Low-bit integer training emerges as a promising approach to mitigate the heavy burden during network training by quantizing the weights, activations, and gradients. However, existing methods cannot well achieve mixed-precision quantization for low-bit training and are commonly limited to INT8 precision. In this paper, we propose a novel low-bit integer training framework that, for the first time, achieves adaptive mixed-precision allocation (AMPA) for weights, activations, and gradients, and pushes the boundaries to a precision level below INT8. We develop a novel magnitude-based sensitivity measurement with regard to the quantization losses of weight, activation, and gradient quantization and the average gradient magnitudes, which is demonstrated as an upper bound of quantization influence in theory. We further design a layer-wise precision update strategy under observations on the quantization losses and their effects on model performance in low-bit training. Extensive experiments on different backbones and datasets show that, compared to INT8 quantization, the proposed method can achieve more than 38% BitOPs reduction with a tolerable loss below 2% in image classification, image segmentation, and language modeling.
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Deep Equilibrium Models are Almost Equivalent to Not-so-deep Explicit Models for High-dimensional Gaussian Mixtures
PDF ↗Deep Learning · Theory
Deep equilibrium models (DEQs), as typical implicit neural networks, have demonstrated remarkable success on various tasks. There is, however, a lack of theoretical understanding of the connections and differences between implicit DEQs and explicit neural network models. In this paper, leveraging recent advances in random matrix theory (RMT), we perform an in-depth analysis on the eigenspectra of the conjugate kernel (CK) and neural tangent kernel (NTK) matrices for implicit DEQs, when the input data are drawn from a high-dimensional Gaussia mixture. We prove that, in this setting, the spectral behavior of these Implicit-CKs and NTKs depend on the DEQ activation function and initial weight variances, *but only via a system of four nonlinear equations*. As a direct consequence of this theoretical result, we demonstrate that a shallow explicit network can be carefully designed to produce the same CK or NTK as a given DEQ. Despite derived here for Gaussian mixture data, empirical results show the proposed theory and design principles also apply to popular real-world datasets.
Social Aspects · Accountability, Transparency and Interpretability
This paper proposes a new algorithm for learning accurate tree-based models while ensuring the existence of recourse actions. Algorithmic Recourse (AR) aims to provide a recourse action for altering the undesired prediction result given by a model. Typical AR methods provide a reasonable action by solving an optimization task of minimizing the required effort among executable actions. In practice, however, such actions do not always exist for models optimized only for predictive performance. To alleviate this issue, we formulate the task of learning an accurate classification tree under the constraint of ensuring the existence of reasonable actions for as many instances as possible. Then, we propose an efficient top-down greedy algorithm by leveraging the adversarial training techniques. We also show that our proposed algorithm can be applied to the random forest, which is known as a popular framework for learning tree ensembles. Experimental results demonstrated that our method successfully provided reasonable actions to more instances than the baselines without significantly degrading accuracy and computational efficiency.
Optimization · Learning for Optimization
Mixed integer linear programs (MILP) are flexible and powerful tools for modeling and solving many difficult real-world combinatorial optimization problems. In this paper, we propose a novel machine learning (ML)-based framework ConPaS that learns to predict solutions to MILPs with contrastive learning. For training, we collect high-quality solutions as positive samples. We also collect low-quality or infeasible solutions as negative samples using novel optimization-based or sampling approaches. We then learn to make discriminative predictions by contrasting the positive and negative samples. During testing, we predict and fix the assignments for a subset of integer variables and then solve the resulting reduced MILP to find high-quality solutions. Empirically, ConPaS achieves state-of-the-art results compared to other ML-based approaches in terms of the quality of and the speed at which solutions are found.
Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-constraint
PDF ↗This paper studies the theoretical framework of the alignment process of generative models with Reinforcement Learning from Human Feedback (RLHF). We consider a standard mathematical formulation, the reverse-KL regularized contextual bandit for RLHF. Despite its widespread practical application, a rigorous theoretical analysis of this formulation remains open. We investigate its behavior in three distinct settings---offline, online, and hybrid---and propose efficient algorithms with finite-sample theoretical guarantees. Moving towards practical applications, our framework, with a robust approximation of the information-theoretical policy improvement oracle, naturally gives rise to several novel RLHF algorithms. This includes an iterative version of the Direct Preference Optimization (DPO) algorithm for online settings, and a multi-step rejection sampling strategy for offline scenarios. Our empirical evaluations on real-world alignment experiment of large language model demonstrate that these proposed methods significantly surpass existing strong baselines, such as DPO and Rejection Sampling Optimization (RSO), showcasing the connections between solid theoretical foundations and their potent practical implementations.
