Siyuan Ma

Yiheng Liu, Tianle Han, Siyuan Ma et al.

This paper presents a comprehensive survey of ChatGPT-related (GPT-3.5 and GPT-4) research, state-of-the-art large language models (LLM) from the GPT series, and their prospective applications across diverse domains. Indeed, key innovations such as large-scale pre-training that captures knowledge across the entire world wide web, instruction fine-tuning and Reinforcement Learning from Human Feedback (RLHF) have played significant roles in enhancing LLMs' adaptability and performance. We performed an in-depth analysis of 194 relevant papers on arXiv, encompassing trend analysis, word cloud representation, and distribution analysis across various application domains. The findings reveal a significant and increasing interest in ChatGPT-related research, predominantly centered on direct natural language processing applications, while also demonstrating considerable potential in areas ranging from education and history to mathematics, medicine, and physics. This study endeavors to furnish insights into ChatGPT's capabilities, potential implications, ethical concerns, and offer direction for future advancements in this field.

Bo Gao, Chang Liu, Yuyang Miao et al.

Recent advancements in Large Generative Models (LGMs) have revolutionized multi-modal generation. However, generating illustrated storybooks remains an open challenge, where prior works mainly decompose this task into separate stages, and thus, holistic multi-modal grounding remains limited. Besides, while safety alignment is studied for text- or image-only generation, existing works rarely integrate child-specific safety constraints into narrative planning and sequence-level multi-modal verification. To address these limitations, we propose BookAgent, a safety-aware multi-agent collaboration framework designed for high-quality, safety-aware visual narratives. Different from prior story visualization models that assume a fixed storyline sequence, BookAgent targets end-to-end storybook synthesis from a user draft by jointly planning, scripting, illustrating, and globally repairing inconsistencies. To ensure precise multi-modal grounding, BookAgent dynamically calibrates page-level alignment between textual scripts and visual layouts. Furthermore, BookAgent calibrates holistic consistency from the temporal dimension, by verifying-then-rectifying global inconsistencies in character identity and storytelling logic. Extensive experiments demonstrate that BookAgent significantly outperforms current methods in narrative coherence, visual consistency, and safety compliance, offering a robust paradigm for reliable agents in complex multi-modal creation. The implementation will be publicly released at https://github.com/bogao-code/BookAgent/tree/main.

Weidi Luo, Siyuan Ma, Xiaogeng Liu et al.

With the rapid advancements in Multimodal Large Language Models (MLLMs), securing these models against malicious inputs while aligning them with human values has emerged as a critical challenge. In this paper, we investigate an important and unexplored question of whether techniques that successfully jailbreak Large Language Models (LLMs) can be equally effective in jailbreaking MLLMs. To explore this issue, we introduce JailBreakV-28K, a pioneering benchmark designed to assess the transferability of LLM jailbreak techniques to MLLMs, thereby evaluating the robustness of MLLMs against diverse jailbreak attacks. Utilizing a dataset of 2, 000 malicious queries that is also proposed in this paper, we generate 20, 000 text-based jailbreak prompts using advanced jailbreak attacks on LLMs, alongside 8, 000 image-based jailbreak inputs from recent MLLMs jailbreak attacks, our comprehensive dataset includes 28, 000 test cases across a spectrum of adversarial scenarios. Our evaluation of 10 open-source MLLMs reveals a notably high Attack Success Rate (ASR) for attacks transferred from LLMs, highlighting a critical vulnerability in MLLMs that stems from their text-processing capabilities. Our findings underscore the urgent need for future research to address alignment vulnerabilities in MLLMs from both textual and visual inputs.

Lingyao Li, Deyi Li, Chen Chen et al.

