Peiyuan Zhang

Kaichen Zhang, Bo Li, Peiyuan Zhang et al.

The advances of large foundation models necessitate wide-coverage, low-cost, and zero-contamination benchmarks. Despite continuous exploration of language model evaluations, comprehensive studies on the evaluation of Large Multi-modal Models (LMMs) remain limited. In this work, we introduce LMMS-EVAL, a unified and standardized multimodal benchmark framework with over 50 tasks and more than 10 models to promote transparent and reproducible evaluations. Although LMMS-EVAL offers comprehensive coverage, we find it still falls short in achieving low cost and zero contamination. To approach this evaluation trilemma, we further introduce LMMS-EVAL LITE, a pruned evaluation toolkit that emphasizes both coverage and efficiency. Additionally, we present Multimodal LIVEBENCH that utilizes continuously updating news and online forums to assess models' generalization abilities in the wild, featuring a low-cost and zero-contamination evaluation approach. In summary, our work highlights the importance of considering the evaluation trilemma and provides practical solutions to navigate the trade-offs in evaluating large multi-modal models, paving the way for more effective and reliable benchmarking of LMMs. We opensource our codebase and maintain leaderboard of LIVEBENCH at https://github.com/EvolvingLMMs-Lab/lmms-eval and https://huggingface.co/spaces/lmms-lab/LiveBench.

Team Seedance, De Chen, Liyang Chen et al. · gatech

Seedance 2.0 is a new native multi-modal audio-video generation model, officially released in China in early February 2026. Compared with its predecessors, Seedance 1.0 and 1.5 Pro, Seedance 2.0 adopts a unified, highly efficient, and large-scale architecture for multi-modal audio-video joint generation. This allows it to support four input modalities: text, image, audio, and video, by integrating one of the most comprehensive suites of multi-modal content reference and editing capabilities available in the industry to date. It delivers substantial, well-rounded improvements across all key sub-dimensions of video and audio generation. In both expert evaluations and public user tests, the model has demonstrated performance on par with the leading levels in the field. Seedance 2.0 supports direct generation of audio-video content with durations ranging from 4 to 15 seconds, with native output resolutions of 480p and 720p. For multi-modal inputs as reference, its current open platform supports up to 3 video clips, 9 images, and 3 audio clips. In addition, we provide Seedance 2.0 Fast version, an accelerated variant of Seedance 2.0 designed to boost generation speed for low-latency scenarios. Seedance 2.0 has delivered significant improvements to its foundational generation capabilities and multi-modal generation performance, bringing an enhanced creative experience for end users.

Bo Li, Yuanhan Zhang, Dong Guo et al.

We present LLaVA-OneVision, a family of open large multimodal models (LMMs) developed by consolidating our insights into data, models, and visual representations in the LLaVA-NeXT blog series. Our experimental results demonstrate that LLaVA-OneVision is the first single model that can simultaneously push the performance boundaries of open LMMs in three important computer vision scenarios: single-image, multi-image, and video scenarios. Importantly, the design of LLaVA-OneVision allows strong transfer learning across different modalities/scenarios, yielding new emerging capabilities. In particular, strong video understanding and cross-scenario capabilities are demonstrated through task transfer from images to videos.

Peiyuan Zhang, Wei Lu

Few-shot relation extraction aims to learn to identify the relation between two entities based on very limited training examples. Recent efforts found that textual labels (i.e., relation names and relation descriptions) could be extremely useful for learning class representations, which will benefit the few-shot learning task. However, what is the best way to leverage such label information in the learning process is an important research question. Existing works largely assume such textual labels are always present during both learning and prediction. In this work, we argue that such approaches may not always lead to optimal results. Instead, we present a novel approach called label prompt dropout, which randomly removes label descriptions in the learning process. Our experiments show that our approach is able to lead to improved class representations, yielding significantly better results on the few-shot relation extraction task.

Bo Li, Peiyuan Zhang, Jingkang Yang et al.

In this paper, we present OtterHD-8B, an innovative multimodal model evolved from Fuyu-8B, specifically engineered to interpret high-resolution visual inputs with granular precision. Unlike conventional models that are constrained by fixed-size vision encoders, OtterHD-8B boasts the ability to handle flexible input dimensions, ensuring its versatility across various inference requirements. Alongside this model, we introduce MagnifierBench, an evaluation framework designed to scrutinize models' ability to discern minute details and spatial relationships of small objects. Our comparative analysis reveals that while current leading models falter on this benchmark, OtterHD-8B, particularly when directly processing high-resolution inputs, outperforms its counterparts by a substantial margin. The findings illuminate the structural variances in visual information processing among different models and the influence that the vision encoders' pre-training resolution disparities have on model effectiveness within such benchmarks. Our study highlights the critical role of flexibility and high-resolution input capabilities in large multimodal models and also exemplifies the potential inherent in the Fuyu architecture's simplicity for handling complex visual data.

