论文检索

Probabilistic Methods/Bayesian Models and Methods

Alexander Immer, Emanuele Palumbo, Alexander Marx, Julia Vogt

Flexibly quantifying both irreducible aleatoric and model-dependent epistemic uncertainties plays an important role for complex regression problems. While deep neural networks in principle can provide this flexibility and learn heteroscedastic aleatoric uncertainties through non-linear functions, recent works highlight that maximizing the log likelihood objective parameterized by mean and variance can lead to compromised mean fits since the gradient are scaled by the predictive variance, and propose adjustments in line with this premise. We instead propose to use the natural parametrization of the Gaussian, which has been shown to be more stable for heteroscedastic regression based on non-linear feature maps and Gaussian processes. Further, we emphasize the significance of principled regularization of the network parameters and prediction. We therefore propose an efficient Laplace approximation for heteroscedastic neural networks that allows automatic regularization through empirical Bayes and provides epistemic uncertainties, both of which improve generalization.We showcase on a range of regression problems—including a new heteroscedastic image regression benchmark—that our methods are scalable, improve over previous approaches for heteroscedastic regression, and provide epistemic uncertainty without requiring hyperparameter tuning.

Deep Learning/Algorithms

Tonghan Wang, Paul Duetting, Dmitry Ivanov, Inbal Talgam-Cohen, David Parkes

Contract design involves a principal who establishes contractual agreements about payments for outcomes that arise from the actions of an agent. In this paper, we initiate the study of deep learning for the automated design of optimal contracts. We introduce a novel representation: the Discontinuous ReLU (DeLU) network, which models the principal's utility as a discontinuous piecewise affine function of the design of a contract where each piece corresponds to the agent taking a particular action. DeLU networks implicitly learn closed-form expressions for the incentive compatibility constraints of the agent and the utility maximization objective of the principal, and support parallel inference on each piece through linear programming or interior-point methods that solve for optimal contracts. We provide empirical results that demonstrate success in approximating the principal's utility function with a small number of training samples and scaling to find approximately optimal contracts on problems with a large number of actions and outcomes.

Deep Learning/Algorithms

Yiwei Lu, Yaoliang Yu, Xinlin Li, Vahid Partovi Nia

In neural network binarization, BinaryConnect (BC) and its variants are considered the standard. These methods apply the sign function in their forward pass and their respective gradients are backpropagated to update the weights. However, the derivative of the sign function is zero whenever defined, which consequently freezes training. Therefore, implementations of BC (e.g., BNN) usually replace the derivative of sign in the backward computation with identity or other approximate gradient alternatives. Although such practice works well empirically, it is largely a heuristic or ``training trick.'' We aim at shedding some light on these training tricks from the optimization perspective. Building from existing theory on ProxConnect (PC, a generalization of BC), we (1) equip PC with different forward-backward quantizers and obtain ProxConnect++ (PC++) that includes existing binarization techniques as special cases; (2) derive a principled way to synthesize forward-backward quantizers with automatic theoretical guarantees; (3) illustrate our theory by proposing an enhanced binarization algorithm BNN++; (4) conduct image classification experiments on CNNs and vision transformers, and empirically verify that BNN++ generally achieves competitive results on binarizing these models.

Applications/Computer Vision

Yuanhao Cai, Yuxin Zheng, Jing Lin, Xin Yuan, Yulun Zhang, Haoqian Wang

Existing deep learning models for hyperspectral image (HSI) reconstruction achieve good performance but require powerful hardwares with enormous memory and computational resources. Consequently, these methods can hardly be deployed on resource-limited mobile devices. In this paper, we propose a novel method, Binarized Spectral-Redistribution Network (BiSRNet), for efficient and practical HSI restoration from compressed measurement in snapshot compressive imaging (SCI) systems. Firstly, we redesign a compact and easy-to-deploy base model to be binarized. Then we present the basic unit, Binarized Spectral-Redistribution Convolution (BiSR-Conv). BiSR-Conv can adaptively redistribute the HSI representations before binarizing activation and uses a scalable hyperbolic tangent function to closer approximate the Sign function in backpropagation. Based on our BiSR-Conv, we customize four binarized convolutional modules to address the dimension mismatch and propagate full-precision information throughout the whole network. Finally, our BiSRNet is derived by using the proposed techniques to binarize the base model. Comprehensive quantitative and qualitative experiments manifest that our proposed BiSRNet outperforms state-of-the-art binarization algorithms. Code and models are publicly available at https://github.com/caiyuanhao1998/BiSCI

