NeurIPS 2022 论文列表

The implicit bias of neural networks has been extensively studied in recent years. Lyu and Li (2019) showed that in homogeneous networks trained with the exponential or the logistic loss, gradient flow converges to a KKT point of the max margin problem in parameter space. However, that leaves open the question of whether this point will generally be an actual optimum of the max margin problem. In this paper, we study this question in detail, for several neural network architectures involving linear and ReLU activations. Perhaps surprisingly, we show that in many cases, the KKT point is not even a local optimum of the max margin problem. On the flip side, we identify multiple settings where a local or global optimum can be guaranteed.

Shapley value is a popular approach for measuring the influence of individual features. While Shapley feature attribution is built upon desiderata from game theory, some of its constraints may be less natural in certain machine learning settings, leading to unintuitive model interpretation. In particular, the Shapley value uses the same weight for all marginal contributions---i.e. it gives the same importance when a large number of other features are given versus when a small number of other features are given. This property can be problematic if larger feature sets are more or less informative than smaller feature sets. Our work performs a rigorous analysis of the potential limitations of Shapley feature attribution. We identify simple settings where the Shapley value is mathematically suboptimal by assigning larger attributions for less influential features. Motivated by this observation, we propose WeightedSHAP, which generalizes the Shapley value and learns which marginal contributions to focus directly from data. On several real-world datasets, we demonstrate that the influential features identified by WeightedSHAP are better able to recapitulate the model's predictions compared to the features identified by the Shapley value.

Multi-head attention empowers the recent success of transformers, the state-of-the-art models that have achieved remarkable success in sequence modeling and beyond. These attention mechanisms compute the pairwise dot products between the queries and keys, which results from the use of unnormalized Gaussian kernels with the assumption that the queries follow a mixture of Gaussian distribution. There is no guarantee that this assumption is valid in practice. In response, we first interpret attention in transformers as a nonparametric kernel regression. We then propose the FourierFormer, a new class of transformers in which the dot-product kernels are replaced by the novel generalized Fourier integral kernels. Different from the dot-product kernels, where we need to choose a good covariance matrix to capture the dependency of the features of data, the generalized Fourier integral kernels can automatically capture such dependency and remove the need to tune the covariance matrix. We theoretically prove that our proposed Fourier integral kernels can efficiently approximate any key and query distributions. Compared to the conventional transformers with dot-product attention, FourierFormers attain better accuracy and reduce the redundancy between attention heads. We empirically corroborate the advantages of FourierFormers over the baseline transformers in a variety of practical applications including language modeling and image classification.

U-Net architectures are ubiquitous in state-of-the-art deep learning, however their regularisation properties and relationship to wavelets are understudied. In this paper, we formulate a multi-resolution framework which identifies U-Nets as finite-dimensional truncations of models on an infinite-dimensional function space. We provide theoretical results which prove that average pooling corresponds to projection within the space of square-integrable functions and show that U-Nets with average pooling implicitly learn a Haar wavelet basis representation of the data. We then leverage our framework to identify state-of-the-art hierarchical VAEs (HVAEs), which have a U-Net architecture, as a type of two-step forward Euler discretisation of multi-resolution diffusion processes which flow from a point mass, introducing sampling instabilities. We also demonstrate that HVAEs learn a representation of time which allows for improved parameter efficiency through weight-sharing. We use this observation to achieve state-of-the-art HVAE performance with half the number of parameters of existing models, exploiting the properties of our continuous-time formulation.

Flow networks are ubiquitous in natural and engineered systems, and in order to understand and manage these networks, one must quantify the flow of commodities across their edges. This paper considers the estimation problem of predicting unlabeled edge flows from nodal supply and demand. We propose an implicit neural network layer that incorporates two fundamental physical laws: conservation of mass, and the existence of a constitutive relationship between edge flows and nodal states (e.g., Ohm's law). Computing the edge flows from these two laws is a nonlinear inverse problem, which our layer solves efficiently with a specialized contraction mapping. Using implicit differentiation to compute the solution's gradients, our model is able to learn the constitutive relationship within a semi-supervised framework. We demonstrate that our approach can accurately predict edge flows in several experiments on AC power networks and water distribution systems.