Yu-Yang Qian, Junda Su, Lanxiang Hu et al.

Diffusion large language models (dLLMs) offer capabilities beyond those of autoregressive (AR) LLMs, such as parallel decoding and random-order generation. However, realizing these benefits in practice is non-trivial, as dLLMs inherently face an accuracy-parallelism trade-off. Despite increasing interest, existing methods typically focus on only one-side of the coin, targeting either efficiency or performance. To address this limitation, we propose d3LLM (Pseudo-Distilled Diffusion Large Language Model), striking a balance between accuracy and parallelism: (i) during training, we introduce pseudo-trajectory distillation to teach the model which tokens can be decoded confidently at early steps, thereby improving parallelism; (ii) during inference, we employ entropy-based multi-block decoding with a KV-cache refresh mechanism to achieve high parallelism while maintaining accuracy. To better evaluate dLLMs, we also introduce AUP (Accuracy Under Parallelism), a new metric that jointly measures accuracy and parallelism. Experiments demonstrate that our d3LLM achieves up to 10$\times$ speedup over vanilla LLaDA/Dream and 5$\times$ speedup over AR models without much accuracy drop. Our code is available at https://github.com/hao-ai-lab/d3LLM.

Peiyuan Zhang, Guangtao Zeng, Tianduo Wang et al.

We present TinyLlama, a compact 1.1B language model pretrained on around 1 trillion tokens for approximately 3 epochs. Building on the architecture and tokenizer of Llama 2, TinyLlama leverages various advances contributed by the open-source community (e.g., FlashAttention and Lit-GPT), achieving better computational efficiency. Despite its relatively small size, TinyLlama demonstrates remarkable performance in a series of downstream tasks. It significantly outperforms existing open-source language models with comparable sizes. Our model checkpoints and code are publicly available on GitHub at https://github.com/jzhang38/TinyLlama.

Xiangyu Zhao, Peiyuan Zhang, Junming Lin et al.

Reinforcement learning (RL) has emerged as a promising paradigm for enhancing image editing and text-to-image (T2I) generation. However, current reward models, which act as critics during RL, often suffer from hallucinations and assign noisy scores, inherently misguiding the optimization process. In this paper, we present FIRM (Faithful Image Reward Modeling), a comprehensive framework that develops robust reward models to provide accurate and reliable guidance for faithful image generation and editing. First, we design tailored data curation pipelines to construct high-quality scoring datasets. Specifically, we evaluate editing using both execution and consistency, while generation is primarily assessed via instruction following. Using these pipelines, we collect the FIRM-Edit-370K and FIRM-Gen-293K datasets, and train specialized reward models (FIRM-Edit-8B and FIRM-Gen-8B) that accurately reflect these criteria. Second, we introduce FIRM-Bench, a comprehensive benchmark specifically designed for editing and generation critics. Evaluations demonstrate that our models achieve superior alignment with human judgment compared to existing metrics. Furthermore, to seamlessly integrate these critics into the RL pipeline, we formulate a novel "Base-and-Bonus" reward strategy that balances competing objectives: Consistency-Modulated Execution (CME) for editing and Quality-Modulated Alignment (QMA) for generation. Empowered by this framework, our resulting models FIRM-Qwen-Edit and FIRM-SD3.5 achieve substantial performance breakthroughs. Comprehensive experiments demonstrate that FIRM mitigates hallucinations, establishing a new standard for fidelity and instruction adherence over existing general models. All of our datasets, models, and code have been publicly available at https://firm-reward.github.io.