Shikai Qiu, Tim G. J. Rudner, Sanyam Kapoor, Andrew Wilson

Standard regularized training procedures correspond to maximizing a posterior distribution over parameters, known as maximum a posteriori (MAP) estimation. However, model parameters are of interest only insomuch as they combine with the functional form of a model to provide a function that can make good predictions. Moreover, the most likely parameters under the parameter posterior do not generally correspond to the most likely function induced by the parameter posterior. In fact, we can re-parametrize a model such that any setting of parameters can maximize the parameter posterior. As an alternative, we investigate the benefits and drawbacks of directly estimating the most likely function implied by the model and the data. We show that this procedure leads to pathological solutions when using neural networks and prove conditions under which the procedure is well-behaved, as well as a scalable approximation. Under these conditions, we find that function-space MAP estimation can lead to flatter minima, better generalization, and improved robustness to overfitting.

Applications/Neuroscience, Cognitive Science

Ankur Sikarwar, Mengmi Zhang

Working memory (WM), a fundamental cognitive process facilitating the temporary storage, integration, manipulation, and retrieval of information, plays a vital role in reasoning and decision-making tasks. Robust benchmark datasets that capture the multifaceted nature of WM are crucial for the effective development and evaluation of AI WM models. Here, we introduce a comprehensive Working Memory (WorM) benchmark dataset for this purpose. WorM comprises 10 tasks and a total of 1 million trials, assessing 4 functionalities, 3 domains, and 11 behavioral and neural characteristics of WM. We jointly trained and tested state-of-the-art recurrent neural networks and transformers on all these tasks. We also include human behavioral benchmarks as an upper bound for comparison. Our results suggest that AI models replicate some characteristics of WM in the brain, most notably primacy and recency effects, and neural clusters and correlates specialized for different domains and functionalities of WM. In the experiments, we also reveal some limitations in existing models to approximate human behavior. This dataset serves as a valuable resource for communities in cognitive psychology, neuroscience, and AI, offering a standardized framework to compare and enhance WM models, investigate WM's neural underpinnings, and develop WM models with human-like capabilities. Our source code and data are available at: https://github.com/ZhangLab-DeepNeuroCogLab/WorM

Social Aspects/Accountability, Transparency and Interpretability

Sarah Schwettmann, Tamar Shaham, Joanna Materzynska, Neil Chowdhury, Shuang Li, Jacob Andreas, David Bau, Antonio Torralba

Labeling neural network submodules with human-legible descriptions is useful for many downstream tasks: such descriptions can surface failures, guide interventions, and perhaps even explain important model behaviors. To date, most mechanistic descriptions of trained networks have involved small models, narrowly delimited phenomena, and large amounts of human labor. Labeling all human-interpretable sub-computations in models of increasing size and complexity will almost certainly require tools that can generate and validate descriptions automatically. Recently, techniques that use learned models in-the-loop for labeling have begun to gain traction, but methods for evaluating their efficacy are limited and ad-hoc. How should we validate and compare open-ended labeling tools? This paper introduces FIND (Function INterpretation and Description), a benchmark suite for evaluating the building blocks of automated interpretability methods. FIND contains functions that resemble components of trained neural networks, and accompanying descriptions of the kind we seek to generate. The functions are procedurally constructed across textual and numeric domains, and involve a range of real-world complexities, including noise, composition, approximation, and bias. We evaluate methods that use pretrained language models (LMs) to produce code-based and natural language descriptions of function behavior. Additionally, we introduce a new interactive method in which an Automated Interpretability Agent (AIA) generates function descriptions. We find that an AIA, built with an off-the-shelf LM augmented with black-box access to functions, can sometimes infer function structure—acting as a scientist by forming hypotheses, proposing experiments, and updating descriptions in light of new data. However, FIND also reveals that LM-based descriptions capture global function behavior while missing local details. These results suggest that FIND will be useful for characterizing the performance of more sophisticated interpretability methods before they are applied to real-world models.

