NeurIPS 2023 论文列表

We investigate theory and algorithms for pool-based active learning for multiclass classification using multinomial logistic regression. Using finite sample analysis, we prove that the Fisher Information Ratio (FIR) lower and upper bounds the excess risk. Based on our theoretical analysis, we propose an active learning algorithm that employs regret minimization to minimize the FIR. To verify our derived excess risk bounds, we conduct experiments on synthetic datasets. Furthermore, we compare FIRAL with five other methods and found that our scheme outperforms them: it consistently produces the smallest classification error in the multiclass logistic regression setting, as demonstrated through experiments on MNIST, CIFAR-10, and 50-class ImageNet.

Reproducing kernel Hilbert $C^*$-module (RKHM) is a generalization of reproducing kernel Hilbert space (RKHS) by means of $C^*$-algebra, and the Perron-Frobenius operator is a linear operator related to the composition of functions. Combining these two concepts, we present deep RKHM, a deep learning framework for kernel methods. We derive a new Rademacher generalization bound in this setting and provide a theoretical interpretation of benign overfitting by means of Perron-Frobenius operators. By virtue of $C^*$-algebra, the dependency of the bound on output dimension is milder than existing bounds. We show that $C^*$-algebra is a suitable tool for deep learning with kernels, enabling us to take advantage of the product structure of operators and to provide a clear connection with convolutional neural networks. Our theoretical analysis provides a new lens through which one can design and analyze deep kernel methods.

Tensor decompositions (TDs) serve as a powerful tool for analyzing multiway data. Traditional TDs incorporate prior knowledge about the data into the model, such as a directed generative process from latent factors to observations. In practice, selecting proper structural or distributional assumptions beforehand is crucial for obtaining a promising TD representation. However, since such prior knowledge is typically unavailable in real-world applications, choosing an appropriate TD model can be challenging. This paper aims to address this issue by introducing a flexible TD framework that discards the structural and distributional assumptions, in order to learn as much information from the data. Specifically, we construct a TD model that captures the joint probability of the data and latent tensor factors through a deep energy-based model (EBM). Neural networks are then employed to parameterize the joint energy function of tensor factors and tensor entries. The flexibility of EBM and neural networks enables the learning of underlying structures and distributions. In addition, by designing the energy function, our model unifies the learning process of different types of tensors, such as static tensors and dynamic tensors with time stamps. The resulting model presents a doubly intractable nature due to the presence of latent tensor factors and the unnormalized probability function. To efficiently train the model, we derive a variational upper bound of the conditional noise-contrastive estimation objective that learns the unnormalized joint probability by distinguishing data from conditional noises. We show advantages of our model on both synthetic and several real-world datasets.

Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, they suffer performance penalties for certain stiff systems, where small steps are required not for reasons of numerical accuracy but for the sake of stability. This issue is greatly alleviated in semi-linear problems by the probabilistic exponential integrators developed in this paper. By including the fast, linear dynamics in the prior, we arrive at a class of probabilistic integrators with favorable properties. Namely, they are proven to be L-stable, and in a certain case reduce to a classic exponential integrator---with the added benefit of providing a probabilistic account of the numerical error. The method is also generalized to arbitrary non-linear systems by imposing piece-wise semi-linearity on the prior via Jacobians of the vector field at the previous estimates, resulting in probabilistic exponential Rosenbrock methods. We evaluate the proposed methods on multiple stiff differential equations and demonstrate their improved stability and efficiency over established probabilistic solvers. The present contribution thus expands the range of problems that can be effectively tackled within probabilistic numerics.

