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Applications · Computer Vision

Yansong Peng, Hebei Li, Peixi Wu, Yueyi Zhang, Xiaoyan Sun, Feng Wu

We introduce D-FINE, a powerful real-time object detector that achieves outstanding localization precision by redefining the bounding box regression task in DETR models. D-FINE comprises two key components: Fine-grained Distribution Refinement (FDR) and Global Optimal Localization Self-Distillation (GO-LSD). FDR transforms the regression process from predicting fixed coordinates to iteratively refining probability distributions, providing a fine-grained intermediate representation that significantly enhances localization accuracy. GO-LSD is a bidirectional optimization strategy that transfers localization knowledge from refined distributions to shallower layers through self-distillation, while also simplifying the residual prediction tasks for deeper layers. Additionally, D-FINE incorporates lightweight optimizations in computationally intensive modules and operations, achieving a better balance between speed and accuracy. Specifically, D-FINE-L / X achieves 54.0% / 55.8% AP on the COCO dataset at 124 / 78 FPS on an NVIDIA T4 GPU. When pretrained on Objects365, D-FINE-L / X attains 57.1% / 59.3% AP, surpassing all existing real-time detectors. Furthermore, our method significantly enhances the performance of a wide range of DETR models by up to 5.3% AP with negligible extra parameters and training costs. Our code and models: https://github.com/Peterande/D-FINE.

Zhihai Wang, Jie Wang, Xilin Xia, Dongsheng Zuo, Lei Chen, Yuzhe Ma, Jianye HAO, Mingxuan Yuan, Feng Wu

Optimizing computing circuits such as multipliers and adders is a fundamental challenge in modern integrated circuit design. Recent efforts propose formulating this optimization problem as a reinforcement learning (RL) proxy task, offering a promising approach to search high-speed and area-efficient circuit design solutions. However, we show that the RL-based formulation (proxy task) converges to a local optimal design solution (original task) due to the deceptive reward signals and incrementally localized actions in the RL-based formulation. To address this challenge, we propose a novel model-based circuit genetic evolution (MUTE) framework, which reformulates the problem as a genetic evolution process by proposing a grid-based genetic representation of design solutions. This novel formulation avoids misleading rewards by evaluating and improving generated solutions using the true objective value rather than proxy rewards. To promote globally diverse exploration, MUTE proposes a multi-granularity genetic crossover operator that recombines design substructures at varying column ranges between two grid-based genetic solutions. To the best of our knowledge, MUTE is the first to reformulate the problem as a circuit genetic evolution process, which enables effectively searching for global optimal design solutions. We evaluate MUTE on several fundamental computing circuits, including multipliers, adders, and multiply-accumulate circuits. Experiments on these circuits demonstrate that MUTE significantly Pareto-dominates state-of-the-art approaches in terms of both area and delay. Moreover, experiments demonstrate that circuits designed by MUTE well generalize to large-scale computation-intensive circuits as well.

Optimization · Global Optimization

Zhaojing Wen, Qiulin Zhang, Yuan Zhang, Rudan Chen, Xichao Yang, Di Xie, Jiang Zhu

Post-Training low-bit Quantization (PTQ) is useful to accelerate DNNs due to its high efficiency, the current SOTAs of which mostly adopt feature reconstruction with self-distillation finetuning. However, when bitwidth goes to be extremely low, we find the current reconstruction optimization space is not optimal. Considering all possible parameters and the ignored fact that integer weight can be obtained early before actual inference, we thoroughly explore different optimization space by quant-step decoupling, where a wider PTQ optimization space, which consistently makes a better optimum, is found out. Based on these, we propose an Adaptive Quantization Transformation (AdaQTransform) for PTQ reconstruction, which makes the quantized output feature better fit the FP32 counterpart with adaptive per-channel transformation, thus achieves lower feature reconstruction error. In addition, it incurs negligible extra finetuning cost and no extra inference cost. Based on AdaQTransform, for the first time, we build a general quantization setting paradigm subsuming current PTQs, QATs and other potential forms. Experiments demonstrate AdaQTransform expands the optimization space for PTQ and helps current PTQs find a better optimum over CNNs, ViTs, LLMs and image super-resolution networks, e.g., it improves NWQ by 5.7% on ImageNet for W2A2-MobileNet-v2.