Deep Learning · Theory
Grokking, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have reported the occurrence of grokking in specific controlled settings, such as DNNs initialized with large-norm parameters or transformers trained on algorithmic datasets. We demonstrate that grokking is actually much more widespread and materializes in a wide range of practical settings, such as training of a convolutional neural network (CNN) on CIFAR10 or a Resnet on Imagenette. We introduce the new concept of delayed robustness, whereby a DNN groks adversarial examples and becomes robust, long after interpolation and/or generalization. We develop an analytical explanation for the emergence of both delayed generalization and delayed robustness based on the local complexity of a DNN's input-output mapping. Our local complexity measures the density of so-called ``linear regions’’ (aka, spline partition regions) that tile the DNN input space and serves as a utile progress measure for training. We provide the first evidence that, for classification problems, the linear regions undergo a phase transition during training whereafter they migrate away from the training samples (making the DNN mapping smoother there) and towards the decision boundary (making the DNN mapping less smooth there). Grokking occurs post phase transition as a robust partition of the input space thanks to the linearization of the DNN mapping around the training points. Web: https://bit.ly/grok-adversarial.
Reinforcement Learning
Temporal action abstractions, along with belief state representations, are a powerful knowledge sharing mechanism for sequential decision making. In this work, we propose a novel view that treats inducing temporal action abstractions as a sequence compression problem. To do so, we bring a subtle but critical component of LLM training pipelines -- input tokenization via byte pair encoding (BPE) -- to bear on the seemingly distant task of learning skills of variable time span in continuous control domains. We introduce an approach called Primitive Sequence Encoding (PRISE) that combines continuous action quantization with BPE to learn powerful action abstractions. We empirically show that high-level skills discovered by PRISE from a multitask set of robotic manipulation demonstrations significantly boost the learning performance of behavior cloning on downstream tasks.
Theory · Optimization
Budget pacing is a popular service that has been offered by major internet advertising platforms since their inception. In the past few years, autobidding products that provide real-time bidding as a service to advertisers have seen a prominent rise in adoption. A popular autobidding stategy is value maximization subject to return-on-spend (ROS) constraints. For historical or business reasons, the systems that govern these two services, namely budget pacing and ROS pacing, are not necessarily always a single unified and coordinated entity that optimizes a global objective subject to both constraints. The purpose of this work is to theoretically and empirically compare algorithms with different degrees of coordination between these two pacing systems. In particular, we compare (a) a fully-decoupled sequential algorithm; (b) a minimally-coupled min-pacing algorithm; (c) a fully-coupled dual-based algorithm. Our main contribution is to theoretically analyze the min-pacing algorithm and show that it attains similar guarantees to the fully-coupled canonical dual-based algorithm. On the other hand, we show that the sequential algorithm, even though appealing by virtue of being fully decoupled, could badly violate the constraints. We validate our theoretical findings empirically by showing that the min-pacing algorithm performs almost as well as the canonical dual-based algorithm on a semi-synthetic dataset that was generated from a large online advertising platform's auction data.
Data-Efficient Learning via Clustering-Based Sensitivity Sampling: Foundation Models and Beyond
PDF ↗Deep Learning · Large Language Models
We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on $k$-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is Holder continuous, our approach provably allows selecting a set of ``typical'' $k + 1/\varepsilon^2$ elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative $(1\pm\varepsilon)$ factor and an additive $\varepsilon \lambda \Phi_k$, where $\Phi_k$ represents the $k$-means cost for the input embeddings and $\lambda$ is the Holder constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performance of leverage score sampling, while being conceptually simpler and more scalable.
Social Aspects · Privacy-preserving Statistics and Machine Learning
We revisit the objective perturbations framework for differential privacy where noise is added to the input $A\in \mathcal{S}$ and the result is then projected back to the space of admissible datasets $\mathcal{S}$. Through this framework, we first design novel efficient algorithms to privately release pair-wise cosine similarities. Second, we derive a novel algorithm to compute $k$-way marginal queries over $n$ features. Prior work could achieve comparable guarantees only for $k$ even. Furthermore, we extend our results to $t$-sparse datasets, where our efficient algorithms yields novel, stronger guarantees whenever $t\le n^{5/6}/\log n.$ Finally, we provide a theoretical perspective on why *fast* input perturbation algorithms works well in practice. The key technical ingredients behind our results are tight sum-of-squares certificates upper bounding the Gaussian complexity of sets of solutions.
Social Aspects · Privacy-preserving Statistics and Machine Learning
This work studies algorithms for learning from aggregate responses. We focus on the construction of aggregation sets (called *bags* in the literature) for event-level loss functions. We prove for linear regression and generalized linear models (GLMs) that the optimal bagging problem reduces to one-dimensional size-constrained $k$-means clustering. Further, we theoretically quantify the advantage of using curated bags over random bags. We then propose the $\texttt{PriorBoost}$ algorithm, which adaptively forms bags of samples that are increasingly homogeneous with respect to (unobserved) individual responses to improve model quality. We study label differential privacy for aggregate learning, and we also provide extensive experiments showing that $\texttt{PriorBoost}$ regularly achieves optimal model quality for event-level predictions, in stark contrast to non-adaptive algorithms.
