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We study the convergence rate of first-order methods for rectangular matrix factorization, which is a canonical nonconvex optimization problem. Specifically, given a rank-$r$ matrix $\mathbf{A}\in\mathbb{R}^{m\times n}$, we prove that gradient descent (GD) can find a pair of $\epsilon$-optimal solutions $\mathbf{X}_T\in\mathbb{R}^{m\times d}$ and $\mathbf{Y}_T\in\mathbb{R}^{n\times d}$, where $d\geq r$, satisfying $\lVert\mathbf{X}_T\mathbf{Y}_T^\top-\mathbf{A}\rVert_\mathrm{F}\leq\epsilon\lVert\mathbf{A}\rVert_\mathrm{F}$ in $T=O(\kappa^2\log\frac{1}{\epsilon})$ iterations with high probability, where $\kappa$ denotes the condition number of $\mathbf{A}$. Furthermore, we prove that Nesterov's accelerated gradient (NAG) attains an iteration complexity of $O(\kappa\log\frac{1}{\epsilon})$, which is the best-known bound of first-order methods for rectangular matrix factorization. Different from small balanced random initialization in the existing literature, we adopt an unbalanced initialization, where $\mathbf{X}_0$ is large and $\mathbf{Y}_0$ is $0$. Moreover, our initialization and analysis can be further extended to linear neural networks, where we prove that NAG can also attain an accelerated linear convergence rate. In particular, we only require the width of the network to be greater than or equal to the rank of the output label matrix. In contrast, previous results achieving the same rate require excessive widths that additionally depend on the condition number and the rank of the input data matrix., Comment: 30 pages (checklist included), fix typos

Large language models (LLMs) have demonstrated remarkable performance across various real-world tasks. However, they often struggle to fully comprehend and effectively utilize their input contexts, resulting in responses that are unfaithful or hallucinated. This difficulty increases for contexts that are long or contain distracting information, which can divert LLMs from fully capturing essential evidence. To address this issue, many works use prompting to help LLMs utilize contextual information more faithfully. For instance, iterative prompting highlights key information in two steps that first ask the LLM to identify important pieces of context and then derive answers accordingly. However, prompting methods are constrained to highlighting key information implicitly in token space, which is often insufficient to fully steer the model's attention. To improve model faithfulness more reliably, we propose AutoPASTA, a method that automatically identifies key contextual information and explicitly highlights it by steering an LLM's attention scores. Like prompting, AutoPASTA is applied at inference time and does not require changing any model parameters. Our experiments on open-book QA demonstrate that AutoPASTA effectively enables models to grasp essential contextual information, leading to substantially improved model faithfulness and performance, e.g., an average improvement of 7.95% for LLAMA3-70B-Instruct. Code will be publicly available at https://github.com/QingruZhang/AutoPASTA ., Comment: 12 pages, 4 figures

Instruction fine-tuning (IFT) elicits instruction following capabilities and steers the behavior of large language models (LLMs) via supervised learning. However, existing models trained on open-source IFT datasets only have the ability to follow instructions from users, and often fail to follow complex role and rules specified by developers, a.k.a. system prompts. The ability to follow these roles and rules is essential for deployment, as it ensures that the model safely interacts with users within developer defined guidelines. To improve such role and rule following ability, we propose \model, an automated data generation pipeline that generates diverse roles and rules from existing IFT instructions, along with corresponding responses. This data can then be used to train models that follow complex system prompts. The models are evaluated on our newly created benchmarks for role and rule following ability, as well as standard instruction-following benchmarks and general NLP tasks. Our framework significantly improves role and rule following capability in LLMs, as evidenced by over 25% increase in pass-rate on rule adherence, i.e. following all requirements, in our experiments with the Alpaca and Ultrachat datasets. Moreover, our models achieves this increase without any regression on popular instruction following benchmarks.

Reinforcement learning from human feedback (RLHF) provides a principled framework for aligning AI systems with human preference data. For various reasons, e.g., personal bias, context ambiguity, lack of training, etc, human annotators may give incorrect or inconsistent preference labels. To tackle this challenge, we propose a robust RLHF approach -- $R^3M$, which models the potentially corrupted preference label as sparse outliers. Accordingly, we formulate the robust reward learning as an $\ell_1$-regularized maximum likelihood estimation problem. Computationally, we develop an efficient alternating optimization algorithm, which only incurs negligible computational overhead compared with the standard RLHF approach. Theoretically, we prove that under proper regularity conditions, $R^3M$ can consistently learn the underlying reward and identify outliers, provided that the number of outlier labels scales sublinearly with the preference sample size. Furthermore, we remark that $R^3M$ is versatile and can be extended to various preference optimization methods, including direct preference optimization (DPO). Our experiments on robotic control and natural language generation with large language models (LLMs) show that $R^3M$ improves robustness of the reward against several types of perturbations to the preference data., Comment: 22 pages, 7 figures

Pre-trained language models, trained on large-scale corpora, demonstrate strong generalizability across various NLP tasks. Fine-tuning these models for specific tasks typically involves updating all parameters, which is resource-intensive. Parameter-efficient fine-tuning (PEFT) methods, such as the popular LoRA family, introduce low-rank matrices to learn only a few parameters efficiently. However, during inference, the product of these matrices updates all pre-trained parameters, complicating tasks like knowledge editing that require selective updates. We propose a novel PEFT method, which conducts \textbf{r}ow and c\textbf{o}lumn-wise spar\textbf{se} \textbf{lo}w-\textbf{r}ank \textbf{a}daptation (RoseLoRA), to address this challenge. RoseLoRA identifies and updates only the most important parameters for a specific task, maintaining efficiency while preserving other model knowledge. By adding a sparsity constraint on the product of low-rank matrices and converting it to row and column-wise sparsity, we ensure efficient and precise model updates. Our theoretical analysis guarantees the lower bound of the sparsity with respective to the matrix product. Extensive experiments on five benchmarks across twenty datasets demonstrate that RoseLoRA outperforms baselines in both general fine-tuning and knowledge editing tasks., Comment: EMNLP 2024 main