Deep Learning · Other Representation Learning

Haoyuan Li, Yanpeng Zhou, Tao Tang, Jifei Song, Yihan Zeng, Michael Kampffmeyer, Hang Xu, Xiaodan Liang

Recent advancements in multi-modal 3D pre-training methods have shown promising efficacy in learning joint representations of text, images, and point clouds. However, adopting point clouds as 3D representation fails to fully capture the intricacies of the 3D world and exhibits a noticeable gap between the discrete points and the dense 2D pixels of images. To tackle this issue, we propose UniGS, integrating 3D Gaussian Splatting (3DGS) into multi-modal pre-training to enhance the 3D representation. We first rely on the 3DGS representation to model the 3D world as a collection of 3D Gaussians with color and opacity, incorporating all the information of the 3D scene while establishing a strong connection with 2D images. Then, to achieve Language-Image-3D pertaining, UniGS starts with a pretrained vision-language model to establish a shared visual and textual space through extensive real-world image-text pairs. Subsequently, UniGS employs a 3D encoder to align the optimized 3DGS with the Language-Image representations to learn unified multi-modal representations. To facilitate the extraction of global explicit 3D features by the 3D encoder and achieve better cross-modal alignment, we additionally introduce a novel Gaussian-Aware Guidance module that guides the learning of fine-grained representations of the 3D domain. Through extensive experiments across the Objaverse, ABO, MVImgNet and SUN RGBD datasets with zero-shot classification, text-driven retrieval and open-world understanding tasks, we demonstrate the effectiveness of UniGS in learning a more general and stronger aligned multi-modal representation. Specifically, UniGS achieves leading results across different 3D tasks with remarkable improvements over previous SOTA, Uni3D, including on zero-shot classification (+9.36%), text-driven retrieval (+4.3%) and open-world understanding (+7.92%).

Deep Learning · Other Representation Learning

Jingyuan Zhang, Yiyang Duan, Shuaicheng Niu, Yang Cao, Wei Yang Bryan Lim

Federated Domain Adaptation (FDA) is a Federated Learning (FL) scenario where models are trained across multiple clients with unique data domains but a shared category space, without transmitting private data. The primary challenge in FDA is data heterogeneity, which causes significant divergences in gradient updates when using conventional averaging-based aggregation methods, reducing the efficacy of the global model. This further undermines both in-domain and out-of-domain performance (within the same federated system but outside the local client), which is critical in certain business applications. To address this, we propose a novel framework called \textbf{M}ulti-domain \textbf{P}rototype-based \textbf{F}ederated Fine-\textbf{T}uning (MPFT). MPFT fine-tunes a pre-trained model using multi-domain prototypes, i.e., several pretrained representations enriched with domain-specific information from category-specific local data. This enables supervised learning on the server to create a globally optimized adapter that is subsequently distributed to local clients, without the intrusion of data privacy. Empirical results show that MPFT significantly improves both in-domain and out-of-domain accuracy over conventional methods, enhancing knowledge preservation and adaptation in FDA. Notably, MPFT achieves convergence within a single communication round, greatly reducing computation and communication costs. To ensure privacy, MPFT applies differential privacy to protect the prototypes. Additionally, we develop a prototype-based feature space hijacking attack to evaluate robustness, confirming that raw data samples remain unrecoverable even after extensive training epochs. The complete implementation of MPFL is available at \url{https://anonymous.4open.science/r/DomainFL/}.