Reinforcement Learning/Function Approximation

Jiaming Guo, Rui Zhang, Shaohui Peng, Qi Yi, Xing Hu, Ruizhi Chen, Zidong Du, xishan zhang, Ling Li, Qi Guo 等

Deep reinforcement learning (DRL) has led to a wide range of advances in sequential decision-making tasks. However, the complexity of neural network policies makes it difficult to understand and deploy with limited computational resources. Currently, employing compact symbolic expressions as symbolic policies is a promising strategy to obtain simple and interpretable policies. Previous symbolic policy methods usually involve complex training processes and pre-trained neural network policies, which are inefficient and limit the application of symbolic policies. In this paper, we propose an efficient gradient-based learning method named Efficient Symbolic Policy Learning (ESPL) that learns the symbolic policy from scratch in an end-to-end way. We introduce a symbolic network as the search space and employ a path selector to find the compact symbolic policy. By doing so we represent the policy with a differentiable symbolic expression and train it in an off-policy manner which further improves the efficiency. In addition, in contrast with previous symbolic policies which only work in single-task RL because of complexity, we expand ESPL on meta-RL to generate symbolic policies for unseen tasks. Experimentally, we show that our approach generates symbolic policies with higher performance and greatly improves data efficiency for single-task RL. In meta-RL, we demonstrate that compared with neural network policies the proposed symbolic policy achieves higher performance and efficiency and shows the potential to be interpretable.

Probabilistic Methods/Variational Inference

Chirag Modi, Robert Gower, Charles Margossian, Yuling Yao, David Blei, Lawrence Saul

Variational inference (VI) is a method to approximate the computationally intractable posterior distributions that arise in Bayesian statistics. Typically, VI fits a simple parametric distribution to be close to the target posterior, optimizing an appropriate objective such as the evidence lower bound (ELBO). In this work, we present a new approach to VI. Our method is based on the principle of score matching---namely, that if two distributions are equal then their score functions (i.e., gradients of the log density) are equal at every point on their support. With this principle, we develop score-matching VI, an iterative algorithm that seeks to match the scores between the variational approximation and the exact posterior. At each iteration, score-matching VI solves an inner optimization, one that minimally adjusts the current variational estimate to match the scores at a newly sampled value of the latent variables. We show that when the variational family is a Gaussian, this inner optimization enjoys a closed-form solution, which we call Gaussian score matching VI (GSM-VI). GSM-VI is a ``black box'' variational algorithm in that it only requires a differentiable joint distribution, and as such it can be applied to a wide class of models. We compare GSM-VI to black box variational inference (BBVI), which has similar requirements but instead optimizes the ELBO. We first study how GSM-VI behaves as a function of the problem dimensionality, the condition number of the target covariance matrix (when the target is Gaussian), and the degree of mismatch between the approximating and exact posterior distribution. We then study GSM-VI on a collection of real-world Bayesian inference problems from the posteriorDB database of datasets and models. We find that GSM-VI is faster than BBVI and equally or more accurate. Specifically, over a wide range of target posteriors, GSM-VI requires 10-100x fewer gradient evaluations than BBVI to obtain a comparable quality of approximation.