Reinforcement learning from human feedback (RLHF) is a prevalent approach to align AI systems with human values by learning rewards from human preference data. Due to various reasons, however, such data typically takes the form of rankings over pairs of trajectory segments, which fails to capture the varying strengths of preferences across different pairs. In this paper, we propose a novel adaptive preference loss, underpinned by distributionally robust optimization (DRO), designed to address this uncertainty in preference strength. By incorporating an adaptive scaling parameter into the loss for each pair, our method increases the flexibility of the reward function. Specifically, it assigns small scaling parameters to pairs with ambiguous preferences, leading to more comparable rewards, and large scaling parameters to those with clear preferences for more distinct rewards. Computationally, our proposed loss function is strictly convex and univariate with respect to each scaling parameter, enabling its efficient optimization through a simple second-order algorithm. Our method is versatile and can be readily adapted to various preference optimization frameworks, including direct preference optimization (DPO). Our experiments with robotic control and natural language generation with large language models (LLMs) show that our method not only improves policy performance but also aligns reward function selection more closely with policy optimization, simplifying the hyperparameter tuning process.

The temperature parameter plays a profound role during training and/or inference with large foundation models (LFMs) such as large language models (LLMs) and CLIP models. Particularly, it adjusts the logits in the softmax function in LLMs, which is crucial for next token generation, and it scales the similarities in the contrastive loss for training CLIP models. A significant question remains: Is it viable to learn a neural network to predict a personalized temperature of any input data for enhancing LFMs"? In this paper, we present a principled framework for learning a small yet generalizable temperature prediction network (TempNet) to improve LFMs. Our solution is composed of a novel learning framework with a robust loss underpinned by constrained distributionally robust optimization (DRO), and a properly designed TempNet with theoretical inspiration. TempNet can be trained together with a large foundation model from scratch or learned separately given a pretrained foundation model. It is not only useful for predicting personalized temperature to promote the training of LFMs but also generalizable and transferable to new tasks. Our experiments on LLMs and CLIP models demonstrate that TempNet greatly improves the performance of existing solutions or models, e.g. Table 1. The code to reproduce the experimental results in this paper can be found at https://github.com/zhqiu/TempNet., Comment: 41 pages, 10 figures, accepted by ICML2024

In modern decentralized applications, ensuring communication efficiency and privacy for the users are the key challenges. In order to train machine-learning models, the algorithm has to communicate to the data center and sample data for its gradient computation, thus exposing the data and increasing the communication cost. This gives rise to the need for a decentralized optimization algorithm that is communication-efficient and minimizes the number of gradient computations. To this end, we propose the primal-dual sliding with conditional gradient sliding framework, which is communication-efficient and achieves an $\varepsilon$-approximate solution with the optimal gradient complexity of $O(1/\sqrt{\varepsilon}+\sigma^2/{\varepsilon^2})$ and $O(\log(1/\varepsilon)+\sigma^2/\varepsilon)$ for the convex and strongly convex setting respectively and an LO (Linear Optimization) complexity of $O(1/\varepsilon^2)$ for both settings given a stochastic gradient oracle with variance $\sigma^2$. Compared with the prior work \cite{wai-fw-2017}, our framework relaxes the assumption of the optimal solution being a strict interior point of the feasible set and enjoys wider applicability for large-scale training using a stochastic gradient oracle. We also demonstrate the efficiency of our algorithms with various numerical experiments.

Key-value (KV) caching has become the de-facto to accelerate generation speed for large language models (LLMs) inference. However, the growing cache demand with increasing sequence length has transformed LLM inference to be a memory bound problem, significantly constraining the system throughput. Existing methods rely on dropping unimportant tokens or quantizing all entries uniformly. Such methods, however, often incur high approximation errors to represent the compressed matrices. The autoregressive decoding process further compounds the error of each step, resulting in critical deviation in model generation and deterioration of performance. To tackle this challenge, we propose GEAR, an efficient KV cache compression framework that achieves near-lossless high-ratio compression. GEAR first applies quantization to majority of entries of similar magnitudes to ultra-low precision. It then employs a low rank matrix to approximate the quantization error, and a sparse matrix to remedy individual errors from outlier entries. By adeptly integrating three techniques, GEAR is able to fully exploit their synergistic potentials. Our experiments demonstrate that compared to alternatives, GEAR achieves near-lossless 4-bit KV cache compression with up to 2.38x throughput improvement, while reducing peak-memory size up to 2.29x. Our code is publicly available at https://github.com/HaoKang-Timmy/GEAR.

Retrieval-augmented Large Language Models (LLMs) offer substantial benefits in enhancing performance across knowledge-intensive scenarios. However, these methods often face challenges with complex inputs and encounter difficulties due to noisy knowledge retrieval, notably hindering model effectiveness. To address this issue, we introduce BlendFilter, a novel approach that elevates retrieval-augmented LLMs by integrating query generation blending with knowledge filtering. BlendFilter proposes the blending process through its query generation method, which integrates both external and internal knowledge augmentation with the original query, ensuring comprehensive information gathering. Additionally, our distinctive knowledge filtering module capitalizes on the intrinsic capabilities of the LLM, effectively eliminating extraneous data. We conduct extensive experiments on three open-domain question answering benchmarks, and the findings clearly indicate that our innovative BlendFilter surpasses state-of-the-art baselines significantly., Comment: EMNLP 2024 main

Recent works have shown that by curating high quality and diverse instruction tuning datasets, we can significantly improve instruction-following capabilities. However, creating such datasets is difficult and most works rely on manual curation or proprietary language models. Automatic data curation is difficult as it is still not clear how we can define diversity for instruction tuning, how diversity and quality depend on one other, and how we can optimize dataset quality and diversity. To resolve these issue, we propose a new algorithm, Quality-Diversity Instruction Tuning (QDIT). QDIT provides a simple method to simultaneously control dataset diversity and quality, allowing us to conduct an in-depth study on the effect of diversity and quality on instruction tuning performance. From this study we draw two key insights (1) there is a natural tradeoff between data diversity and quality and (2) increasing data diversity significantly improves the worst case instruction following performance, therefore improving robustness. We validate the performance of QDIT on several large scale instruction tuning datasets, where we find it can substantially improve worst and average case performance compared to quality-driven data selection., Comment: 22 pages, 18 figures