Deep Learning · Large Language Models

Zhuoqun Li, Xuanang Chen, Haiyang Yu, Hongyu Lin, Yaojie Lu, Qiaoyu Tang, Fei Huang, Xianpei Han, Le Sun, Yongbin Li

Retrieval-augmented generation (RAG) is a key means to effectively enhance large language models (LLMs) in many knowledge-based tasks. However, existing RAG methods struggle with knowledge-intensive reasoning tasks, because useful information required to these tasks are badly scattered. This characteristic makes it difficult for existing RAG methods to accurately identify key information and perform global reasoning with such noisy augmentation.In this paper, motivated by the cognitive theories that humans convert raw information into various structured knowledge when tackling knowledge-intensive reasoning, we proposes a new framework, StructRAG, which can identify the optimal structure type for the task at hand, reconstruct original documents into this structured format, and infer answers based on the resulting structure. Extensive experiments across various knowledge-intensive tasks show that StructRAG achieves state-of-the-art performance, particularly excelling in challenging scenarios, demonstrating its potential as an effective solution for enhancing LLMs in complex real-world applications.

Deep Learning · Everything Else

Changlong Shi, Jinmeng Li, He Zhao, Dandan Guo, Yi Chang

In Federated Learning (FL), weighted aggregation of local models is conducted to generate a new global model, and the aggregation weights are typically normalized to 1. A recent study identifies the global weight shrinking effect in FL, indicating an enhancement in the global model’s generalization when the sum of weights (i.e., the shrinking factor) is smaller than 1, where how to learn the shrinking factor becomes crucial. However, principled approaches to this solution have not been carefully studied from the adequate consideration of privacy concerns and layer-wise distinctions. To this end, we propose a novel model aggregation strategy, Federated Learning with Adaptive Layer-wise Weight Shrinking (FedLWS), which adaptively designs the shrinking factor in a layer-wise manner and avoids optimizing the shrinking factors on a proxy dataset. We initially explored the factors affecting the shrinking factor during the training process. Then we calculate the layer-wise shrinking factors by considering the distinctions among each layer of the global model. FedLWS can be easily incorporated with various existing methods due to its flexibility. Extensive experiments under diverse scenarios demonstrate the superiority of our method over several state-of-the-art approaches, providing a promising tool for enhancing the global model in FL.

Reinforcement Learning · Planning

Yining Li, Peizhong Ju, Ness Shroff

Multi-Objective Markov Decision Processes (MO-MDPs) are receiving increasing attention, as real-world decision-making problems often involve conflicting objectives that cannot be addressed by a single-objective MDP. The Pareto front identifies the set of policies that cannot be dominated, providing a foundation for finding Pareto optimal solutions that can efficiently adapt to various preferences.However, finding the Pareto front is a highly challenging problem. Most existing methods either (i) rely on traversing the *continuous preference space*, which is impractical and results in approximations that are difficult to evaluate against the true Pareto front, or (ii) focus solely on deterministic Pareto optimal policies, from which there are no known techniques to characterize the full Pareto front. Moreover, finding the structure of the Pareto front itself remains unclear even in the context of dynamic programming, where the MDP is fully known in advance.In this work, we address the challenge of efficiently discovering the Pareto front, involving both deterministic and stochastic Pareto optimal policies.By investigating the geometric structure of the Pareto front in MO-MDPs, we uncover a key property: the Pareto front is on the boundary of a convex polytope whose vertices all correspond to deterministic policies, and neighboring vertices of the Pareto front differ by only one state-action pair of the deterministic policy, almost surely.This insight transforms the global comparison across all policies into a localized search among deterministic policies that differ by only one state-action pair, drastically reducing the complexity of searching for the exact Pareto front. We develop an efficient algorithm that identifies the vertices of the Pareto front by solving a single-objective MDP only once and then traversing the edges of the Pareto front, making it more efficient than existing methods. Furthermore, the entire Pareto front can be found in $V$ iterations, where $V$ represents the number of vertices on the Pareto front.Our empirical studies demonstrate the effectiveness of our theoretical strategy in discovering the Pareto front efficiently.

Deep Learning · Generative Models and Autoencoders

Connor Mooney, Zhongjian Wang, Jack Xin, Yifeng Yu

We establish global well-posedness and convergence of the score-based generative models (SGM) under minimal general assumptions of initial data for score estimation. For the smooth case, we start from a Lipschitz bound of the score function with optimal time length. The optimality is validated by an example whose Lipschitz constant of scores is bounded at initial but blows up in finite time. This necessitates the separation of time scales in conventional bounds for non-log-concave distributions. In contrast, our follow up analysis only relies on a local Lipschitz condition and is valid globally in time. This leads to the convergence of numerical scheme without time separation. For the non-smooth case, we show that the optimal Lipschitz bound is $O(1/t)$ in the point-wise sense for distributions supported on a compact, smooth and low-dimensional manifold with boundary.