Large language models (LLMs) are increasingly deployed across healthcare applications, including clinical documentation, diagnostic reasoning, medicine recommendation, and medical education. Their outputs are largely unstructured clinical text, which is difficult to reliably evaluate at scale. LLM-as-a-Judge, in which an LLM evaluates another system's output against task-specific criteria, offers a scalable alternative and is increasingly used in clinical evaluation, yet its validity in healthcare remains underexamined. Existing reviews focus on general-purpose LLM evaluation or on risk framework, rather than systematically characterizing how LLM-as-a-Judge is applied in healthcare and how well their judgments align with human experts. We therefore conduct a PRISMA-guided comprehensive review of LLM-as-a-Judge applications in healthcare, searching five databases for studies published between January 2023 and February 2026. After screening 541 records, 134 studies meet the eligibility and are coded by health scenario, judge configuration, technical approach, and validation design. LLM-as-a-Judge is concentrated in clinical decision support, clinical natural language processing (NLP), medical knowledge and question answering (QA), and medical communication. OpenAI models are the most frequently used judges, and prompt engineering appears in nearly all studies, with ensemble, multi-agent, and retrieval-augmented designs as common extensions. Among studies reporting human validation, LLM judges often show moderate to strong alignment with expert judgments, although reliability varies substantially across tasks. Overall, this review positions LLM-as-a-Judge as a promising framework for scalable healthcare AI evaluation, while emphasizing that its clinical value depends on model design and rigorous validation.

Soroosh Mariooryad, Matt Shannon, Siyuan Ma et al.

We present a noisy channel generative model of two sequences, for example text and speech, which enables uncovering the association between the two modalities when limited paired data is available. To address the intractability of the exact model under a realistic data setup, we propose a variational inference approximation. To train this variational model with categorical data, we propose a KL encoder loss approach which has connections to the wake-sleep algorithm. Identifying the joint or conditional distributions by only observing unpaired samples from the marginals is only possible under certain conditions in the data distribution and we discuss under what type of conditional independence assumptions that might be achieved, which guides the architecture designs. Experimental results show that even tiny amount of paired data (5 minutes) is sufficient to learn to relate the two modalities (graphemes and phonemes here) when a massive amount of unpaired data is available, paving the path to adopting this principled approach for all seq2seq models in low data resource regimes.

Yu Qi, Xinyi Xu, Ziyu Guo et al.

Video generative models show emerging reasoning behaviors. It is essential to ensure that generated events remain causally consistent across frames for reliable deployment, a property we define as reasoning coherence. To bridge the gap in literature for missing reasoning coherence evaluation, we propose MME-CoF-Pro, a comprehensive video reasoning benchmark to assess reasoning coherence in video models. Specifically, MME-CoF-Pro contains 303 samples across 16 categories, ranging from visual logical to scientific reasoning. It introduces Reasoning Score as evaluation metric for assessing process-level necessary intermediate reasoning steps, and includes three evaluation settings, (a) no hint (b) text hint and (c) visual hint, enabling a controlled investigation into the underlying mechanisms of reasoning hint guidance. Evaluation results in 7 open and closed-source video models reveals insights including: (1) Video generative models exhibit weak reasoning coherence, decoupled from generation quality. (2) Text hints boost apparent correctness but often cause inconsistency and hallucinated reasoning (3) Visual hints benefit structured perceptual tasks but struggle with fine-grained perception. Website: https://video-reasoning-coherence.github.io/

Binghao Yan, Yunbi Nam, Lingyao Li et al.

Recent advancements in deep learning, particularly large language models (LLMs), made a significant impact on how researchers study microbiome and metagenomics data. Microbial protein and genomic sequences, like natural languages, form a language of life, enabling the adoption of LLMs to extract useful insights from complex microbial ecologies. In this paper, we review applications of deep learning and language models in analyzing microbiome and metagenomics data. We focus on problem formulations, necessary datasets, and the integration of language modeling techniques. We provide an extensive overview of protein/genomic language modeling and their contributions to microbiome studies. We also discuss applications such as novel viromics language modeling, biosynthetic gene cluster prediction, and knowledge integration for metagenomics studies.

Siyuan Ma, Bo Gao, Zikai Xiao et al.