We study streaming algorithms for the $\ell_p$ subspace approximation problem. Given points $a_1, \ldots, a_n$ as an insertion-only stream and a rank parameter $k$, the $\ell_p$ subspace approximation problem is to find a $k$-dimensional subspace $V$ such that $(\sum_{i=1}^n d(a_i, V)^p)^{1/p}$ is minimized, where $d(a, V)$ denotes the Euclidean distance between $a$ and $V$ defined as $\min_{v \in V} ||a - v||$. When $p = \infty$, we need to find a subspace $V$ that minimizes $\max_i d(a_i, V)$. For $\ell_{\infty}$ subspace approximation, we give a deterministic strong coreset construction algorithm and show that it can be used to compute a $\mathrm{poly}(k, \log n)$ approximate solution. We show that the distortion obtained by our coreset is nearly tight for any sublinear space algorithm. For $\ell_p$ subspace approximation, we show that suitably scaling the points and then using our $\ell_{\infty}$ coreset construction, we can compute a $\mathrm{poly}(k, \log n)$ approximation. Our algorithms are easy to implement and run very fast on large datasets. We also use our strong coreset construction to improve the results in a recent work of Woodruff and Yasuda (FOCS 2022) which gives streaming algorithms for high-dimensional geometric problems such as width estimation, convex hull estimation, and volume estimation.
Deep Learning · Attention Mechanisms
We introduce an Outlier-Efficient Modern Hopfield Model (termed `OutEffHop`) and use it to address the outlier inefficiency problem of training gigantic transformer-based models. Our main contribution is a novel associative memory model facilitating _outlier-efficient_ associative memory retrievals. Interestingly, this memory model manifests a model-based interpretation of an outlier-efficient attention mechanism (`Softmax_1`): it is an approximation of the memory retrieval process of `OutEffHop`. Methodologically, this allows us to introduce novel outlier-efficient Hopfield layers as powerful alternatives to traditional attention mechanisms, with superior post-quantization performance. Theoretically, the Outlier-Efficient Modern Hopfield Model retains and improves the desirable properties of standard modern Hopfield models, including fixed point convergence and exponential storage capacity. Empirically, we demonstrate the efficacy of the proposed model across large-scale transformer-based and Hopfield-based models (including BERT, OPT, ViT, and STanHop-Net), benchmarking against state-of-the-art methods like `Clipped_Softmax` and `Gated_Attention`. Notably, `OutEffHop` achieves an average reduction of 22+% in average kurtosis and 26+% in the maximum infinity norm of model outputs across four models. Code is available at [GitHub](https://github.com/MAGICS-LAB/OutEffHop); future updates are on [arXiv](https://arxiv.org/abs/2404.03828).
Reinforcement Learning · Function Approximation
Value-based reinforcement learning is the current State-Of-The-Art due to high sampling efficiency. However, our study shows it suffers from low exploitation in early training period and bias sensitiveness. To address these issues, we propose to augment the decision-making process with hypothesis, a weak form of environment description. Our approach relies on prompting the learning agent with accurate hypotheses, and designing a ready-to-adapt policy through incremental learning. We propose the ALH algorithm, showing detailed analyses on a typical learning scheme and a diverse set of Mujoco benchmarks. Our algorithm produces a significant improvement over value-based learning algorithms and other strong baselines. Our code is available at [Github URL](https://github.com/nbtpj/ALH).
Deep Learning · Theory
Deep neural networks (DNNs) have become pivotal in machine learning, but the impact of weight precision, such as in networks with rectified linear units (ReLU), remains underexplored. We analytically investigate the interplay of three key factors: the precision of ReLU network weights, the number of neurons, and the time of the preprocessing algorithm that generates the network description. Our study, which, to the best of our knowledge, is the first formal work on weight precision, yields three main results. (1) We present an exponential time preprocessing algorithm that showcases the possibility of trading ReLU nodes for weight precision. Specifically, our method achieves an exponential reduction in neuron count when computing any function of high complexity with boolean input encoding. What is the implication of the above result in theoretical and practical works? (2) In theory of computing, in general, there is no free lunch. In our case, if you significantly reduce the number of neurons then you should pay the cost in weight precision. To address this, we introduce a notion of network size that considers weight precision in addition to the network's number of neurons. We establish that under this redefined notion of network size, it is generally impossible to exchange neurons for weight precision in ReLU networks of the same (redefined) size. (3) In practice, we show that high weight precision alone cannot help in reducing the neuron count. If instead of our exponential time preprocessing algorithm one uses any polynomial time algorithm, then it is impossible to non-trivially reduce the neuron count, regardless of the high weight precision.