Machine learning systems perform well on pattern matching tasks, but their ability to perform algorithmic or logical reasoning is not well understood. One important reasoning capability is algorithmic extrapolation, in which models trained only on small/simple reasoning problems can synthesize complex strategies for large/complex problems at test time. Algorithmic extrapolation can be achieved through recurrent systems, which can be iterated many times to solve difficult reasoning problems. We observe that this approach fails to scale to highly complex problems because behavior degenerates when many iterations are applied -- an issue we refer to as "overthinking." We propose a recall architecture that keeps an explicit copy of the problem instance in memory so that it cannot be forgotten. We also employ a progressive training routine that prevents the model from learning behaviors that are specific to iteration number and instead pushes it to learn behaviors that can be repeated indefinitely. These innovations prevent the overthinking problem, and enable recurrent systems to solve extremely hard extrapolation tasks.

We consider finite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can sometimes be overly conservative. In this paper, we propose a new formulation, Bayesian risk Markov decision process (BR-MDP), to address parameter uncertainty in MDPs, where a risk functional is applied in nested form to the expected total cost with respect to the Bayesian posterior distributions of the unknown parameters. The proposed formulation provides more flexible risk attitudes towards parameter uncertainty and takes into account the availability of data in future time stages. To solve the proposed formulation with the conditional value-at-risk (CVaR) risk functional, we propose an efficient approximation algorithm by deriving an analytical approximation of the value function and utilizing the convexity of CVaR. We demonstrate the empirical performance of the BR-MDP formulation and proposed algorithms on a gambler’s betting problem and an inventory control problem.

We develop Temporal Quantile Adjustment (TQA), a general method to construct efficient and valid prediction intervals (PIs) for regression on cross-sectional time series data. Such data is common in many domains, including econometrics and healthcare. A canonical example in healthcare is predicting patient outcomes using physiological time-series data, where a population of patients composes a cross-section. Reliable PI estimators in this setting must address two distinct notions of coverage: cross-sectional coverage across a cross-sectional slice, and longitudinal coverage along the temporal dimension for each time series. Recent works have explored adapting Conformal Prediction (CP) to obtain PIs in the time series context. However, none handles both notions of coverage simultaneously. CP methods typically query a pre-specified quantile from the distribution of nonconformity scores on a calibration set. TQA adjusts the quantile to query in CP at each time $t$, accounting for both cross-sectional and longitudinal coverage in a theoretically-grounded manner. The post-hoc nature of TQA facilitates its use as a general wrapper around any time series regression model. We validate TQA's performance through extensive experimentation: TQA generally obtains efficient PIs and improves longitudinal coverage while preserving cross-sectional coverage.

We study the problem of best arm identification in linear bandits in the fixed-budget setting. By leveraging properties of the G-optimal design and incorporating it into the arm allocation rule, we design a parameter-free algorithm, Optimal Design-based Linear Best Arm Identification (OD-LinBAI). We provide a theoretical analysis of the failure probability of OD-LinBAI. Instead of all the optimality gaps, the performance of OD-LinBAI depends only on the gaps of the top $d$ arms, where $d$ is the effective dimension of the linear bandit instance. Complementarily, we present a minimax lower bound for this problem. The upper and lower bounds show that OD-LinBAI is minimax optimal up to constant multiplicative factors in the exponent, which is a significant theoretical improvement over existing methods (e.g., BayesGap, Peace, LinearExploration and GSE), and settles the question of ascertaining the difficulty of learning the best arm in the fixed-budget setting. Finally, numerical experiments demonstrate considerable empirical improvements over existing algorithms on a variety of real and synthetic datasets.