Peiyuan Zhang, Jiaye Teng, Jingzhao Zhang

This work studies the generalization error of gradient methods. More specifically, we focus on how training steps $T$ and step-size $η$ might affect generalization in smooth stochastic convex optimization (SCO) problems. We first provide tight excess risk lower bounds for Gradient Descent (GD) and Stochastic Gradient Descent (SGD) under the general non-realizable smooth SCO setting, suggesting that existing stability analyses are tight in step-size and iteration dependence, and that overfitting provably happens. Next, we study the case when the loss is realizable, i.e. an optimal solution minimizes all the data points. Recent works show better rates can be attained but the improvement is reduced when training time is long. Our paper examines this observation by providing excess risk lower bounds for GD and SGD in two realizable settings: 1) $ηT = \bigO{n}$, and (2) $ηT = \bigOmega{n}$, where $n$ is the size of dataset. In the first case $ηT = \bigOmega{n}$, our lower bounds tightly match and certify the respective upper bounds. However, for the case $ηT = \bigOmega{n}$, our analysis indicates a gap between the lower and upper bounds. A conjecture is proposed that the gap can be closed by improving upper bounds, supported by analyses in two special scenarios.

Syamantak Kumar, Purnamrita Sarkar, Kevin Tian et al.

Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance $Σ$, whose top eigenvector $v \in R^d$ is $s$-sparse. Existing sparse PCA algorithms can be broadly categorized into (1) combinatorial algorithms (e.g., diagonal or elementwise covariance thresholding) and (2) SDP-based algorithms. While combinatorial algorithms are much simpler, they are typically only analyzed under the spiked identity model (where $Σ= I_d + γvv^\top$ for some $γ> 0$), whereas SDP-based algorithms require no additional assumptions on $Σ$. We demonstrate explicit counterexample covariances $Σ$ against the success of standard combinatorial algorithms for sparse PCA, when moving beyond the spiked identity model. In light of this discrepancy, we give the first combinatorial method for sparse PCA that provably succeeds for general $Σ$ using $s^2 \cdot \mathrm{polylog}(d)$ samples and $d^2 \cdot \mathrm{poly}(s, \log(d))$ time, by providing a global convergence guarantee on a variant of the truncated power method of Yuan and Zhang (2013). We provide a natural generalization of our method to recovering a vector in a sparse leading eigenspace. Finally, we evaluate our method on synthetic and real-world sparse PCA datasets.

Peiyuan Zhang, Yongqi Chen, Runlong Su et al.

Diffusion Transformers (DiTs) with 3D full attention power state-of-the-art video generation, but suffer from prohibitive compute cost -- when generating just a 5-second 720P video, attention alone takes 800 out of 945 seconds of total inference time. This paper introduces sliding tile attention (STA) to address this challenge. STA leverages the observation that attention scores in pretrained video diffusion models predominantly concentrate within localized 3D windows. By sliding and attending over the local spatial-temporal region, STA eliminates redundancy from full attention. Unlike traditional token-wise sliding window attention (SWA), STA operates tile-by-tile with a novel hardware-aware sliding window design, preserving expressiveness while being hardware-efficient. With careful kernel-level optimizations, STA offers the first efficient 2D/3D sliding-window-like attention implementation, achieving 58.79% MFU. Precisely, STA accelerates attention by 2.8-17x over FlashAttention-2 (FA2) and 1.6-10x over FlashAttention-3 (FA3). On the leading video DiT, HunyuanVideo, STA reduces end-to-end latency from 945s (FA3) to 685s without quality degradation, requiring no training. Enabling finetuning further lowers latency to 268s with only a 0.09% drop on VBench. We make our codebase public at https://github.com/hao-ai-lab/FastVideo.

Peiyuan Zhang, Yongqi Chen, Haofeng Huang et al.

Scaling video diffusion transformers (DiTs) is limited by their quadratic 3D attention, even though most of the attention mass concentrates on a small subset of positions. We turn this observation into VSA, a trainable, hardware-efficient sparse attention that replaces full attention at \emph{both} training and inference. In VSA, a lightweight coarse stage pools tokens into tiles and identifies high-weight \emph{critical tokens}; a fine stage computes token-level attention only inside those tiles subjecting to block computing layout to ensure hard efficiency. This leads to a single differentiable kernel that trains end-to-end, requires no post-hoc profiling, and sustains 85\% of FlashAttention3 MFU. We perform a large sweep of ablation studies and scaling-law experiments by pretraining DiTs from 60M to 1.4B parameters. VSA reaches a Pareto point that cuts training FLOPS by 2.53$\times$ with no drop in diffusion loss. Retrofitting the open-source Wan-2.1 model speeds up attention time by 6$\times$ and lowers end-to-end generation time from 31s to 18s with comparable quality. These results establish trainable sparse attention as a practical alternative to full attention and a key enabler for further scaling of video diffusion models. Code will be available at https://github.com/hao-ai-lab/FastVideo.