Applications · Computer Vision

Qingxuan Wu, Zhiyang Dou, Sirui Xu, Soshi Shimada, Chen Wang, Zhengming Yu, Yuan Liu, Cheng Lin, Zeyu Cao, Taku Komura 等

Reconstructing 3D hand-face interactions with deformations from a single image is a challenging yet crucial task with broad applications in AR, VR, and gaming. The challenges stem from self-occlusions during single-view hand-face interactions, diverse spatial relationships between hands and face, complex deformations, and the ambiguity of the single-view setting. The previous state-of-the-art, Decaf, employs a global fitting optimization guided by contact and deformation estimation networks trained on studio-collected data with 3D annotations. However, Decaf suffers from a time-consuming optimization process and limited generalization capability due to its reliance on 3D annotations of hand-face interaction data. To address these issues, we present DICE, the first end-to-end method for Deformation-aware hand-face Interaction reCovEry from a single image. DICE estimates the poses of hands and faces, contacts, and deformations simultaneously using a Transformer-based architecture. It features disentangling the regression of local deformation fields and global mesh vertex locations into two network branches, enhancing deformation and contact estimation for precise and robust hand-face mesh recovery. To improve generalizability, we propose a weakly-supervised training approach that augments the training set using in-the-wild images without 3D ground-truth annotations, employing the depths of 2D keypoints estimated by off-the-shelf models and adversarial priors of poses for supervision. Our experiments demonstrate that DICE achieves state-of-the-art performance on a standard benchmark and in-the- wild data in terms of accuracy and physical plausibility. Additionally, our method operates at an interactive rate (20 fps) on an Nvidia 4090 GPU, whereas Decaf requires more than 15 seconds for a single image. The code will be available at: https://github.com/Qingxuan-Wu/DICE.

Applications · Neuroscience, Cognitive Science

Jenelle Feather, David Lipshutz, Sarah Harvey, Alex Williams, Eero Simoncelli

Image representations (artificial or biological) are often compared in terms of their global geometric structure; however, representations with similar global structure can have strikingly different local geometries. Here, we propose a framework for comparing a set of image representations in terms of their local geometries. We quantify the local geometry of a representation using the Fisher information matrix, a standard statistical tool for characterizing the sensitivity to local stimulus distortions, and use this as a substrate for a metric on the local geometry in the vicinity of a base image. This metric may then be used to optimally differentiate a set of models, by finding a pair of "principal distortions" that maximize the variance of the models under this metric. As an example, we use this framework to compare a set of simple models of the early visual system, identifying a novel set of image distortions that allow immediate comparison of the models by visual inspection. In a second example, we apply our method to a set of deep neural network models and reveal differences in the local geometry that arise due to architecture and training types. These examples demonstrate how our framework can be used to probe for informative differences in local sensitivities between complex models, and suggest how it could be used to compare model representations with human perception.

Deep Learning · Large Language Models

Wenxuan Zhang, Philip Torr, Mohamed Elhoseiny, Adel Bibi

Fine-tuning large language models (LLMs) on human preferences, typically through reinforcement learning from human feedback (RLHF), has proven successful in enhancing their capabilities. However, ensuring the safety of LLMs during fine-tuning remains a critical concern, and mitigating the potential conflicts in safety and helpfulness is costly in RLHF. To address this issue, we propose a supervised learning framework called Bi-Factorial Preference Optimization (BFPO), which re-parameterizes a joint RLHF objective of both safety and helpfulness into a single supervised learning objective. In the supervised optimization, a labeling function is used to capture global preferences ranking to balance both safety and helpfulness. To evaluate BFPO, we develop a benchmark including comprehensive discriminative and generative tasks for helpfulness and harmlessness. The results indicate that our method significantly outperforms existing approaches in both safety and helpfulness. Moreover, BFPO eliminates the need for human prompting and annotation in LLM fine-tuning while achieving the same level of safety as methods that heavily rely on human labor, with less than 10\% of the computational resources. The training recipes and models will be released.