Applications · Genetics, Cell Biology, etc
We introduce Cell2Sentence (C2S), a novel method to directly adapt large language models to a biological context, specifically single-cell transcriptomics. By transforming gene expression data into "cell sentences," C2S bridges the gap between natural language processing and biology. We demonstrate cell sentences enable the fine-tuning of language models for diverse tasks in biology, including cell generation, complex cell-type annotation, and direct data-driven text generation. Our experiments reveal that GPT-2, when fine-tuned with C2S, can generate biologically valid cells based on cell type inputs, and accurately predict cell types from cell sentences. This illustrates that language models, through C2S fine-tuning, can acquire a significant understanding of single-cell biology while maintaining robust text generation capabilities. C2S offers a flexible, accessible framework to integrate natural language processing with transcriptomics, utilizing existing models and libraries for a wide range of biological applications.
Monitoring AI-Modified Content at Scale: A Case Study on the Impact of ChatGPT on AI Conference Peer Reviews
PDF ↗Social Aspects · Accountability, Transparency and Interpretability
We present an approach for estimating the fraction of text in a large corpus which is likely to be substantially modified or produced by a large language model (LLM). Our maximum likelihood model leverages expert-written and AI-generated reference texts to accurately and efficiently examine real-world LLM-use at the corpus level. We apply this approach to a case study of scientific peer review in AI conferences that took place after the release of ChatGPT: *ICLR* 2024, *NeurIPS* 2023, *CoRL* 2023 and *EMNLP* 2023. Our results suggest that between 6.5% and 16.9% of text submitted as peer reviews to these conferences could have been substantially modified by LLMs, i.e. beyond spell-checking or minor writing updates. The circumstances in which generated text occurs offer insight into user behavior: the estimated fraction of LLM-generated text is higher in reviews which report lower confidence, were submitted close to the deadline, and from reviewers who are less likely to respond to author rebuttals. We also observe corpus-level trends in generated text which may be too subtle to detect at the individual level, and discuss the implications of such trends on peer review. We call for future interdisciplinary work to examine how LLM use is changing our information and knowledge practices.
We present an approach for estimating the fraction of text in a large corpus which is likely to be substantially modified or produced by a large language model (LLM). Our maximum likelihood model leverages expert-written and AI-generated reference texts to accurately and efficiently examine real-world LLM-use at the corpus level. We apply this approach to a case study of scientific peer review in AI conferences that took place after the release of ChatGPT: *ICLR* 2024, *NeurIPS* 2023, *CoRL* 2023 and *EMNLP* 2023. Our results suggest that between 6.5% and 16.9% of text submitted as peer reviews to these conferences could have been substantially modified by LLMs, i.e. beyond spell-checking or minor writing updates. The circumstances in which generated text occurs offer insight into user behavior: the estimated fraction of LLM-generated text is higher in reviews which report lower confidence, were submitted close to the deadline, and from reviewers who are less likely to respond to author rebuttals. We also observe corpus-level trends in generated text which may be too subtle to detect at the individual level, and discuss the implications of such trends on peer review. We call for future interdisciplinary work to examine how LLM use is changing our information and knowledge practices.
The complex and unpredictable nature of deep neural networks prevents their safe use in many high-stakes applications. There have been many techniques developed to interpret deep neural networks, but all have substantial limitations. Algorithmic tasks have proven to be a fruitful test ground for interpreting a neural network end-to-end. Building on previous work, we completely reverse engineer fully connected one-hidden layer networks that have ``grokked'' the arithmetic of the permutation groups $S_5$ and $S_6$. The models discover the true subgroup structure of the full group and converge on neural circuits that decompose the group arithmetic using the permutation group's subgroups. We relate how we reverse engineered the model's mechanisms and confirmed our theory was a faithful description of the circuit's functionality. We also draw attention to current challenges in conducting interpretability research by comparing our work to Chughtai et al. (2023) which alleges to find a different algorithm for this same problem.
${\rm E}(3)$-Equivariant Actor-Critic Methods for Cooperative Multi-Agent Reinforcement Learning
PDF ↗Reinforcement Learning · Multi-agent
Identification and analysis of symmetrical patterns in the natural world have led to significant discoveries across various scientific fields, such as the formulation of gravitational laws in physics and advancements in the study of chemical structures. In this paper, we focus on exploiting Euclidean symmetries inherent in certain cooperative multi-agent reinforcement learning (MARL) problems and prevalent in many applications. We begin by formally characterizing a subclass of Markov games with a general notion of symmetries that admits the existence of symmetric optimal values and policies. Motivated by these properties, we design neural network architectures with symmetric constraints embedded as an inductive bias for multi-agent actor-critic methods. This inductive bias results in superior performance in various cooperative MARL benchmarks and impressive generalization capabilities such as zero-shot learning and transfer learning in unseen scenarios with repeated symmetric patterns.