Xiangyu Zhao, Peiyuan Zhang, Kexian Tang et al. · pku

Large Multi-modality Models (LMMs) have made significant progress in visual understanding and generation, but they still face challenges in General Visual Editing, particularly in following complex instructions, preserving appearance consistency, and supporting flexible input formats. To study this gap, we introduce RISEBench, the first benchmark for evaluating Reasoning-Informed viSual Editing (RISE). RISEBench focuses on four key reasoning categories: Temporal, Causal, Spatial, and Logical Reasoning. We curate high-quality test cases for each category and propose an robust evaluation framework that assesses Instruction Reasoning, Appearance Consistency, and Visual Plausibility with both human judges and the LMM-as-a-judge approach. We conducted experiments evaluating nine prominent visual editing models, comprising both open-source and proprietary models. The evaluation results demonstrate that current models face significant challenges in reasoning-based editing tasks. Even the most powerful model evaluated, GPT-4o-Image, achieves an accuracy of merely 28.8%. RISEBench effectively highlights the limitations of contemporary editing models, provides valuable insights, and indicates potential future directions for the field of reasoning-aware visual editing. Our code and data have been released at https://github.com/PhoenixZ810/RISEBench.

Yi Yu, Botao Ren, Peiyuan Zhang et al.

With the rapidly increasing demand for oriented object detection (OOD), recent research involving weakly-supervised detectors for learning OOD from point annotations has gained great attention. In this paper, we rethink this challenging task setting with the layout among instances and present Point2RBox-v2. At the core are three principles: 1) Gaussian overlap loss. It learns an upper bound for each instance by treating objects as 2D Gaussian distributions and minimizing their overlap. 2) Voronoi watershed loss. It learns a lower bound for each instance through watershed on Voronoi tessellation. 3) Consistency loss. It learns the size/rotation variation between two output sets with respect to an input image and its augmented view. Supplemented by a few devised techniques, e.g. edge loss and copy-paste, the detector is further enhanced. To our best knowledge, Point2RBox-v2 is the first approach to explore the spatial layout among instances for learning point-supervised OOD. Our solution is elegant and lightweight, yet it is expected to give a competitive performance especially in densely packed scenes: 62.61%/86.15%/34.71% on DOTA/HRSC/FAIR1M. Code is available at https://github.com/VisionXLab/point2rbox-v2.

Peiyuan Zhang, Junwei Luo, Xue Yang et al.

With the growing demand for oriented object detection (OOD), recent studies on point-supervised OOD have attracted significant interest. In this paper, we propose PointOBB-v3, a stronger single point-supervised OOD framework. Compared to existing methods, it generates pseudo rotated boxes without additional priors and incorporates support for the end-to-end paradigm. PointOBB-v3 functions by integrating three unique image views: the original view, a resized view, and a rotated/flipped (rot/flp) view. Based on the views, a scale augmentation module and an angle acquisition module are constructed. In the first module, a Scale-Sensitive Consistency (SSC) loss and a Scale-Sensitive Feature Fusion (SSFF) module are introduced to improve the model's ability to estimate object scale. To achieve precise angle predictions, the second module employs symmetry-based self-supervised learning. Additionally, we introduce an end-to-end version that eliminates the pseudo-label generation process by integrating a detector branch and introduces an Instance-Aware Weighting (IAW) strategy to focus on high-quality predictions. We conducted extensive experiments on the DIOR-R, DOTA-v1.0/v1.5/v2.0, FAIR1M, STAR, and RSAR datasets. Across all these datasets, our method achieves an average improvement in accuracy of 3.56% in comparison to previous state-of-the-art methods. The code will be available at https://github.com/ZpyWHU/PointOBB-v3.

Peiyuan Zhang, Kaichen Zhang, Bo Li et al.

Video sequences offer valuable temporal information, but existing large multimodal models (LMMs) fall short in understanding extremely long videos. Many works address this by reducing the number of visual tokens using visual resamplers. Alternatively, in this paper, we approach this problem from the perspective of the language model. By simply extrapolating the context length of the language backbone, we enable LMMs to comprehend orders of magnitude more visual tokens without any video training. We call this phenomenon long context transfer and carefully ablate its properties. To effectively measure LMMs' ability to generalize to long contexts in the vision modality, we develop V-NIAH (Visual Needle-In-A-Haystack), a purely synthetic long vision benchmark inspired by the language model's NIAH test. Our proposed Long Video Assistant (LongVA) can process 2000 frames or over 200K visual tokens without additional complexities. With its extended context length, LongVA achieves state-of-the-art performance on Video-MME among 7B-scale models by densely sampling more input frames. Our work is open-sourced at https://github.com/EvolvingLMMs-Lab/LongVA.