Recent test-time reasoning methods improve performance by generating more candidate chains or searching over larger reasoning trees, but they typically lack explicit control over when to expand, what to prune, how to repair, and when to abstain. We introduce CoT2-Meta, a training-free metacognitive reasoning framework that combines object-level chain-of-thought generation with meta-level control over partial reasoning trajectories. The framework integrates four components: strategy-conditioned thought generation, tree-structured search, an online process oracle for step-level reasoning evaluation, and a meta-controller that allocates computation through expansion, pruning, repair, stopping, and fallback decisions. Under matched inference budgets, CoT2-Meta consistently outperforms strong single-path, sampling-based, and search-based baselines, including ReST-MCTS. On the default backbone, it achieves 92.8 EM on MATH, 90.4 accuracy on GPQA, 98.65 EM on GSM8K, 75.8 accuracy on BBEH, 85.6 accuracy on MMMU-Pro, and 48.8 accuracy on HLE, with gains over the strongest non-CoT2-Meta baseline of +3.6, +5.2, +1.15, +2.0, +4.3, and +4.3 points, respectively. Beyond these core results, the framework remains effective across a broader 15-benchmark suite spanning knowledge and QA, multi-hop reasoning, coding, and out-of-distribution evaluation. Additional analyses show better compute scaling, improved calibration, stronger selective prediction, targeted repair behavior, and consistent gains across backbone families. These results suggest that explicit metacognitive control is a practical design principle for reliable and compute-efficient test-time reasoning systems.

Peipei Xu, SiYuan Ma, Yaohua Liu et al.

Generating feasible Pareto fronts for constrained bi-objective continuous optimization is central to multi-criteria decision-making. Existing methods usually rely on iterative scalarization, evolutionary search, or problem-specific solvers, requiring repeated optimization for each instance. We introduce DIPS, an end-to-end framework that fine-tunes large language models as amortized Pareto-front generators for constrained bi-objective convex optimization. Given a textual problem description, DIPS directly outputs an ordered set of feasible continuous decision vectors approximating the Pareto front. To make continuous optimization compatible with autoregressive language modeling, DIPS combines a compact discretization scheme, Numerically Grounded Token Initialization for new numerical tokens, and Three-Phase Curriculum Optimization, which progressively aligns structural validity, feasibility, and Pareto-front quality. Across five families of constrained bi-objective convex problems, a fine-tuned 7B-parameter model achieves normalized hypervolume ratios of 95.29% to 98.18% relative to reference fronts. With vLLM-accelerated inference, DIPS solves one instance in as little as 0.16 seconds and outperforms general-purpose and reasoning LLM baselines under the evaluated setting. These results suggest that LLMs can serve as effective amortized generators for continuous Pareto-front approximation.

Xinlei Yu, Zhangquan Chen, Yongbo He et al.

Latent space is rapidly emerging as a native substrate for language-based models. While modern systems are still commonly understood through explicit token-level generation, an increasing body of work shows that many critical internal processes are more naturally carried out in continuous latent space than in human-readable verbal traces. This shift is driven by the structural limitations of explicit-space computation, including linguistic redundancy, discretization bottlenecks, sequential inefficiency, and semantic loss. This survey aims to provide a unified and up-to-date landscape of latent space in language-based models. We organize the survey into five sequential perspectives: Foundation, Evolution, Mechanism, Ability, and Outlook. We begin by delineating the scope of latent space, distinguishing it from explicit or verbal space and from the latent spaces commonly studied in generative visual models. We then trace the field's evolution from early exploratory efforts to the current large-scale expansion. To organize the technical landscape, we examine existing work through the complementary lenses of mechanism and ability. From the perspective of Mechanism, we identify four major lines of development: Architecture, Representation, Computation, and Optimization. From the perspective of Ability, we show how latent space supports a broad capability spectrum spanning Reasoning, Planning, Modeling, Perception, Memory, Collaboration, and Embodiment. Beyond consolidation, we discuss the key open challenges, and outline promising directions for future research. We hope this survey serves not only as a reference for existing work, but also as a foundation for understanding latent space as a general computational and systems paradigm for next-generation intelligence.

Yingzi Ma, Jiongxiao Wang, Fei Wang et al.