Deep Learning · Large Language Models

Minghui Chen, Ruinan Jin, Wenlong Deng, Yuanyuan Chen, Zhi Huang, Han Yu, Xiaoxiao Li

Recent studies highlight the promise of LLM-based prompt optimization, especially with TextGrad, which automates ``differentiation'' via texts and backpropagates textual feedback provided by LLMs. This approach facilitates training in various real-world applications that do not support numerical gradient propagation or loss calculation. It opens new avenues for optimization in decentralized, resource-constrained environments, suggesting that users of black-box LLMs (e.g., ChatGPT) could enhance components of LLM agentic systems (such as prompt optimization) through collaborative paradigms like federated learning (FL). In this paper, we systematically explore the potential and challenges of incorporating textual gradient into FL. Our contributions are fourfold.**Firstly**, we introduce a novel FL paradigm, Federated Textual Gradient (FedTextGrad), that allows FL clients to upload their locally optimized prompts derived from textual gradients, while the FL server aggregates the received prompts through text summarization. Unlike traditional FL frameworks, which are designed for numerical aggregation, FedTextGrad is specifically tailored for handling textual data, expanding the applicability of FL to a broader range of problems that lack well-defined numerical loss functions. **Secondly**, building on this design, we conduct extensive experiments to explore the feasibility of federated textual gradients. Our findings highlight the importance of properly tuning key factors (e.g., local steps) in FL training to effectively integrate textual gradients. **Thirdly**, we highlight a major challenge in federated textual gradient aggregation: retaining essential information from distributed prompt updates. Concatenation often produces prompts that exceed the LLM API’s context window, while summarization can degrade performance by generating overly condensed or complex text that lacks key context. **Last but not least**, in response to this issue, we improve the vanilla variant of FedTextGrad by providing actionable guidance to the LLM when summarizing client prompts by leveraging the Uniform Information Density principle. Such a design reduces the complexity of the aggregated global prompt, thereby better incentivizing the LLM's reasoning ability. Through this principled study, we enable the adoption of textual gradients in FL for optimizing LLMs, identify important issues, and pinpoint future directions, thereby opening up a new research area that warrants further investigation.

Social Aspects · Trustworthy Machine Learning

Fanhu Zeng, Zhen Cheng, Fei Zhu, Hongxin Wei, Xu-yao Zhang

Out-of-Distribution (OOD) detection, aiming to distinguish outliers from known categories, has gained prominence in practical scenarios. Recently, the advent of vision-language models (VLM) has heightened interest in enhancing OOD detection for VLM through few-shot tuning. However, existing methods mainly focus on optimizing global prompts, ignoring refined utilization of local information with regard to outliers. Motivated by this, we freeze global prompts and introduce Local-Prompt, a novel coarse-to-fine tuning paradigm to emphasize regional enhancement with local prompts. Our method comprises two integral components: global prompt guided negative augmentation and local prompt enhanced regional regularization. The former utilizes frozen, coarse global prompts as guiding cues to incorporate negative augmentation, thereby leveraging local outlier knowledge. The latter employs trainable local prompts and a regional regularization to capture local information effectively, aiding in outlier identification. We also propose regional-related metric to empower the enrichment of OOD detection. Moreover, since our approach explores enhancing local prompts only, it can be seamlessly integrated with trained global prompts during inference to boost the performance. Comprehensive experiments demonstrate the effectiveness and potential of our method. Notably, our method reduces average FPR95 by 5.17% against state-of-the-art method in 4-shot tuning on challenging ImageNet-1k dataset, even outperforming 16-shot results of previous methods.