Jingkang Yang, Shuai Liu, Hongming Guo et al.

We introduce EgoLife, a project to develop an egocentric life assistant that accompanies and enhances personal efficiency through AI-powered wearable glasses. To lay the foundation for this assistant, we conducted a comprehensive data collection study where six participants lived together for one week, continuously recording their daily activities - including discussions, shopping, cooking, socializing, and entertainment - using AI glasses for multimodal egocentric video capture, along with synchronized third-person-view video references. This effort resulted in the EgoLife Dataset, a comprehensive 300-hour egocentric, interpersonal, multiview, and multimodal daily life dataset with intensive annotation. Leveraging this dataset, we introduce EgoLifeQA, a suite of long-context, life-oriented question-answering tasks designed to provide meaningful assistance in daily life by addressing practical questions such as recalling past relevant events, monitoring health habits, and offering personalized recommendations. To address the key technical challenges of (1) developing robust visual-audio models for egocentric data, (2) enabling identity recognition, and (3) facilitating long-context question answering over extensive temporal information, we introduce EgoButler, an integrated system comprising EgoGPT and EgoRAG. EgoGPT is an omni-modal model trained on egocentric datasets, achieving state-of-the-art performance on egocentric video understanding. EgoRAG is a retrieval-based component that supports answering ultra-long-context questions. Our experimental studies verify their working mechanisms and reveal critical factors and bottlenecks, guiding future improvements. By releasing our datasets, models, and benchmarks, we aim to stimulate further research in egocentric AI assistants.

Hangliang Ding, Dacheng Li, Runlong Su et al.

Despite the promise of synthesizing high-fidelity videos, Diffusion Transformers (DiTs) with 3D full attention suffer from expensive inference due to the complexity of attention computation and numerous sampling steps. For example, the popular Open-Sora-Plan model consumes more than 9 minutes for generating a single video of 29 frames. This paper addresses the inefficiency issue from two aspects: 1) Prune the 3D full attention based on the redundancy within video data; We identify a prevalent tile-style repetitive pattern in the 3D attention maps for video data, and advocate a new family of sparse 3D attention that holds a linear complexity w.r.t. the number of video frames. 2) Shorten the sampling process by adopting existing multi-step consistency distillation; We split the entire sampling trajectory into several segments and perform consistency distillation within each one to activate few-step generation capacities. We further devise a three-stage training pipeline to conjoin the low-complexity attention and few-step generation capacities. Notably, with 0.1% pretraining data, we turn the Open-Sora-Plan-1.2 model into an efficient one that is 7.4x -7.8x faster for 29 and 93 frames 720p video generation with a marginal performance trade-off in VBench. In addition, we demonstrate that our approach is amenable to distributed inference, achieving an additional 3.91x speedup when running on 4 GPUs with sequence parallelism.

Mingxin Liu, Peiyuan Zhang, Yuan Liu et al.

The growing demand for oriented object detection (OOD) across various domains has driven significant research in this area. However, the high cost of dataset annotation remains a major concern. Current mainstream OOD algorithms can be mainly categorized into three types: (1) fully supervised methods using complete oriented bounding box (OBB) annotations, (2) semi-supervised methods using partial OBB annotations, and (3) weakly supervised methods using weak annotations such as horizontal boxes or points. However, these algorithms inevitably increase the cost of models in terms of annotation speed or annotation cost. To address this issue, we propose:(1) the first Partial Weakly-Supervised Oriented Object Detection (PWOOD) framework based on partially weak annotations (horizontal boxes or single points), which can efficiently leverage large amounts of unlabeled data, significantly outperforming weakly supervised algorithms trained with partially weak annotations, also offers a lower cost solution; (2) Orientation-and-Scale-aware Student (OS-Student) model capable of learning orientation and scale information with only a small amount of orientation-agnostic or scale-agnostic weak annotations; and (3) Class-Agnostic Pseudo-Label Filtering strategy (CPF) to reduce the model's sensitivity to static filtering thresholds. Comprehensive experiments on DOTA-v1.0/v1.5/v2.0 and DIOR datasets demonstrate that our PWOOD framework performs comparably to, or even surpasses, traditional semi-supervised algorithms.