Machine unlearning has emerged as an effective strategy for forgetting specific information in the training data. However, with the increasing integration of visual data, privacy concerns in Vision Language Models (VLMs) remain underexplored. To address this, we introduce Facial Identity Unlearning Benchmark (FIUBench), a novel VLM unlearning benchmark designed to robustly evaluate the effectiveness of unlearning algorithms under the Right to be Forgotten setting. Specifically, we formulate the VLM unlearning task via constructing the Fictitious Facial Identity VQA dataset and apply a two-stage evaluation pipeline that is designed to precisely control the sources of information and their exposure levels. In terms of evaluation, since VLM supports various forms of ways to ask questions with the same semantic meaning, we also provide robust evaluation metrics including membership inference attacks and carefully designed adversarial privacy attacks to evaluate the performance of algorithms. Through the evaluation of four baseline VLM unlearning algorithms within FIUBench, we find that all methods remain limited in their unlearning performance, with significant trade-offs between model utility and forget quality. Furthermore, our findings also highlight the importance of privacy attacks for robust evaluations. We hope FIUBench will drive progress in developing more effective VLM unlearning algorithms.

Siddhartha Raman Sundara Raman, Siyuan Ma, Lizy Kurian John

Compute-in-memory (PIM) mitigates the memory wall by performing computation within memory, reducing data movement and improving energy efficiency. DRAM-based PIM is particularly attractive due to its high density, mature manufacturing ecosystem, and compatibility with existing systems. Recent works exploit multiple levels of the DRAM hierarchy - including subarrays, banks, and 3D-stacked organizations - to enable in-memory computation using mechanisms such as multi-row activation, row-buffer operations, and near-bank compute units. However, these approaches introduce non-traditional current demand patterns that challenge the power delivery network (PDN). This paper surveys PDN challenges in DRAM-based PIM systems and proposes a unified taxonomy that characterizes PIM-induced current behavior along temporal (burst vs. sustained) and spatial (localized vs. distributed) dimensions. Using this framework, we analyze how representative PIM techniques stress the PDN through bursty activations, multi-row concurrency, and large-scale parallel execution, leading to voltage droop, IR drop, and thermal hotspots. We further discuss DRAM-specific mitigation strategies leveraging existing architectural and circuit-level mechanisms, including timing constraints, memory controller scheduling, data placement, and bank- and vault-level power management. This survey highlights the importance of PDN-aware design for scalable and reliable DRAM-based PIM systems and outlines key future research directions.

Zhengjia Wang, Danding Wang, Qiang Sheng et al.

Understanding the intent behind information is crucial. However, news as a medium of public discourse still lacks a structured investigation of perceived news intent and its application. To advance this field, this paper reviews interdisciplinary studies on intentional action and introduces a conceptual deconstruction-based news intent understanding framework (NINT). This framework identifies the components of intent, facilitating a structured representation of news intent and its applications. Building upon NINT, we contribute a new intent perception dataset. Moreover, we investigate the potential of intent assistance on news-related tasks, such as significant improvement (+2.2% macF1) in the task of fake news detection. We hope that our findings will provide valuable insights into action-based intent cognition and computational social science.

Yu Qi, Haibo Zhao, Ziyu Guo et al.

Embodied capabilities refer to a suite of fundamental abilities for an agent to perceive, comprehend, and interact with the physical world. While multimodal large language models (MLLMs) show promise as embodied agents, a thorough and systematic evaluation of their embodied capabilities remains underexplored, as existing benchmarks primarily focus on specific domains such as planning or spatial understanding. To bridge this gap, we introduce BEAR, a comprehensive and fine-grained benchmark that evaluates MLLMs on atomic embodied capabilities. BEAR comprises 4,469 interleaved image-video-text entries across 14 domains in 6 categories, including tasks from low-level pointing, trajectory understanding, spatial reasoning, to high-level planning. Extensive evaluation results of 20 representative MLLMs reveal their persistent limitations across all domains of embodied capabilities. To tackle the shortfall, we propose BEAR-Agent, a multimodal conversable agent that integrates pretrained vision models to strengthen MLLM perception, 3D understanding, and planning capabilities. It substantially enhances MLLM performance across diverse embodied capabilities on BEAR, yielding a 9.12% absolute gain and a relative improvement of 17.5% on GPT-5. Furthermore, our experiments indicate that improving MLLM embodied capabilities can benefit embodied tasks in simulated environments. Project website: https://bear-official66.github.io/

Xiaoran Xu, Zhaoqian Xue, Chi Zhang et al.