Theory · Learning Theory

Zhenyu Zhu, Fanghui Liu, Volkan Cevher

This paper investigates the fundamental regression task of learning $k$ neurons (\emph{a.k.a.} teachers) from Gaussian input, using two-layer ReLU neural networks with width $m$ (\emph{a.k.a.} students) and $m, k= \mathcal{O}(1)$, trained via gradient descent under proper initialization and a small step-size. Our analysis follows a three-phase structure: \emph{alignment} after weak recovery, \emph{tangential growth}, and \emph{local convergence}, providing deeper insights into the learning dynamics of gradient descent (GD). We prove the global convergence at the rate of $\mathcal{O}(T^{-3})$ for the zero loss of excess risk. Additionally, our results show that GD automatically groups and balances student neurons, revealing an implicit bias toward achieving the minimum ``balanced'' $\ell_2$-norm in the solution. Our work extends beyond previous studies in exact-parameterization setting ($m = k = 1$, (Yehudai and Ohad, 2020)) and single-neuron setting ($m \geq k = 1$, (Xu and Du, 2023)). The key technical challenge lies in handling the interactions between multiple teachers and students during training, which we address by refining the alignment analysis in Phase 1 and introducing a new dynamic system analysis for tangential components in Phase 2. Our results pave the way for further research on optimizing neural network training dynamics and understanding implicit biases in more complex architectures.

Reinforcement Learning · Everything Else

Shicheng Liu, Minghui Zhu

Reinforcement learning (RL) faces two challenges: (1) The RL agent lacks explainability. (2) The trained RL agent is, in many cases, non-optimal and even far from optimal. To address the first challenge, explainable reinforcement learning (XRL) is proposed to explain the decision-making of the RL agent. In this paper, we demonstrate that XRL can also be used to address the second challenge, i.e., improve RL performance. Our method has two parts. The first part provides a two-level explanation for why the RL agent is not optimal by identifying the mistakes made by the RL agent. Since this explanation includes the mistakes of the RL agent, it has the potential to help correct the mistakes and thus improve RL performance. The second part formulates a constrained bi-level optimization problem to learn how to best utilize the two-level explanation to improve RL performance. In specific, the upper level learns how to use the high-level explanation to shape the reward so that the corresponding policy can maximize the cumulative ground truth reward, and the lower level learns the corresponding policy by solving a constrained RL problem formulated using the low-level explanation. We propose a novel algorithm to solve this constrained bi-level optimization problem, and theoretically guarantee that the algorithm attains global optimality. We use MuJoCo experiments to show that our method outperforms state-of-the-art baselines.

Deep Learning · Generative Models and Autoencoders

Dingdong Yang, Yizhi Wang, Konrad Schindler, Ali Mahdavi Amiri, Hao Zhang

We propose GALA, a novel representation of 3D shapes that (i) excels at capturing and reproducing complex geometry and surface details, (ii) is computationally efficient, and (iii) lends itself to 3D generative modelling with modern, diffusion-based schemes. The key idea of GALA is to exploit both the global sparsity of surfaces within a 3D volume and their local surface properties. *Sparsity* is promoted by covering only the 3D object boundaries, not empty space, with an ensemble of tree root voxels. Each voxel contains an octree to further limit storage and compute to regions that contain surfaces. *Adaptivity* is achieved by fitting one local and geometry-aware coordinate frame in each non-empty leaf node. Adjusting the orientation of the local grid, as well as the anisotropic scales of its axes, to the local surface shape greatly increases the amount of detail that can be stored in a given amount of memory, which in turn allows for quantization without loss of quality. With our optimized C++/CUDA implementation, GALA can be fitted to an object in less than 10 seconds. Moreover, the representation can efficiently be flattened and manipulated with transformer networks. We provide a cascaded generation pipeline capable of generating 3D shapes with great geometric detail. For more information, please visit our [project page](https://santisy.github.io/GALA/).