In human-written articles, we often leverage the subtleties of text style, such as bold and italics, to guide the attention of readers. These textual emphases are vital for the readers to grasp the conveyed information. When interacting with large language models (LLMs), we have a similar need -- steering the model to pay closer attention to user-specified information, e.g., an instruction. Existing methods, however, are constrained to process plain text and do not support such a mechanism. This motivates us to introduce PASTA -- Post-hoc Attention STeering Approach, a method that allows LLMs to read text with user-specified emphasis marks. To this end, PASTA identifies a small subset of attention heads and applies precise attention reweighting on them, directing the model attention to user-specified parts. Like prompting, PASTA is applied at inference time and does not require changing any model parameters. Experiments demonstrate that PASTA can substantially enhance an LLM's ability to follow user instructions or integrate new knowledge from user inputs, leading to a significant performance improvement on a variety of tasks, e.g., an average accuracy improvement of 22% for LLAMA-7B. Our code is publicly available at https://github.com/QingruZhang/PASTA ., Comment: The 12th International Conference on Learning Representations (ICLR 2024)

ReParameterization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. However, recent studies have revealed that, when applied to long-term reinforcement learning problems, model-based RP PGMs may experience chaotic and non-smooth optimization landscapes with exploding gradient variance, which leads to slow convergence. This is in contrast to the conventional belief that reparameterization methods have low gradient estimation variance in problems such as training deep generative models. To comprehend this phenomenon, we conduct a theoretical examination of model-based RP PGMs and search for solutions to the optimization difficulties. Specifically, we analyze the convergence of the model-based RP PGMs and pinpoint the smoothness of function approximators as a major factor that affects the quality of gradient estimation. Based on our analysis, we propose a spectral normalization method to mitigate the exploding variance issue caused by long model unrolls. Our experimental results demonstrate that proper normalization significantly reduces the gradient variance of model-based RP PGMs. As a result, the performance of the proposed method is comparable or superior to other gradient estimators, such as the Likelihood Ratio (LR) gradient estimator. Our code is available at https://github.com/agentification/RP_PGM., Comment: Published at NeurIPS 2023

Large learning rates, when applied to gradient descent for nonconvex optimization, yield various implicit biases including the edge of stability (Cohen et al., 2021), balancing (Wang et al., 2022), and catapult (Lewkowycz et al., 2020). These phenomena cannot be well explained by classical optimization theory. Though significant theoretical progress has been made in understanding these implicit biases, it remains unclear for which objective functions would they be more likely. This paper provides an initial step in answering this question and also shows that these implicit biases are in fact various tips of the same iceberg. To establish these results, we develop a global convergence theory under large learning rates, for a family of nonconvex functions without globally Lipschitz continuous gradient, which was typically assumed in existing convergence analysis. Specifically, these phenomena are more likely to occur when the optimization objective function has good regularity. This regularity, together with gradient descent using a large learning rate that favors flatter regions, results in these nontrivial dynamical behaviors. Another corollary is the first non-asymptotic convergence rate bound for large-learning-rate gradient descent optimization of nonconvex functions. Although our theory only applies to specific functions so far, the possibility of extrapolating it to neural networks is also experimentally validated, for which different choices of loss, activation functions, and other techniques such as batch normalization can all affect regularity significantly and lead to very different training dynamics.

Transformer Hawkes process models have shown to be successful in modeling event sequence data. However, most of the existing training methods rely on maximizing the likelihood of event sequences, which involves calculating some intractable integral. Moreover, the existing methods fail to provide uncertainty quantification for model predictions, e.g., confidence intervals for the predicted event's arrival time. To address these issues, we propose SMURF-THP, a score-based method for learning Transformer Hawkes process and quantifying prediction uncertainty. Specifically, SMURF-THP learns the score function of events' arrival time based on a score-matching objective that avoids the intractable computation. With such a learned score function, we can sample arrival time of events from the predictive distribution. This naturally allows for the quantification of uncertainty by computing confidence intervals over the generated samples. We conduct extensive experiments in both event type prediction and uncertainty quantification of arrival time. In all the experiments, SMURF-THP outperforms existing likelihood-based methods in confidence calibration while exhibiting comparable prediction accuracy.

Spatio-temporal point processes (STPPs) are potent mathematical tools for modeling and predicting events with both temporal and spatial features. Despite their versatility, most existing methods for learning STPPs either assume a restricted form of the spatio-temporal distribution, or suffer from inaccurate approximations of the intractable integral in the likelihood training objective. These issues typically arise from the normalization term of the probability density function. Moreover, current techniques fail to provide uncertainty quantification for model predictions, such as confidence intervals for the predicted event's arrival time and confidence regions for the event's location, which is crucial given the considerable randomness of the data. To tackle these challenges, we introduce SMASH: a Score MAtching-based pSeudolikeliHood estimator for learning marked STPPs with uncertainty quantification. Specifically, our framework adopts a normalization-free objective by estimating the pseudolikelihood of marked STPPs through score-matching and offers uncertainty quantification for the predicted event time, location and mark by computing confidence regions over the generated samples. The superior performance of our proposed framework is demonstrated through extensive experiments in both event prediction and uncertainty quantification.