Peiyuan Zhang, Amin Karbasi

Classical optimization theory requires a small step-size for gradient-based methods to converge. Nevertheless, recent findings challenge the traditional idea by empirically demonstrating Gradient Descent (GD) converges even when the step-size $η$ exceeds the threshold of $2/L$, where $L$ is the global smooth constant. This is usually known as the Edge of Stability (EoS) phenomenon. A widely held belief suggests that an objective function with subquadratic growth plays an important role in incurring EoS. In this paper, we provide a more comprehensive answer by considering the task of finding linear interpolator $β\in R^{d}$ for regression with loss function $l(\cdot)$, where $β$ admits parameterization as $β= w^2_{+} - w^2_{-}$. Contrary to the previous work that suggests a subquadratic $l$ is necessary for EoS, our novel finding reveals that EoS occurs even when $l$ is quadratic under proper conditions. This argument is made rigorous by both empirical and theoretical evidence, demonstrating the GD trajectory converges to a linear interpolator in a non-asymptotic way. Moreover, the model under quadratic $l$, also known as a depth-$2$ diagonal linear network, remains largely unexplored under the EoS regime. Our analysis then sheds some new light on the implicit bias of diagonal linear networks when a larger step-size is employed, enriching the understanding of EoS on more practical models.

Guangtao Zeng, Peiyuan Zhang, Wei Lu

Fine-tuning pre-trained language models for multiple tasks tends to be expensive in terms of storage. To mitigate this, parameter-efficient transfer learning (PETL) methods have been proposed to address this issue, but they still require a significant number of parameters and storage when being applied to broader ranges of tasks. To achieve even greater storage reduction, we propose PROPETL, a novel method that enables efficient sharing of a single PETL module which we call prototype network (e.g., adapter, LoRA, and prefix-tuning) across layers and tasks. We then learn binary masks to select different sub-networks from the shared prototype network and apply them as PETL modules into different layers. We find that the binary masks can determine crucial information from the network, which is often ignored in previous studies. Our work can also be seen as a type of pruning method, where we find that overparameterization also exists in the seemingly small PETL modules. We evaluate PROPETL on various downstream tasks and show that it can outperform other PETL methods with approximately 10% of the parameter storage required by the latter.

Peiyuan Zhang, Jingzhao Zhang, Suvrit Sra

Deciding whether saddle points exist or are approximable for nonconvex-nonconcave problems is usually intractable. This paper takes a step towards understanding a broad class of nonconvex-nonconcave minimax problems that do remain tractable. Specifically, it studies minimax problems over geodesic metric spaces, which provide a vast generalization of the usual convex-concave saddle point problems. The first main result of the paper is a geodesic metric space version of Sion's minimax theorem; we believe our proof is novel and broadly accessible as it relies on the finite intersection property alone. The second main result is a specialization to geodesically complete Riemannian manifolds: here, we devise and analyze the complexity of first-order methods for smooth minimax problems.

Peiyuan Zhang, Antonio Orvieto, Hadi Daneshmand et al.

Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often supposed to be linked to the quality of the integrator (accuracy, energy preservation, symplecticity). In this work, we propose a novel ordinary differential equation that questions this connection: both the explicit and the semi-implicit (a.k.a symplectic) Euler discretizations on this ODE lead to an accelerated algorithm for convex programming. Although semi-implicit methods are well-known in numerical analysis to enjoy many desirable features for the integration of physical systems, our findings show that these properties do not necessarily relate to acceleration.

Peiyuan Zhang, Hadi Daneshmand, Thomas Hofmann

We study the mixing properties for stochastic accelerated gradient descent (SAGD) on least-squares regression. First, we show that stochastic gradient descent (SGD) and SAGD are simulating the same invariant distribution. Motivated by this, we then establish mixing rate for SAGD-iterates and compare it with those of SGD-iterates. Theoretically, we prove that the chain of SAGD iterates is geometrically ergodic --using a proper choice of parameters and under regularity assumptions on the input distribution. More specifically, we derive an explicit mixing rate depending on the first 4 moments of the data distribution. By means of illustrative examples, we prove that SAGD-iterate chain mixes faster than the chain of iterates obtained by SGD. Furthermore, we highlight applications of the established mixing rate in the convergence analysis of SAGD on realizable objectives. The proposed analysis is based on a novel non-asymptotic analysis of products of random matrices. This theoretical result is substantiated and validated by experiments.