Miscellaneous Aspects of Machine Learning/Online Learning, Active Learning and Bandits

Abhishek Sinha, Ativ Joshi, Rajarshi Bhattacharjee, Cameron Musco, Mohammad Hajiesmaili

We consider a fair resource allocation problem in the no-regret setting against an unrestricted adversary. The objective is to allocate resources equitably among several agents in an online fashion so that the difference of the aggregate $\alpha$-fair utilities of the agents achieved by an optimal static clairvoyant allocation and the online policy grows sublinearly with time. The problem inherits its difficulty from the non-separable nature of the global $\alpha$-fairness function. Previously, it was shown that no online policy could achieve a sublinear standard regret in this problem. In this paper, we propose an efficient online resource allocation policy, called Online Fair Allocation ($\texttt{OFA}$), that achieves sublinear $c_\alpha$-approximate regret with approximation factor $c_\alpha=(1-\alpha)^{-(1-\alpha)}\leq 1.445,$ for $0\leq \alpha < 1$. Our upper bound on the $c_\alpha$-regret for this problem exhibits a surprising \emph{phase transition} phenomenon -- transitioning from a power-law to a constant at the critical exponent $\alpha=\frac{1}{2}.$ Our result also resolves an open problem in designing an efficient no-regret policy for the online job scheduling problem in certain parameter regimes. Along the way, we introduce new algorithmic and analytical techniques, including greedy estimation of the future gradients for non-additive global reward functions and bootstrapping second-order regret bounds, which may be of independent interest.

Reinforcement Learning

GUOJUN XIONG, Jian Li

Whittle index policy is a heuristic to the intractable restless multi-armed bandits (RMAB) problem. Although it is provably asymptotically optimal, finding Whittle indices remains difficult. In this paper, we present Neural-Q-Whittle, a Whittle index based Q-learning algorithm for RMAB with neural network function approximation, which is an example of nonlinear two-timescale stochastic approximation with Q-function values updated on a faster timescale and Whittle indices on a slower timescale. Despite the empirical success of deep Q-learning, the non-asymptotic convergence rate of Neural-Q-Whittle, which couples neural networks with two-timescale Q-learning largely remains unclear. This paper provides a finite-time analysis of Neural-Q-Whittle, where data are generated from a Markov chain, and Q-function is approximated by a ReLU neural network. Our analysis leverages a Lyapunov drift approach to capture the evolution of two coupled parameters, and the nonlinearity in value function approximation further requires us to characterize the approximation error. Combing these provide Neural-Q-Whittle with $\mathcal{O}(1/k^{2/3})$ convergence rate, where $k$ is the number of iterations.

Miscellaneous Aspects of Machine Learning/Supervised Learning

Naoki Nishikawa, Yuichi Ike, Kenji Yamanishi

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often effective to incorporate global topological features, which are typically extracted by persistent homology. In the calculation of persistent homology for a point cloud, we choose a filtration for the point cloud, an increasing sequence of spaces. Since the performance of machine learning methods combined with persistent homology is highly affected by the choice of a filtration, we need to tune it depending on data and tasks. In this paper, we propose a framework that learns a filtration adaptively with the use of neural networks. In order to make the resulting persistent homology isometry-invariant, we develop a neural network architecture with such invariance. Additionally, we show a theoretical result on a finite-dimensional approximation of filtration functions, which justifies the proposed network architecture. Experimental results demonstrated the efficacy of our framework in several classification tasks.

Probabilistic Methods/Bayesian Models and Methods

Daolang Huang, Ayush Bharti, Amauri Souza, Luigi Acerbi, Samuel Kaski

Simulation-based inference (SBI) methods such as approximate Bayesian computation (ABC), synthetic likelihood, and neural posterior estimation (NPE) rely on simulating statistics to infer parameters of intractable likelihood models. However, such methods are known to yield untrustworthy and misleading inference outcomes under model misspecification, thus hindering their widespread applicability. In this work, we propose the first general approach to handle model misspecification that works across different classes of SBI methods. Leveraging the fact that the choice of statistics determines the degree of misspecification in SBI, we introduce a regularized loss function that penalizes those statistics that increase the mismatch between the data and the model. Taking NPE and ABC as use cases, we demonstrate the superior performance of our method on high-dimensional time-series models that are artificially misspecified. We also apply our method to real data from the field of radio propagation where the model is known to be misspecified. We show empirically that the method yields robust inference in misspecified scenarios, whilst still being accurate when the model is well-specified.