Investigating the public experience of urgent care facilities is essential for promoting community healthcare development. Traditional survey methods often fall short due to limited scope, time, and spatial coverage. Crowdsourcing through online reviews or social media offers a valuable approach to gaining such insights. With recent advancements in large language models (LLMs), extracting nuanced perceptions from reviews has become feasible. This study collects Google Maps reviews across the DMV and Florida areas and conducts prompt engineering with the GPT model to analyze the aspect-based sentiment of urgent care. We first analyze the geospatial patterns of various aspects, including interpersonal factors, operational efficiency, technical quality, finances, and facilities. Next, we determine Census Block Group(CBG)-level characteristics underpinning differences in public perception, including population density, median income, GINI Index, rent-to-income ratio, household below poverty rate, no insurance rate, and unemployment rate. Our results show that interpersonal factors and operational efficiency emerge as the strongest determinants of patient satisfaction in urgent care, while technical quality, finances, and facilities show no significant independent effects when adjusted for in multivariate models. Among socioeconomic and demographic factors, only population density demonstrates a significant but modest association with patient ratings, while the remaining factors exhibit no significant correlations. Overall, this study highlights the potential of crowdsourcing to uncover the key factors that matter to residents and provide valuable insights for stakeholders to improve public satisfaction with urgent care.

Amirhesam Abedsoltan, Siyuan Ma, Parthe Pandit et al.

Classical kernel machines have historically faced significant challenges in scaling to large datasets and model sizes--a key ingredient that has driven the success of neural networks. In this paper, we present a new methodology for building kernel machines that can scale efficiently with both data size and model size. Our algorithm introduces delayed projections to Preconditioned Stochastic Gradient Descent (PSGD) allowing the training of much larger models than was previously feasible, pushing the practical limits of kernel-based learning. We validate our algorithm, EigenPro4, across multiple datasets, demonstrating drastic training speed up over the existing methods while maintaining comparable or better classification accuracy.

Zhijie Duan, Kai Wei, Zhaoqian Xue et al.

Social media is a rich source of real-world data that captures valuable patient experience information for pharmacovigilance. However, mining data from unstructured and noisy social media content remains a challenging task. We present a systematic framework that leverages large language models (LLMs) to extract medication side effects from social media and organize them into a knowledge graph (KG). We apply this framework to semaglutide for weight loss using data from Reddit. Using the constructed knowledge graph, we perform comprehensive analyses to investigate reported side effects across different semaglutide brands over time. These findings are further validated through comparison with adverse events reported in the FAERS database, providing important patient-centered insights into semaglutide's side effects that complement its safety profile and current knowledge base of semaglutide for both healthcare professionals and patients. Our work demonstrates the feasibility of using LLMs to transform social media data into structured KGs for pharmacovigilance.

Minghao Liu, Shengqi Ren, Siyuan Ma et al.

Deep learning model (primarily convolutional networks and LSTM) for time series classification has been studied broadly by the community with the wide applications in different domains like healthcare, finance, industrial engineering and IoT. Meanwhile, Transformer Networks recently achieved frontier performance on various natural language processing and computer vision tasks. In this work, we explored a simple extension of the current Transformer Networks with gating, named Gated Transformer Networks (GTN) for the multivariate time series classification problem. With the gating that merges two towers of Transformer which model the channel-wise and step-wise correlations respectively, we show how GTN is naturally and effectively suitable for the multivariate time series classification task. We conduct comprehensive experiments on thirteen dataset with full ablation study. Our results show that GTN is able to achieve competing results with current state-of-the-art deep learning models. We also explored the attention map for the natural interpretability of GTN on time series modeling. Our preliminary results provide a strong baseline for the Transformer Networks on multivariate time series classification task and grounds the foundation for future research.