Pretrained transformer models have demonstrated remarkable performance across various natural language processing tasks. These models leverage the attention mechanism to capture long- and short-range dependencies in the sequence. However, the (full) attention mechanism incurs high computational cost - quadratic in the sequence length, which is not affordable in tasks with long sequences, e.g., inputs with 8k tokens. Although sparse attention can be used to improve computational efficiency, as suggested in existing work, it has limited modeling capacity and often fails to capture complicated dependencies in long sequences. To tackle this challenge, we propose MASFormer, an easy-to-implement transformer variant with Mixed Attention Spans. Specifically, MASFormer is equipped with full attention to capture long-range dependencies, but only at a small number of layers. For the remaining layers, MASformer only employs sparse attention to capture short-range dependencies. Our experiments on natural language modeling and generation tasks show that a decoder-only MASFormer model of 1.3B parameters can achieve competitive performance to vanilla transformers with full attention while significantly reducing computational cost (up to 75%). Additionally, we investigate the effectiveness of continual training with long sequence data and how sequence length impacts downstream generation performance, which may be of independent interest., Comment: The 2023 Conference on Empirical Methods in Natural Language Processing (EMNLP 2023 Findings)

Multi-Agent Reinforcement Learning (MARL) has shown promising results across several domains. Despite this promise, MARL policies often lack robustness and are therefore sensitive to small changes in their environment. This presents a serious concern for the real world deployment of MARL algorithms, where the testing environment may slightly differ from the training environment. In this work we show that we can gain robustness by controlling a policy's Lipschitz constant, and under mild conditions, establish the existence of a Lipschitz and close-to-optimal policy. Based on these insights, we propose a new robust MARL framework, ERNIE, that promotes the Lipschitz continuity of the policies with respect to the state observations and actions by adversarial regularization. The ERNIE framework provides robustness against noisy observations, changing transition dynamics, and malicious actions of agents. However, ERNIE's adversarial regularization may introduce some training instability. To reduce this instability, we reformulate adversarial regularization as a Stackelberg game. We demonstrate the effectiveness of the proposed framework with extensive experiments in traffic light control and particle environments. In addition, we extend ERNIE to mean-field MARL with a formulation based on distributionally robust optimization that outperforms its non-robust counterpart and is of independent interest. Our code is available at https://github.com/abukharin3/ERNIE., Comment: 33 pages, 10 figures

Quantization is an indispensable technique for serving Large Language Models (LLMs) and has recently found its way into LoRA fine-tuning. In this work we focus on the scenario where quantization and LoRA fine-tuning are applied together on a pre-trained model. In such cases it is common to observe a consistent gap in the performance on downstream tasks between full fine-tuning and quantization plus LoRA fine-tuning approach. In response, we propose LoftQ (LoRA-Fine-Tuning-aware Quantization), a novel quantization framework that simultaneously quantizes an LLM and finds a proper low-rank initialization for LoRA fine-tuning. Such an initialization alleviates the discrepancy between the quantized and full-precision model and significantly improves the generalization in downstream tasks. We evaluate our method on natural language understanding, question answering, summarization, and natural language generation tasks. Experiments show that our method is highly effective and outperforms existing quantization methods, especially in the challenging 2-bit and 2/4-bit mixed precision regimes. We will release our code.

Pre-trained multimodal foundation models have demonstrated remarkable generalizability but pose challenges for deployment due to their large sizes. One effective approach to reducing their sizes is layerwise distillation, wherein small student models are trained to match the hidden representations of large teacher models at each layer. Motivated by our observation that certain architecture components, referred to as modules, contribute more significantly to the student's performance than others, we propose to track the contributions of individual modules by recording the loss decrement after distillation each module and choose the module with a greater contribution to distill more frequently. Such an approach can be naturally formulated as a multi-armed bandit (MAB) problem, where modules and loss decrements are considered as arms and rewards, respectively. We then develop a modified-Thompson sampling algorithm named OPTIMA to address the nonstationarity of module contributions resulting from model updating. Specifically, we leverage the observed contributions in recent history to estimate the changing contribution of each module and select modules based on these estimations to maximize the cumulative contribution. We evaluate the effectiveness of OPTIMA through distillation experiments on various multimodal understanding and image captioning tasks, using the CoCa-Large model (Yu et al., 2022) as the teacher model.

Policy gradient methods equipped with deep neural networks have achieved great success in solving high-dimensional reinforcement learning (RL) problems. However, current analyses cannot explain why they are resistant to the curse of dimensionality. In this work, we study the sample complexity of the neural policy mirror descent (NPMD) algorithm with deep convolutional neural networks (CNN). Motivated by the empirical observation that many high-dimensional environments have state spaces possessing low-dimensional structures, such as those taking images as states, we consider the state space to be a $d$-dimensional manifold embedded in the $D$-dimensional Euclidean space with intrinsic dimension $d\ll D$. We show that in each iteration of NPMD, both the value function and the policy can be well approximated by CNNs. The approximation errors are controlled by the size of the networks, and the smoothness of the previous networks can be inherited. As a result, by properly choosing the network size and hyperparameters, NPMD can find an $\epsilon$-optimal policy with $\widetilde{O}(\epsilon^{-\frac{d}{\alpha}-2})$ samples in expectation, where $\alpha\in(0,1]$ indicates the smoothness of environment. Compared to previous work, our result exhibits that NPMD can leverage the low-dimensional structure of state space to escape from the curse of dimensionality, explaining the efficacy of deep policy gradient algorithms.

We consider the linear discriminant analysis problem in the high-dimensional settings. In this work, we propose PANDA(PivotAl liNear Discriminant Analysis), a tuning-insensitive method in the sense that it requires very little effort to tune the parameters. Moreover, we prove that PANDA achieves the optimal convergence rate in terms of both the estimation error and misclassification rate. Our theoretical results are backed up by thorough numerical studies using both simulated and real datasets. In comparison with the existing methods, we observe that our proposed PANDA yields equal or better performance, and requires substantially less effort in parameter tuning.