Xuan Shen, Hangyu Zheng, Yifan Gong, Zhenglun Kong, Changdi Yang, Zheng Zhan, Yushu Wu, Xue Lin, Yanzhi Wang, Pu Zhao 等

Transformer models have been widely investigated in different domains by providing long-range dependency handling and global contextual awareness, driving the development of popular AI applications such as ChatGPT, Gemini, and Alexa.State Space Models (SSMs) have emerged as strong contenders in the field of sequential modeling, challenging the dominance of Transformers. SSMs incorporate a selective mechanism that allows for dynamic parameter adjustment based on input data, enhancing their performance.However, this mechanism also comes with increasing computational complexity and bandwidth demands, posing challenges for deployment on resource-constraint mobile devices.To address these challenges without sacrificing the accuracy of the selective mechanism, we propose a sparse learning framework that integrates architecture-aware compiler optimizations. We introduce an end-to-end solution--$\mathbf{C}_4^n$ kernel sparsity, which prunes $n$ elements from every four contiguous weights, and develop a compiler-based acceleration solution to ensure execution efficiency for this sparsity on mobile devices.Based on the kernel sparsity, our framework generates optimized sparse models targeting specific sparsity or latency requirements for various model sizes. We further leverage pruned weights to compensate for the remaining weights, enhancing downstream task performance.For practical hardware acceleration, we propose $\mathbf{C}_4^n$-specific optimizations combined with a layout transformation elimination strategy. This approach mitigates inefficiencies arising from fine-grained pruning in linear layers and improves performance across other operations. Experimental results demonstrate that our method achieves superior task performance compared to other semi-structured pruning methods and achieves up-to 7$\times$ speedup compared to llama.cpp framework on mobile devices.

Optimization · Global Optimization

Depen Morwani, Itai Shapira, Nikhil Vyas, Eran Malach, Sham Kakade, Lucas Janson

Shampoo, a second-order optimization algorithm that uses a Kronecker product preconditioner, has recently received increasing attention from the machine learning community. Despite the increasing popularity of Shampoo, the theoretical foundations of its effectiveness are not well understood. The preconditioner used by Shampoo can be viewed as either an approximation of the Gauss--Newton component of the Hessian or the covariance matrix of the gradients maintained by Adagrad. Our key contribution is providing an explicit and novel connection between the optimal Kronecker product approximation of these matrices and the approximationmade by Shampoo. Our connection highlights a subtle but common misconception about Shampoo’s approximation. In particular, the square of the approximation used by the Shampoo optimizer is equivalent to a single step of the poweriteration algorithm for computing the aforementioned optimal Kronecker product approximation. Across a variety of datasets and architectures we empiricallydemonstrate that this is close to the optimal Kronecker product approximation. We also study the impact of batch gradients and empirical Fisher on the quality of Hessian approximation. Our findings not only advance the theoretical understanding of Shampoo but also illuminate potential pathways for enhancing its practical performance.

Optimization · Global Optimization

Nikhil Vyas, Depen Morwani, Rosie Zhao, Itai Shapira, David Brandfonbrener, Lucas Janson, Sham Kakade

There is growing evidence of the effectiveness of Shampoo, a higher-order preconditioning method, over Adam in deep learning optimization tasks. However, Shampoo's drawbacks include additional hyperparameters and computational overhead when compared to Adam, which only updates running averages of first- and second-moment quantities. This work establishes a formal connection between Shampoo (implemented with the 1/2 power) and Adafactor --- a memory-efficient approximation of Adam --- showing that Shampoo is equivalent to running Adafactor in the eigenbasis of Shampoo's preconditioner. This insight leads to the design of a simpler and computationally efficient algorithm: **S**hampo**O** with **A**dam in the **P**reconditioner's eigenbasis (SOAP).With regards to improving Shampoo's computational efficiency, the most straightforward approach would be to simply compute Shampoo's eigendecomposition less frequently. Unfortunately, as our empirical results show, this leads to performance degradation that worsens with this frequency. SOAP mitigates this degradation by continually updating the running average of the second moment, just as Adam does, but in the current (slowly changing) coordinate basis. Furthermore, since SOAP is equivalent to running Adam in a rotated space, it introduces only one additional hyperparameter (the preconditioning frequency) compared to Adam. We empirically evaluate SOAP on language model pre-training with 360m and 660m sized models. In the large batch regime, SOAP reduces the number of iterations by over 40\% and wall clock time by over 35\% compared to AdamW, with approximately 20\% improvements in both metrics compared to Shampoo. An implementation of SOAP is available at https://github.com/nikhilvyas/SOAP.