Mikhail Belkin, Daniel Hsu, Siyuan Ma et al.

Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to be at odds with the observed behavior of methods used in the modern machine learning practice. The bias-variance trade-off implies that a model should balance under-fitting and over-fitting: rich enough to express underlying structure in data, simple enough to avoid fitting spurious patterns. However, in the modern practice, very rich models such as neural networks are trained to exactly fit (i.e., interpolate) the data. Classically, such models would be considered over-fit, and yet they often obtain high accuracy on test data. This apparent contradiction has raised questions about the mathematical foundations of machine learning and their relevance to practitioners. In this paper, we reconcile the classical understanding and the modern practice within a unified performance curve. This "double descent" curve subsumes the textbook U-shaped bias-variance trade-off curve by showing how increasing model capacity beyond the point of interpolation results in improved performance. We provide evidence for the existence and ubiquity of double descent for a wide spectrum of models and datasets, and we posit a mechanism for its emergence. This connection between the performance and the structure of machine learning models delineates the limits of classical analyses, and has implications for both the theory and practice of machine learning.

Raef Bassily, Mikhail Belkin, Siyuan Ma

Large over-parametrized models learned via stochastic gradient descent (SGD) methods have become a key element in modern machine learning. Although SGD methods are very effective in practice, most theoretical analyses of SGD suggest slower convergence than what is empirically observed. In our recent work [8] we analyzed how interpolation, common in modern over-parametrized learning, results in exponential convergence of SGD with constant step size for convex loss functions. In this note, we extend those results to a much broader non-convex function class satisfying the Polyak-Lojasiewicz (PL) condition. A number of important non-convex problems in machine learning, including some classes of neural networks, have been recently shown to satisfy the PL condition. We argue that the PL condition provides a relevant and attractive setting for many machine learning problems, particularly in the over-parametrized regime.

Like Hui, Siyuan Ma, Mikhail Belkin

We apply a fast kernel method for mask-based single-channel speech enhancement. Specifically, our method solves a kernel regression problem associated to a non-smooth kernel function (exponential power kernel) with a highly efficient iterative method (EigenPro). Due to the simplicity of this method, its hyper-parameters such as kernel bandwidth can be automatically and efficiently selected using line search with subsamples of training data. We observe an empirical correlation between the regression loss (mean square error) and regular metrics for speech enhancement. This observation justifies our training target and motivates us to achieve lower regression loss by training separate kernel model per frequency subband. We compare our method with the state-of-the-art deep neural networks on mask-based HINT and TIMIT. Experimental results show that our kernel method consistently outperforms deep neural networks while requiring less training time.

Siyuan Ma, Mikhail Belkin

Modern machine learning models are typically trained using Stochastic Gradient Descent (SGD) on massively parallel computing resources such as GPUs. Increasing mini-batch size is a simple and direct way to utilize the parallel computing capacity. For small batch an increase in batch size results in the proportional reduction in the training time, a phenomenon known as linear scaling. However, increasing batch size beyond a certain value leads to no further improvement in training time. In this paper we develop the first analytical framework that extends linear scaling to match the parallel computing capacity of a resource. The framework is designed for a class of classical kernel machines. It automatically modifies a standard kernel machine to output a mathematically equivalent prediction function, yet allowing for extended linear scaling, i.e., higher effective parallelization and faster training time on given hardware. The resulting algorithms are accurate, principled and very fast. For example, using a single Titan Xp GPU, training on ImageNet with $1.3\times 10^6$ data points and $1000$ labels takes under an hour, while smaller datasets, such as MNIST, take seconds. As the parameters are chosen analytically, based on the theoretical bounds, little tuning beyond selecting the kernel and the kernel parameter is needed, further facilitating the practical use of these methods.