Reward design is a fundamental, yet challenging aspect of reinforcement learning (RL). Researchers typically utilize feedback signals from the environment to handcraft a reward function, but this process is not always effective due to the varying scale and intricate dependencies of the feedback signals. This paper shows by exploiting certain structures, one can ease the reward design process. Specifically, we propose a hierarchical reward modeling framework -- HERON for scenarios: (I) The feedback signals naturally present hierarchy; (II) The reward is sparse, but with less important surrogate feedback to help policy learning. Both scenarios allow us to design a hierarchical decision tree induced by the importance ranking of the feedback signals to compare RL trajectories. With such preference data, we can then train a reward model for policy learning. We apply HERON to several RL applications, and we find that our framework can not only train high performing agents on a variety of difficult tasks, but also provide additional benefits such as improved sample efficiency and robustness. Our code is available at \url{https://github.com/abukharin3/HERON}., Comment: 28 Pages, 14 figures

For a real-world decision-making problem, the reward function often needs to be engineered or learned. A popular approach is to utilize human feedback to learn a reward function for training. The most straightforward way to do so is to ask humans to provide ratings for state-action pairs on an absolute scale and take these ratings as reward samples directly. Another popular way is to ask humans to rank a small set of state-action pairs by preference and learn a reward function from these preference data. Recently, preference-based methods have demonstrated substantial success in empirical applications such as InstructGPT. In this work, we develop a theoretical comparison between these human feedback approaches in offline contextual bandits and show how human bias and uncertainty in feedback modelings can affect the theoretical guarantees of these approaches. Through this, our results seek to provide a theoretical explanation for the empirical successes of preference-based methods from a modeling perspective.

Convolutional residual neural networks (ConvResNets), though overparameterized, can achieve remarkable prediction performance in practice, which cannot be well explained by conventional wisdom. To bridge this gap, we study the performance of ConvResNeXts, which cover ConvResNets as a special case, trained with weight decay from the perspective of nonparametric classification. Our analysis allows for infinitely many building blocks in ConvResNeXts, and shows that weight decay implicitly enforces sparsity on these blocks. Specifically, we consider a smooth target function supported on a low-dimensional manifold, then prove that ConvResNeXts can adapt to the function smoothness and low-dimensional structures and efficiently learn the function without suffering from the curse of dimensionality. Our findings partially justify the advantage of overparameterized ConvResNeXts over conventional machine learning models., Comment: 20 pages, 1 figure

Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data structures. In real world applications, such an assumption of data lying exactly on a low dimensional manifold is stringent. This paper introduces a relaxed assumption that the input data are concentrated around a subset of $\mathbb{R}^d$ denoted by $\mathcal{S}$, and the intrinsic dimension of $\mathcal{S}$ can be characterized by a new complexity notation -- effective Minkowski dimension. We prove that, the sample complexity of deep nonparametric regression only depends on the effective Minkowski dimension of $\mathcal{S}$ denoted by $p$. We further illustrate our theoretical findings by considering nonparametric regression with an anisotropic Gaussian random design $N(0,\Sigma)$, where $\Sigma$ is full rank. When the eigenvalues of $\Sigma$ have an exponential or polynomial decay, the effective Minkowski dimension of such an Gaussian random design is $p=\mathcal{O}(\sqrt{\log n})$ or $p=\mathcal{O}(n^\gamma)$, respectively, where $n$ is the sample size and $\gamma\in(0,1)$ is a small constant depending on the polynomial decay rate. Our theory shows that, when the manifold assumption does not hold, deep neural networks can still adapt to the effective Minkowski dimension of the data, and circumvent the curse of the ambient dimensionality for moderate sample sizes.

Transformer models have achieved remarkable results in various natural language tasks, but they are often prohibitively large, requiring massive memories and computational resources. To reduce the size and complexity of these models, we propose LoSparse (Low-Rank and Sparse approximation), a novel model compression technique that approximates a weight matrix by the sum of a low-rank matrix and a sparse matrix. Our method combines the advantages of both low-rank approximations and pruning, while avoiding their limitations. Low-rank approximation compresses the coherent and expressive parts in neurons, while pruning removes the incoherent and non-expressive parts in neurons. Pruning enhances the diversity of low-rank approximations, and low-rank approximation prevents pruning from losing too many expressive neurons. We evaluate our method on natural language understanding, question answering, and natural language generation tasks. We show that it significantly outperforms existing compression methods.

Machine learning force fields (MLFF) have been proposed to accelerate molecular dynamics (MD) simulation, which finds widespread applications in chemistry and biomedical research. Even for the most data-efficient MLFFs, reaching chemical accuracy can require hundreds of frames of force and energy labels generated by expensive quantum mechanical algorithms, which may scale as $O(n^3)$ to $O(n^7)$, with $n$ proportional to the number of basis functions. To address this issue, we propose a multi-stage computational framework -- ASTEROID, which lowers the data cost of MLFFs by leveraging a combination of cheap inaccurate data and expensive accurate data. The motivation behind ASTEROID is that inaccurate data, though incurring large bias, can help capture the sophisticated structures of the underlying force field. Therefore, we first train a MLFF model on a large amount of inaccurate training data, employing a bias-aware loss function to prevent the model from overfitting tahe potential bias of this data. We then fine-tune the obtained model using a small amount of accurate training data, which preserves the knowledge learned from the inaccurate training data while significantly improving the model's accuracy. Moreover, we propose a variant of ASTEROID based on score matching for the setting where the inaccurate training data are unlabeled. Extensive experiments on MD datasets and downstream tasks validate the efficacy of ASTEROID. Our code and data are available at https://github.com/abukharin3/asteroid.

Fine-tuning large pre-trained language models on downstream tasks has become an important paradigm in NLP. However, common practice fine-tunes all of the parameters in a pre-trained model, which becomes prohibitive when a large number of downstream tasks are present. Therefore, many fine-tuning methods are proposed to learn incremental updates of pre-trained weights in a parameter efficient way, e.g., low-rank increments. These methods often evenly distribute the budget of incremental updates across all pre-trained weight matrices, and overlook the varying importance of different weight parameters. As a consequence, the fine-tuning performance is suboptimal. To bridge this gap, we propose AdaLoRA, which adaptively allocates the parameter budget among weight matrices according to their importance score. In particular, AdaLoRA parameterizes the incremental updates in the form of singular value decomposition. Such a novel approach allows us to effectively prune the singular values of unimportant updates, which is essentially to reduce their parameter budget but circumvent intensive exact SVD computations. We conduct extensive experiments with several pre-trained models on natural language processing, question answering, and natural language generation to validate the effectiveness of AdaLoRA. Results demonstrate that AdaLoRA manifests notable improvement over baselines, especially in the low budget settings. Our code is publicly available at https://github.com/QingruZhang/AdaLoRA ., Comment: The 11th International Conference on Learning Representations (ICLR 2023)

