several heavier architectures, near state of the art on MNIST and competitive results on CIFAR100 and SVHN. We also outperformed the much larger and deeper architectures such as VGGNet and popular variants of ResNets among others on the ImageNet dataset. Models are made available at: https://github.com/Coderx7/SimpleNet

Generating texts with a large language model (LLM) consumes massive amounts of memory. Apart from the already-large model parameters, the key/value (KV) cache that holds information about previous tokens in a sequence can grow to be even larger than the model itself. This problem is exacerbated in one of the current LLM serving frameworks which reserves the maximum sequence length of memory for the KV cache to guarantee generating a complete sequence as they do not know the output sequence length. This restricts us to use a smaller batch size leading to lower GPU utilization and above all, lower throughput. We argue that designing a system with a priori knowledge of the output sequence can mitigate this problem. To this end, we propose S^{3}, which predicts the output sequence length, schedules generation queries based on the prediction to increase device resource utilization and throughput, and handle mispredictions. Our proposed method achieves 6.49times throughput over those systems that assume the worst case for the output sequence length.

We consider the problem of answering complex questions, given access to a large unstructured document corpus. The de facto approach to solving the problem is to leverage language models that (iteratively) retrieve and reason through the retrieved documents, until the model has sufficient information to generate an answer. Attempts at improving this approach focus on retrieval-augmented generation (RAG) metrics such as accuracy and recall and can be categorized into two types: (a) fine-tuning on large question answering (QA) datasets augmented with chain-of-thought traces, and (b) leveraging RL-based fine-tuning techniques that rely on question-document relevance signals. However, efficiency in the number of retrieval searches is an equally important metric, which has received less attention. In this work, we show that: (1) Large-scale fine-tuning is not needed to improve RAG metrics, contrary to popular claims in recent literature. Specifically, a standard ReAct pipeline with improved prompts can outperform state-of-the-art methods on benchmarks such as HotPotQA. (2) Supervised and RL-based fine-tuning can help RAG from the perspective of frugality, i.e., the latency due to number of searches at inference time. For example, we show that we can achieve competitive RAG metrics at nearly half the cost (in terms of number of searches) on popular RAG benchmarks, using the same base model, and at a small training cost (1000 examples).