Mikhail Belkin, Siyuan Ma, Soumik Mandal

Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on test data, a phenomenon not yet fully understood. The first point of our paper is that strong performance of overfitted classifiers is not a unique feature of deep learning. Using six real-world and two synthetic datasets, we establish experimentally that kernel machines trained to have zero classification or near zero regression error perform very well on test data, even when the labels are corrupted with a high level of noise. We proceed to give a lower bound on the norm of zero loss solutions for smooth kernels, showing that they increase nearly exponentially with data size. We point out that this is difficult to reconcile with the existing generalization bounds. Moreover, none of the bounds produce non-trivial results for interpolating solutions. Second, we show experimentally that (non-smooth) Laplacian kernels easily fit random labels, a finding that parallels results for ReLU neural networks. In contrast, fitting noisy data requires many more epochs for smooth Gaussian kernels. Similar performance of overfitted Laplacian and Gaussian classifiers on test, suggests that generalization is tied to the properties of the kernel function rather than the optimization process. Certain key phenomena of deep learning are manifested similarly in kernel methods in the modern "overfitted" regime. The combination of the experimental and theoretical results presented in this paper indicates a need for new theoretical ideas for understanding properties of classical kernel methods. We argue that progress on understanding deep learning will be difficult until more tractable "shallow" kernel methods are better understood.

Siyuan Ma, Raef Bassily, Mikhail Belkin

In this paper we aim to formally explain the phenomenon of fast convergence of SGD observed in modern machine learning. The key observation is that most modern learning architectures are over-parametrized and are trained to interpolate the data by driving the empirical loss (classification and regression) close to zero. While it is still unclear why these interpolated solutions perform well on test data, we show that these regimes allow for fast convergence of SGD, comparable in number of iterations to full gradient descent. For convex loss functions we obtain an exponential convergence bound for {\it mini-batch} SGD parallel to that for full gradient descent. We show that there is a critical batch size $m^*$ such that: (a) SGD iteration with mini-batch size $m\leq m^*$ is nearly equivalent to $m$ iterations of mini-batch size $1$ (\emph{linear scaling regime}). (b) SGD iteration with mini-batch $m> m^*$ is nearly equivalent to a full gradient descent iteration (\emph{saturation regime}). Moreover, for the quadratic loss, we derive explicit expressions for the optimal mini-batch and step size and explicitly characterize the two regimes above. The critical mini-batch size can be viewed as the limit for effective mini-batch parallelization. It is also nearly independent of the data size, implying $O(n)$ acceleration over GD per unit of computation. We give experimental evidence on real data which closely follows our theoretical analyses. Finally, we show how our results fit in the recent developments in training deep neural networks and discuss connections to adaptive rates for SGD and variance reduction.

Siyuan Ma, Mikhail Belkin

In this paper we first identify a basic limitation in gradient descent-based optimization methods when used in conjunctions with smooth kernels. An analysis based on the spectral properties of the kernel demonstrates that only a vanishingly small portion of the function space is reachable after a polynomial number of gradient descent iterations. This lack of approximating power drastically limits gradient descent for a fixed computational budget leading to serious over-regularization/underfitting. The issue is purely algorithmic, persisting even in the limit of infinite data. To address this shortcoming in practice, we introduce EigenPro iteration, based on a preconditioning scheme using a small number of approximately computed eigenvectors. It can also be viewed as learning a new kernel optimized for gradient descent. It turns out that injecting this small (computationally inexpensive and SGD-compatible) amount of approximate second-order information leads to major improvements in convergence. For large data, this translates into significant performance boost over the standard kernel methods. In particular, we are able to consistently match or improve the state-of-the-art results recently reported in the literature with a small fraction of their computational budget. Finally, we feel that these results show a need for a broader computational perspective on modern large-scale learning to complement more traditional statistical and convergence analyses. In particular, many phenomena of large-scale high-dimensional inference are best understood in terms of optimization on infinite dimensional Hilbert spaces, where standard algorithms can sometimes have properties at odds with finite-dimensional intuition. A systematic analysis concentrating on the approximation power of such algorithms within a budget of computation may lead to progress both in theory and practice.