Generative networks have experienced great empirical successes in distribution learning. Many existing experiments have demonstrated that generative networks can generate high-dimensional complex data from a low-dimensional easy-to-sample distribution. However, this phenomenon can not be justified by existing theories. The widely held manifold hypothesis speculates that real-world data sets, such as natural images and signals, exhibit low-dimensional geometric structures. In this paper, we take such low-dimensional data structures into consideration by assuming that data distributions are supported on a low-dimensional manifold. We prove statistical guarantees of generative networks under the Wasserstein-1 loss. We show that the Wasserstein-1 loss converges to zero at a fast rate depending on the intrinsic dimension instead of the ambient data dimension. Our theory leverages the low-dimensional geometric structures in data sets and justifies the practical power of generative networks. We require no smoothness assumptions on the data distribution which is desirable in practice.

Knowledge distillation has been shown to be a powerful model compression approach to facilitate the deployment of pre-trained language models in practice. This paper focuses on task-agnostic distillation. It produces a compact pre-trained model that can be easily fine-tuned on various tasks with small computational costs and memory footprints. Despite the practical benefits, task-agnostic distillation is challenging. Since the teacher model has a significantly larger capacity and stronger representation power than the student model, it is very difficult for the student to produce predictions that match the teacher's over a massive amount of open-domain training data. Such a large prediction discrepancy often diminishes the benefits of knowledge distillation. To address this challenge, we propose Homotopic Distillation (HomoDistil), a novel task-agnostic distillation approach equipped with iterative pruning. Specifically, we initialize the student model from the teacher model, and iteratively prune the student's neurons until the target width is reached. Such an approach maintains a small discrepancy between the teacher's and student's predictions throughout the distillation process, which ensures the effectiveness of knowledge transfer. Extensive experiments demonstrate that HomoDistil achieves significant improvements on existing baselines.

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality., Comment: 52 pages, 4 figures

Transformer models have achieved superior performance in various natural language processing tasks. However, the quadratic computational cost of the attention mechanism limits its practicality for long sequences. There are existing attention variants that improve the computational efficiency, but they have limited ability to effectively compute global information. In parallel to Transformer models, state space models (SSMs) are tailored for long sequences, but they are not flexible enough to capture complicated local information. We propose SPADE, short for $\underline{\textbf{S}}$tate s$\underline{\textbf{P}}$ace $\underline{\textbf{A}}$ugmente$\underline{\textbf{D}}$ Transform$\underline{\textbf{E}}$r. Specifically, we augment a SSM into the bottom layer of SPADE, and we employ efficient local attention methods for the other layers. The SSM augments global information, which complements the lack of long-range dependency issue in local attention methods. Experimental results on the Long Range Arena benchmark and language modeling tasks demonstrate the effectiveness of the proposed method. To further demonstrate the scalability of SPADE, we pre-train large encoder-decoder models and present fine-tuning results on natural language understanding and natural language generation tasks.

Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of the label shift, e.g., balancing the training data. However, these methods often consider the underparametrized regime, where the sample size is much larger than the data dimension. The research under the overparametrized regime is very limited. To bridge this gap, we propose a new asymptotic analysis of the Fisher Linear Discriminant classifier for binary classification with label shift. Specifically, we prove that there exists a phase transition phenomenon: Under certain overparametrized regime, the classifier trained using imbalanced data outperforms the counterpart with reduced balanced data. Moreover, we investigate the impact of regularization to the label shift: The aforementioned phase transition vanishes as the regularization becomes strong.

Layer-wise distillation is a powerful tool to compress large models (i.e. teacher models) into small ones (i.e., student models). The student distills knowledge from the teacher by mimicking the hidden representations of the teacher at every intermediate layer. However, layer-wise distillation is difficult. Since the student has a smaller model capacity than the teacher, it is often under-fitted. Furthermore, the hidden representations of the teacher contain redundant information that the student does not necessarily need for the target task's learning. To address these challenges, we propose a novel Task-aware layEr-wise Distillation (TED). TED designs task-aware filters to align the hidden representations of the student and the teacher at each layer. The filters select the knowledge that is useful for the target task from the hidden representations. As such, TED reduces the knowledge gap between the two models and helps the student to fit better on the target task. We evaluate TED in two scenarios: continual pre-training and fine-tuning. TED demonstrates significant and consistent improvements over existing distillation methods in both scenarios. Code is available at https://github.com/cliang1453/task-aware-distillation., Comment: Proceedings of ICML 2023

We consider the problem of solving robust Markov decision process (MDP), which involves a set of discounted, finite state, finite action space MDPs with uncertain transition kernels. The goal of planning is to find a robust policy that optimizes the worst-case values against the transition uncertainties, and thus encompasses the standard MDP planning as a special case. For $(\mathbf{s},\mathbf{a})$-rectangular uncertainty sets, we establish several structural observations on the robust objective, which facilitates the development of a policy-based first-order method, namely the robust policy mirror descent (RPMD). An $\mathcal{O}(\log(1/\epsilon))$ iteration complexity for finding an $\epsilon$-optimal policy is established with linearly increasing stepsizes. We further develop a stochastic variant of the robust policy mirror descent method, named SRPMD, when the first-order information is only available through online interactions with the nominal environment. We show that the optimality gap converges linearly up to the noise level, and consequently establish an $\tilde{\mathcal{O}}(1/\epsilon^2)$ sample complexity by developing a temporal difference learning method for policy evaluation. Both iteration and sample complexities are also discussed for RPMD with a constant stepsize. To the best of our knowledge, all the aforementioned results appear to be new for policy-based first-order methods applied to the robust MDP problem.