Deep Learning/Attention Mechanisms

Jerry Yao-Chieh Hu, Donglin Yang, Dennis Wu, Chenwei Xu, Bo-Yu Chen, Han Liu

We introduce the sparse modern Hopfield model as a sparse extension of the modern Hopfield model.Like its dense counterpart, the sparse modern Hopfield model equips a memory-retrieval dynamics whose one-step approximation corresponds to the sparse attention mechanism. Theoretically, our key contribution is a principled derivation of a closed-form sparse Hopfield energy using the convex conjugate of the sparse entropic regularizer.Building upon this, we derive the sparse memory retrieval dynamics from the sparse energy function and show its one-step approximation is equivalent to the sparse-structured attention.Importantly, we provide a sparsity-dependent memory retrieval error bound which is provably tighter than its dense analog.The conditions for the benefits of sparsity to arise are therefore identified and discussed.In addition, we show that the sparse modern Hopfield model maintains the robust theoretical properties of its dense counterpart, including rapid fixed point convergence and exponential memory capacity.Empirically, we use both synthetic and real-world datasets to demonstrate that the sparse Hopfield model outperforms its dense counterpart in many situations.

Reinforcement Learning/Function Approximation

Sattar Vakili, Julia Olkhovskaya

Modern reinforcement learning (RL) has shown empirical success in various real world settings with complex models and large state-action spaces. The existing analytical results, however, typically focus on settings with a small number of state-actions or simple models such as linearly modeled state-action value functions. To derive RL policies that efficiently handle large state-action spaces with more general value functions, some recent works have considered nonlinear function approximation using kernel ridge regression. We propose $\pi$-KRVI, an optimistic modification of least-squares value iteration, when the action-value function is represented by an RKHS. We prove the first order-optimal regret guarantees under a general setting. Our results show a significant polynomial in the number of episodes improvement over the state of the art. In particular, with highly non-smooth kernels (such as Neural Tangent kernel or some Matérn kernels) the existing results lead to trivial (superlinear in the number of episodes) regret bounds. We show a sublinear regret bound that is order optimal in the cases where a lower bound on regret is known (which includes the kernels mentioned above).

Applications/Physics

Benjamin Holzschuh, Simona Vegetti, Nils Thuerey

We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an approximate inverse physics simulator and a learned correction function. A central insight of our work is that training the learned correction with a single-step loss is equivalent to a score matching objective, while recursively predicting longer parts of the trajectory during training relates to maximum likelihood training of a corresponding probability flow.We highlight the advantages of our algorithm compared to standard denoising score matching and implicit score matching, as well as fully learned baselines for a wide range of inverse physics problems. The resulting inverse solver has excellent accuracy and temporal stability and, in contrast to other learned inverse solvers, allows for sampling the posterior of the solutions. Code and experiments are available at https://github.com/tum-pbs/SMDP.

Deep Learning/Graph Neural Networks

Zian Li, Xiyuan Wang, Yinan Huang, Muhan Zhang

Graph Neural Networks (GNNs) are often used for tasks involving the 3D geometry of a given graph, such as molecular dynamics simulation. While incorporating Euclidean distance into Message Passing Neural Networks (referred to as Vanilla DisGNN) is a straightforward way to learn the geometry, it has been demonstrated that Vanilla DisGNN is geometrically incomplete. In this work, we first construct families of novel and symmetric geometric graphs that Vanilla DisGNN cannot distinguish even when considering all-pair distances, which greatly expands the existing counterexample families. Our counterexamples show the inherent limitation of Vanilla DisGNN to capture symmetric geometric structures. We then propose $k$-DisGNNs, which can effectively exploit the rich geometry contained in the distance matrix. We demonstrate the high expressive power of $k$-DisGNNs from three perspectives: 1. They can learn high-order geometric information that cannot be captured by Vanilla DisGNN. 2. They can unify some existing well-designed geometric models. 3. They are universal function approximators from geometric graphs to scalars (when $k\geq 2$) and vectors (when $k\geq 3$). Most importantly, we establish a connection between geometric deep learning (GDL) and traditional graph representation learning (GRL), showing that those highly expressive GNN models originally designed for GRL can also be applied to GDL with impressive performance, and that existing complicated, equivariant models are not the only solution. Experiments verify our theory. Our $k$-DisGNNs achieve many new state-of-the-art results on MD17.