Mislabeled, duplicated, or biased data in real-world scenarios can lead to prolonged training and even hinder model convergence. Traditional solutions prioritizing easy or hard samples lack the flexibility to handle such a variety simultaneously. Recent work has proposed a more reasonable data selection principle by examining the data's impact on the model's generalization loss. However, its practical adoption relies on less principled approximations and additional holdout data. This work solves these problems by leveraging a lightweight Bayesian treatment and incorporating off-the-shelf zero-shot predictors built on large-scale pre-trained models. The resulting algorithm is efficient and easy to implement. We perform extensive empirical studies on challenging benchmarks with considerable data noise and imbalance in the online batch selection scenario, and observe superior training efficiency over competitive baselines. Notably, on the challenging WebVision benchmark, our method can achieve similar predictive performance with significantly fewer training iterations than leading data selection methods.

Research in statistical learning has polarized into two general approaches to perform regression analysis: Transductive methods construct estimates directly based on exemplar data using generic relational principles which might suffer from the curse of dimensionality. Conversely, inductive methods can potentially fit highly complex functions at the cost of compute-intensive solution searches. In this work, we leverage the theory of vector-valued Reproducing Kernel Banach Spaces (RKBS) to propose a hybrid approach: We show that transductive regression systems can be meta-learned with gradient descent to form efficient _in-context_ neural approximators of function defined over both finite and infinite-dimensional spaces (operator regression). Once trained, our _Transducer_ can almost instantaneously capture new functional relationships and produce original image estimates, given a few pairs of input and output examples. We demonstrate the benefit of our meta-learned transductive approach to model physical systems influenced by varying external factors with little data at a fraction of the usual deep learning training costs for partial differential equations and climate modeling applications.

In theoretical Machine Learning, the teacher-student paradigm is often employed as an effective metaphor for real-life tuition. A student network is trained on data generated by a fixed teacher network until it matches the instructor’s ability to cope with the assigned task. The above scheme proves particularly relevant when the student network is overparameterized (namely, when larger layer sizes are employed) as compared to the underlying teacher network. Under these operating conditions, it is tempting to speculate that the student ability to handle the given task could be eventually stored in a sub-portion of the whole network. This latter should be to some extent reminiscent of the frozen teacher structure, according to suitable metrics, while being approximately invariant across different architectures of the student candidate network. Unfortunately, state-of-the-art conventional learning techniques could not help in identifying the existence of such an invariant subnetwork, due to the inherent degree of non-convexity that characterizes the examined problem. In this work, we take a decisive leap forward by proposing a radically different optimization scheme which builds on a spectral representation of the linear transfer of information between layers. The gradient is hence calculated with respect to both eigenvalues and eigenvectors with negligible increase in terms of computational and complexity load, as compared to standard training algorithms. Working in this framework, we could isolate a stable student substructure, that mirrors the true complexity of the teacher in terms of computing neurons, path distribution and topological attributes. When pruning unimportant nodes of the trained student, as follows a ranking that reflects the optimized eigenvalues, no degradation in the recorded performance is seen above a threshold that corresponds to the effective teacher size. The observed behavior can be pictured as a genuine second-order phase transition that bears universality traits.

Geometric representation learning of molecules is challenging yet essential for applications in multiple domains. Despite the impressive breakthroughs made by geometric deep learning in various molecular representation learning tasks, effectively capturing complicated geometric features across spatial dimensions is still underexplored due to the significant difficulties in modeling efficient geometric representations and learning the inherent correlation in 3D structural modeling. These include computational inefficiency, underutilization of vectorial embeddings, and limited generalizability to integrate various geometric properties. To address the raised concerns, we introduce an efficient and effective framework, Scalable Vector Network (SaVeNet), designed to accommodate a range of geometric requirements without depending on costly embeddings. In addition, the proposed framework scales effectively with introduced direction noise. Theoretically, we analyze the desired properties (i.e., invariance and equivariant) and framework efficiency of the SaVeNet. Empirically, we conduct a comprehensive series of experiments to evaluate the efficiency and expressiveness of the proposed model. Our efficiency-focused experiments underscore the model's empirical superiority over existing methods. Experimental results on synthetic and real-world datasets demonstrate the expressiveness of our model, which achieves state-of-the-art performance across various tasks within molecular representation learning.