Room impulse response (RIR) functions capture how the surrounding physical environment transforms the sounds heard by a listener, with implications for various applications in AR, VR, and robotics. Whereas traditional methods to estimate RIRs assume dense geometry and/or sound measurements throughout the environment, we explore how to infer RIRs based on a sparse set of images and echoes observed in the space. Towards that goal, we introduce a transformer-based method that uses self-attention to build a rich acoustic context, then predicts RIRs of arbitrary query source-receiver locations through cross-attention. Additionally, we design a novel training objective that improves the match in the acoustic signature between the RIR predictions and the targets. In experiments using a state-of-the-art audio-visual simulator for 3D environments, we demonstrate that our method successfully generates arbitrary RIRs, outperforming state-of-the-art methods and---in a major departure from traditional methods---generalizing to novel environments in a few-shot manner. Project: http://vision.cs.utexas.edu/projects/fs_rir

We prove identifiability of a broad class of deep latent variable models that (a) have universal approximation capabilities and (b) are the decoders of variational autoencoders that are commonly used in practice. Unlike existing work, our analysis does not require weak supervision, auxiliary information, or conditioning in the latent space. Specifically, we show that for a broad class of generative (i.e. unsupervised) models with universal approximation capabilities, the side information $u$ is not necessary: We prove identifiability of the entire generative model where we do not observe $u$ and only observe the data $x$. The models we consider match autoencoder architectures used in practice that leverage mixture priors in the latent space and ReLU/leaky-ReLU activations in the encoder, such as VaDE and MFC-VAE. Our main result is an identifiability hierarchy that significantly generalizes previous work and exposes how different assumptions lead to different ``strengths'' of identifiability, and includes certain ``vanilla'' VAEs with isotropic Gaussian priors as a special case. For example, our weakest result establishes (unsupervised) identifiability up to an affine transformation, and thus partially resolves an open problem regarding model identifiability raised in prior work. These theoretical results are augmented with experiments on both simulated and real data.

We study square loss in a realizable time-series framework with martingale difference noise. Our main result is a fast rate excess risk bound which shows that whenever a trajectory hypercontractivity condition holds, the risk of the least-squares estimator on dependent data matches the iid rate order-wise after a burn-in time. In comparison, many existing results in learning from dependent data have rates where the effective sample size is deflated by a factor of the mixing-time of the underlying process, even after the burn-in time. Furthermore, our results allow the covariate process to exhibit long range correlations which are substantially weaker than geometric ergodicity. We call this phenomenon learning with little mixing, and present several examples for when it occurs: bounded function classes for which the $L^2$ and $L^{2+\epsilon}$ norms are equivalent, finite state irreducible and aperiodic Markov chains, various parametric models, and a broad family of infinite dimensional $\ell^2(\mathbb{N})$ ellipsoids. By instantiating our main result to system identification of nonlinear dynamics with generalized linear model transitions, we obtain a nearly minimax optimal excess risk bound after only a polynomial burn-in time.

In this paper, we study the problem of fair sequential decision making with biased linear bandit feedback. At each round, a player selects an action described by a covariate and by a sensitive attribute. The perceived reward is a linear combination of the covariates of the chosen action, but the player only observes a biased evaluation of this reward, depending on the sensitive attribute. To characterize the difficulty of this problem, we design a phased elimination algorithm that corrects the unfair evaluations, and establish upper bounds on its regret. We show that the worst-case regret is smaller than $\mathcal{O}(\kappa_* ^{1/3}\log(T)^{1/3}T^{2/3})$, where $\kappa_*$ is an explicit geometrical constant characterizing the difficulty of bias estimation. We prove lower bounds on the worst-case regret for some sets of actions showing that this rate is tight up to a possible sub-logarithmic factor. We also derive gap-dependent upper bounds on the regret, and matching lower bounds for some problem instance. Interestingly, these results reveal a transition between a regime where the problem is as difficult as its unbiased counterpart, and a regime where it can be much harder.

We propose Differentiable Temporal Logic (DTL), a model-agnostic framework that introduces temporal constraints to deep networks. DTL treats the outputs of a network as a truth assignment of a temporal logic formula, and computes a temporal logic loss reflecting the consistency between the output and the constraints. We propose a comprehensive set of constraints, which are implicit in data annotations, and incorporate them with deep networks via DTL. We evaluate the effectiveness of DTL on the temporal action segmentation task and observe improved performance and reduced logical errors in the output of different task models. Furthermore, we provide an extensive analysis to visualize the desirable effects of DTL.