Reinforcement Learning

Xuyang Chen, Lin Zhao

Actor-critic methods have achieved significant success in many challenging applications. However, its finite-time convergence is still poorly understood in the most practical single-timescale form. Existing works on analyzing single-timescale actor-critic have been limited to i.i.d. sampling or tabular setting for simplicity. We investigate the more practical online single-timescale actor-critic algorithm on continuous state space, where the critic assumes linear function approximation and updates with a single Markovian sample per actor step. Previous analysis has been unable to establish the convergence for such a challenging scenario. We demonstrate that the online single-timescale actor-critic method provably finds an $\epsilon$-approximate stationary point with $\widetilde{\mathcal{O}}(\epsilon^{-2})$ sample complexity under standard assumptions, which can be further improved to $\mathcal{O}(\epsilon^{-2})$ under the i.i.d. sampling. Our novel framework systematically evaluates and controls the error propagation between the actor and critic. It offers a promising approach for analyzing other single-timescale reinforcement learning algorithms as well.

Reinforcement Learning/Online

Lucas N. Alegre, Ana Bazzan, Ann Nowe, Bruno C. da Silva

We introduce a principled method for performing zero-shot transfer in reinforcement learning (RL) by exploiting approximate models of the environment. Zero-shot transfer in RL has been investigated by leveraging methods rooted in generalized policy improvement (GPI) and successor features (SFs). Although computationally efficient, these methods are model-free: they analyze a library of policies---each solving a particular task---and identify which action the agent should take. We investigate the more general setting where, in addition to a library of policies, the agent has access to an approximate environment model. Even though model-based RL algorithms can identify near-optimal policies, they are typically computationally intensive. We introduce $h$-GPI, a multi-step extension of GPI that interpolates between these extremes---standard model-free GPI and fully model-based planning---as a function of a parameter, $h$, regulating the amount of time the agent has to reason. We prove that $h$-GPI's performance lower bound is strictly better than GPI's, and show that $h$-GPI generally outperforms GPI as $h$ increases. Furthermore, we prove that as $h$ increases, $h$-GPI's performance becomes arbitrarily less susceptible to sub-optimality in the agent's policy library. Finally, we introduce novel bounds characterizing the gains achievable by $h$-GPI as a function of approximation errors in both the agent's policy library and its (possibly learned) model. These bounds strictly generalize those known in the literature. We evaluate $h$-GPI on challenging tabular and continuous-state problems under value function approximation and show that it consistently outperforms GPI and state-of-the-art competing methods under various levels of approximation errors.

Optimization/Discrete and Combinatorial Optimization

Yossi Azar, Debmalya Panigrahi, Noam Touitou

In recent years, there has been an increasing focus on designing online algorithms with (machine-learned) predictions. The ideal learning-augmented algorithm is comparable to the optimum when given perfect predictions (consistency), to the best online approximation for arbitrary predictions (robustness), and should interpolate between these extremes as a smooth function of the prediction error. In this paper, we quantify these guarantees in terms of a general property that we call discrete-smoothness, and achieve discrete-smooth algorithms for online covering, specifically the facility location and set cover problems. For set cover, our work improves the results of Bamas, Maggiori, and Svensson (2020) by augmenting consistency and robustness with smoothness guarantees. For facility location, our work improves on prior work by Almanza et al. (2021) by generalizing to nonuniform costs and also providing smoothness guarantees by augmenting consistency and robustness.