E-commerce queries are often short and ambiguous. Consequently, query understanding often uses query rewriting to disambiguate user-input queries. While using e-commerce search tools, users tend to enter multiple searches, which we call context, before purchasing. These history searches contain contextual insights about users' true shopping intents. Therefore, modeling such contextual information is critical to a better query rewriting model. However, existing query rewriting models ignore users' history behaviors and consider only the instant search query, which is often a short string offering limited information about the true shopping intent. We propose an end-to-end context-aware query rewriting model to bridge this gap, which takes the search context into account. Specifically, our model builds a session graph using the history search queries and their contained words. We then employ a graph attention mechanism that models cross-query relations and computes contextual information of the session. The model subsequently calculates session representations by combining the contextual information with the instant search query using an aggregation network. The session representations are then decoded to generate rewritten queries. Empirically, we demonstrate the superiority of our method to state-of-the-art approaches under various metrics. On in-house data from an online shopping platform, by introducing contextual information, our model achieves 11.6% improvement under the MRR (Mean Reciprocal Rank) metric and 20.1% improvement under the HIT@16 metric (a hit rate metric), in comparison with the best baseline method (Transformer-based model).

Graph neural network (GNN) pre-training methods have been proposed to enhance the power of GNNs. Specifically, a GNN is first pre-trained on a large-scale unlabeled graph and then fine-tuned on a separate small labeled graph for downstream applications, such as node classification. One popular pre-training method is to mask out a proportion of the edges, and a GNN is trained to recover them. However, such a generative method suffers from graph mismatch. That is, the masked graph inputted to the GNN deviates from the original graph. To alleviate this issue, we propose DiP-GNN (Discriminative Pre-training of Graph Neural Networks). Specifically, we train a generator to recover identities of the masked edges, and simultaneously, we train a discriminator to distinguish the generated edges from the original graph's edges. In our framework, the graph seen by the discriminator better matches the original graph because the generator can recover a proportion of the masked edges. Extensive experiments on large-scale homogeneous and heterogeneous graphs demonstrate the effectiveness of the proposed framework.

Point process models are of great importance in real world applications. In certain critical applications, estimation of point process models involves large amounts of sensitive personal data from users. Privacy concerns naturally arise which have not been addressed in the existing literature. To bridge this glaring gap, we propose the first general differentially private estimation procedure for point process models. Specifically, we take the Hawkes process as an example, and introduce a rigorous definition of differential privacy for event stream data based on a discretized representation of the Hawkes process. We then propose two differentially private optimization algorithms, which can efficiently estimate Hawkes process models with the desired privacy and utility guarantees under two different settings. Experiments are provided to back up our theoretical analysis.

Large Transformer-based models have exhibited superior performance in various natural language processing and computer vision tasks. However, these models contain enormous amounts of parameters, which restrict their deployment to real-world applications. To reduce the model size, researchers prune these models based on the weights' importance scores. However, such scores are usually estimated on mini-batches during training, which incurs large variability/uncertainty due to mini-batch sampling and complicated training dynamics. As a result, some crucial weights could be pruned by commonly used pruning methods because of such uncertainty, which makes training unstable and hurts generalization. To resolve this issue, we propose PLATON, which captures the uncertainty of importance scores by upper confidence bound (UCB) of importance estimation. In particular, for the weights with low importance scores but high uncertainty, PLATON tends to retain them and explores their capacity. We conduct extensive experiments with several Transformer-based models on natural language understanding, question answering and image classification to validate the effectiveness of PLATON. Results demonstrate that PLATON manifests notable improvement under different sparsity levels. Our code is publicly available at https://github.com/QingruZhang/PLATON., Comment: Proceedings of the 39th International Conference on Machine Learning (ICML 2022)

Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation theories suggest that with sufficiently many parameters, neural networks can well approximate certain classes of functions in terms of the function value. The neural network themselves, however, can be highly nonsmooth. To bridge this gap, we take convolutional residual networks (ConvResNets) as an example, and prove that large ConvResNets can not only approximate a target function in terms of function value, but also exhibit sufficient first-order smoothness. Moreover, we extend our theory to approximating functions supported on a low-dimensional manifold. Our theory partially justifies the benefits of using deep and wide networks in practice. Numerical experiments on adversarial robust image classification are provided to support our theory.

We consider the off-policy evaluation problem of reinforcement learning using deep convolutional neural networks. We analyze the deep fitted Q-evaluation method for estimating the expected cumulative reward of a target policy, when the data are generated from an unknown behavior policy. We show that, by choosing network size appropriately, one can leverage any low-dimensional manifold structure in the Markov decision process and obtain a sample-efficient estimator without suffering from the curse of high data ambient dimensionality. Specifically, we establish a sharp error bound for fitted Q-evaluation, which depends on the intrinsic dimension of the state-action space, the smoothness of Bellman operator, and a function class-restricted $\chi^2$-divergence. It is noteworthy that the restricted $\chi^2$-divergence measures the behavior and target policies' {\it mismatch in the function space}, which can be small even if the two policies are not close to each other in their tabular forms. We also develop a novel approximation result for convolutional neural networks in Q-function estimation. Numerical experiments are provided to support our theoretical analysis., Comment: 52 pages, 2 figures

Two-sample tests are important areas aiming to determine whether two collections of observations follow the same distribution or not. We propose two-sample tests based on integral probability metric (IPM) for high-dimensional samples supported on a low-dimensional manifold. We characterize the properties of proposed tests with respect to the number of samples $n$ and the structure of the manifold with intrinsic dimension $d$. When an atlas is given, we propose two-step test to identify the difference between general distributions, which achieves the type-II risk in the order of $n^{-1/\max\{d,2\}}$. When an atlas is not given, we propose H\"older IPM test that applies for data distributions with $(s,\beta)$-H\"older densities, which achieves the type-II risk in the order of $n^{-(s+\beta)/d}$. To mitigate the heavy computation burden of evaluating the H\"older IPM, we approximate the H\"older function class using neural networks. Based on the approximation theory of neural networks, we show that the neural network IPM test has the type-II risk in the order of $n^{-(s+\beta)/d}$, which is in the same order of the type-II risk as the H\"older IPM test. Our proposed tests are adaptive to low-dimensional geometric structure because their performance crucially depends on the intrinsic dimension instead of the data dimension., Comment: 32 pages, 2 figures, 3 tables. Accepted by Information and Inference: A Journal of the IMA