This paper introduces a new interpretation of the Variational Autoencoder framework by taking a fully geometric point of view. We argue that vanilla VAE models unveil naturally a Riemannian structure in their latent space and that taking into consideration those geometrical aspects can lead to better interpolations and an improved generation procedure. This new proposed sampling method consists in sampling from the uniform distribution deriving intrinsically from the learned Riemannian latent space and we show that using this scheme can make a vanilla VAE competitive and even better than more advanced versions on several benchmark datasets. Since generative models are known to be sensitive to the number of training samples we also stress the method's robustness in the low data regime.

Recently there is a large amount of work devoted to the study of Markov chain stochastic gradient methods (MC-SGMs) which mainly focus on their convergence analysis for solving minimization problems. In this paper, we provide a comprehensive generalization analysis of MC-SGMs for both minimization and minimax problems through the lens of algorithmic stability in the framework of statistical learning theory. For empirical risk minimization (ERM) problems, we establish the optimal excess population risk bounds for both smooth and non-smooth cases by introducing on-average argument stability. For minimax problems, we develop a quantitative connection between on-average argument stability and generalization error which extends the existing results for uniform stability (Lei et al., 2021). We further develop the first nearly optimal convergence rates for convex-concave problems both in expectation and with high probability, which, combined with our stability results, show that the optimal generalization bounds can be attained for both smooth and non-smooth cases. To the best of our knowledge, this is the first generalization analysis of SGMs when the gradients are sampled from a Markov process.

LiDAR-produced point clouds are the major source for most state-of-the-art 3D object detectors. Yet, small, distant, and incomplete objects with sparse or few points are often hard to detect. We present Sparse2Dense, a new framework to efficiently boost 3D detection performance by learning to densify point clouds in latent space. Specifically, we first train a dense point 3D detector (DDet) with a dense point cloud as input and design a sparse point 3D detector (SDet) with a regular point cloud as input. Importantly, we formulate the lightweight plug-in S2D module and the point cloud reconstruction module in SDet to densify 3D features and train SDet to produce 3D features, following the dense 3D features in DDet. So, in inference, SDet can simulate dense 3D features from regular (sparse) point cloud inputs without requiring dense inputs. We evaluate our method on the large-scale Waymo Open Dataset and the Waymo Domain Adaptation Dataset, showing its high performance and efficiency over the state of the arts.

Decision trees are well-known due to their ease of interpretability. To improve accuracy, we need to grow deep trees or ensembles of trees. These are hard to interpret, offsetting their original benefits. Shapley values have recently become a popular way to explain the predictions of tree-based machine learning models. It provides a linear weighting to features independent of the tree structure. The rise in popularity is mainly due to TreeShap, which solves a general exponential complexity problem in polynomial time. Following extensive adoption in the industry, more efficient algorithms are required. This paper presents a more efficient and straightforward algorithm: Linear TreeShap. Like TreeShap, Linear TreeShap is exact and requires the same amount of memory.

Succinct representation of complex signals using coordinate-based neural representations (CNRs) has seen great progress, and several recent efforts focus on extending them for handling videos. Here, the main challenge is how to (a) alleviate a compute-inefficiency in training CNRs to (b) achieve high-quality video encoding while (c) maintaining the parameter-efficiency. To meet all requirements (a), (b), and (c) simultaneously, we propose neural video representations with learnable positional features (NVP), a novel CNR by introducing "learnable positional features" that effectively amortize a video as latent codes. Specifically, we first present a CNR architecture based on designing 2D latent keyframes to learn the common video contents across each spatio-temporal axis, which dramatically improves all of those three requirements. Then, we propose to utilize existing powerful image and video codecs as a compute-/memory-efficient compression procedure of latent codes. We demonstrate the superiority of NVP on the popular UVG benchmark; compared with prior arts, NVP not only trains 2 times faster (less than 5 minutes) but also exceeds their encoding quality as 34.07$\rightarrow$34.57 (measured with the PSNR metric), even using $>$8 times fewer parameters. We also show intriguing properties of NVP, e.g., video inpainting, video frame interpolation, etc.