Pre-trained language models have demonstrated superior performance in various natural language processing tasks. However, these models usually contain hundreds of millions of parameters, which limits their practicality because of latency requirements in real-world applications. Existing methods train small compressed models via knowledge distillation. However, performance of these small models drops significantly compared with the pre-trained models due to their reduced model capacity. We propose MoEBERT, which uses a Mixture-of-Experts structure to increase model capacity and inference speed. We initialize MoEBERT by adapting the feed-forward neural networks in a pre-trained model into multiple experts. As such, representation power of the pre-trained model is largely retained. During inference, only one of the experts is activated, such that speed can be improved. We also propose a layer-wise distillation method to train MoEBERT. We validate the efficiency and effectiveness of MoEBERT on natural language understanding and question answering tasks. Results show that the proposed method outperforms existing task-specific distillation algorithms. For example, our method outperforms previous approaches by over 2% on the MNLI (mismatched) dataset. Our code is publicly available at https://github.com/SimiaoZuo/MoEBERT., Comment: NAACL 2022

Model ensemble is a popular approach to produce a low-variance and well-generalized model. However, it induces large memory and inference costs, which are often not affordable for real-world deployment. Existing work has resorted to sharing weights among models. However, when increasing the proportion of the shared weights, the resulting models tend to be similar, and the benefits of using model ensemble diminish. To retain ensemble benefits while maintaining a low memory cost, we propose a consistency-regularized ensemble learning approach based on perturbed models, named CAMERO. Specifically, we share the weights of bottom layers across all models and apply different perturbations to the hidden representations for different models, which can effectively promote the model diversity. Meanwhile, we apply a prediction consistency regularizer across the perturbed models to control the variance due to the model diversity. Our experiments using large language models demonstrate that CAMERO significantly improves the generalization performance of the ensemble model. Specifically, CAMERO outperforms the standard ensemble of 8 BERT-base models on the GLUE benchmark by 0.7 with a significantly smaller model size (114.2M vs. 880.6M)., Comment: Proceedings of ACL 2022

User sessions empower many search and recommendation tasks on a daily basis. Such session data are semi-structured, which encode heterogeneous relations between queries and products, and each item is described by the unstructured text. Despite recent advances in self-supervised learning for text or graphs, there lack of self-supervised learning models that can effectively capture both intra-item semantics and inter-item interactions for semi-structured sessions. To fill this gap, we propose CERES, a graph-based transformer model for semi-structured session data. CERES learns representations that capture both inter- and intra-item semantics with (1) a graph-conditioned masked language pretraining task that jointly learns from item text and item-item relations; and (2) a graph-conditioned transformer architecture that propagates inter-item contexts to item-level representations. We pretrained CERES using ~468 million Amazon sessions and find that CERES outperforms strong pretraining baselines by up to 9% in three session search and entity linking tasks.

We investigate the role of noise in optimization algorithms for learning over-parameterized models. Specifically, we consider the recovery of a rank one matrix $Y^*\in R^{d\times d}$ from a noisy observation $Y$ using an over-parameterization model. We parameterize the rank one matrix $Y^*$ by $XX^\top$, where $X\in R^{d\times d}$. We then show that under mild conditions, the estimator, obtained by the randomly perturbed gradient descent algorithm using the square loss function, attains a mean square error of $O(\sigma^2/d)$, where $\sigma^2$ is the variance of the observational noise. In contrast, the estimator obtained by gradient descent without random perturbation only attains a mean square error of $O(\sigma^2)$. Our result partially justifies the implicit regularization effect of noise when learning over-parameterized models, and provides new understanding of training over-parameterized neural networks.

Recent research has shown the existence of significant redundancy in large Transformer models. One can prune the redundant parameters without significantly sacrificing the generalization performance. However, we question whether the redundant parameters could have contributed more if they were properly trained. To answer this question, we propose a novel training strategy that encourages all parameters to be trained sufficiently. Specifically, we adaptively adjust the learning rate for each parameter according to its sensitivity, a robust gradient-based measure reflecting this parameter's contribution to the model performance. A parameter with low sensitivity is redundant, and we improve its fitting by increasing its learning rate. In contrast, a parameter with high sensitivity is well-trained, and we regularize it by decreasing its learning rate to prevent further overfitting. We conduct extensive experiments on natural language understanding, neural machine translation, and image classification to demonstrate the effectiveness of the proposed schedule. Analysis shows that the proposed schedule indeed reduces the redundancy and improves generalization performance., Comment: Proceedings of ICLR 2022

We propose a new policy gradient method, named homotopic policy mirror descent (HPMD), for solving discounted, infinite horizon MDPs with finite state and action spaces. HPMD performs a mirror descent type policy update with an additional diminishing regularization term, and possesses several computational properties that seem to be new in the literature. We first establish the global linear convergence of HPMD instantiated with Kullback-Leibler divergence, for both the optimality gap, and a weighted distance to the set of optimal policies. Then local superlinear convergence is obtained for both quantities without any assumption. With local acceleration and diminishing regularization, we establish the first result among policy gradient methods on certifying and characterizing the limiting policy, by showing, with a non-asymptotic characterization, that the last-iterate policy converges to the unique optimal policy with the maximal entropy. We then extend all the aforementioned results to HPMD instantiated with a broad class of decomposable Bregman divergences, demonstrating the generality of the these computational properties. As a by product, we discover the finite-time exact convergence for some commonly used Bregman divergences, implying the continuing convergence of HPMD to the limiting policy even if the current policy is already optimal. Finally, we develop a stochastic version of HPMD and establish similar convergence properties. By exploiting the local acceleration, we show that for small optimality gap, a better than $\tilde{\mathcal{O}}(\left|\mathcal{S}\right| \left|\mathcal{A}\right| / \epsilon^2)$ sample complexity holds with high probability, when assuming a generative model for policy evaluation.