口语理解

Network quantization, one of the most widely studied model compression methods, effectively quantizes a floating-point model to obtain a fixed-point one with negligible accuracy loss. Although great success was achieved in reducing the model size, it may exacerbate the unfairness in model accuracy across different groups of datasets. This paper considers two widely used algorithms: Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT), with an attempt to understand how they cause this critical issue. Theoretical analysis with empirical verifications reveals two responsible factors, as well as how they influence a metric of fairness in depth. A comparison between PTQ and QAT is then made, explaining an observation that QAT behaves even worse than PTQ in fairness, although it often preserves a higher accuracy at lower bit-widths in quantization. Finally, the paper finds out that several simple data augmentation methods can be adopted to alleviate the disparate impacts of quantization, based on a further observation that class imbalance produces distinct values of the aforementioned factors among different attribute classes. We experiment on either imbalanced (UTK-Face and FER2013) or balanced (CIFAR-10 and MNIST) datasets using ResNet and VGG models for empirical evaluation.

Recent years have seen significant progress in developing spiking neural networks (SNNs) as a potential solution to the energy challenges posed by conventional artificial neural networks (ANNs). However, our theoretical understanding of SNNs remains relatively limited compared to the ever-growing body of literature on ANNs. In this paper, we study a discrete-time model of SNNs based on leaky integrate-and-fire (LIF) neurons, referred to as discrete-time LIF-SNNs, a widely used framework that still lacks solid theoretical foundations. We demonstrate that discrete-time LIF-SNNs realize piecewise constant functions defined on polyhedral regions, and more importantly, we quantify the network size required to approximate continuous functions. Moreover, we investigate the impact of latency (number of time steps) and depth (number of layers) on the complexity of the input space partitioning induced by discrete-time LIF-SNNs. Our analysis highlights the importance of latency and contrasts these networks with ANNs that use piecewise linear activation functions. Finally, we present numerical experiments to support our theoretical findings.

Predictive posterior densities (PPDs) are essential in approximate inference for quantifying predictive uncertainty and comparing inference methods. Typically, PPDs are estimated by simple Monte Carlo (MC) averages. In this paper, we expose a critical under-recognized issue: the signal-to-noise ratio (SNR) of the simple MC estimator can sometimes be extremely low, leading to unreliable estimates. Our main contribution is a theoretical analysis demonstrating that even with exact inference, SNR can decay rapidly with an increase in (a) the mismatch between training and test data, (b) the dimensionality of the latent space, or (c) the size of test data relative to training data. Through several examples, we empirically verify these claims and show that these factors indeed lead to poor SNR and unreliable PPD estimates (sometimes, estimates are off by hundreds of nats even with a million samples). While not the primary focus, we also explore an adaptive importance sampling approach as an illustrative way to mitigate the problem, where we learn the proposal distribution by maximizing a variational proxy to the SNR. Taken together, our findings highlight an important challenge and provide essential insights for reliable estimation.

In this paper, we investigate the properties of the Sliced Wasserstein Distance (SW) when employed as an objective functional. The SW metric has gained significant interest in the optimal transport and machine learning literature, due to its ability to capture intricate geometric properties of probability distributions while remaining computationally tractable, making it a valuable tool for various applications, including generative modeling and domain adaptation. Our study aims to provide a rigorous analysis of the critical points arising from the optimization of the SW objective. By computing explicit perturbations, we establish that stable critical points of SW cannot concentrate on segments. This stability analysis is crucial for understanding the behaviour of optimization algorithms for models trained using the SW objective. Furthermore, we investigate the properties of the SW objective, shedding light on the existence and convergence behavior of critical points. We illustrate our theoretical results through numerical experiments.

Personalized federated learning (PFL) offers a flexible framework for aggregating information across distributed clients with heterogeneous data. This work considers a personalized federated learning setting that simultaneously learns global and local models. While purely local training has no communication cost, collaborative learning among the clients can leverage shared knowledge to improve statistical accuracy, presenting an accuracy-communication trade-off in personalized federated learning. However, the theoretical analysis of how personalization quantitatively influences sample and algorithmic efficiency and their inherent trade-off is largely unexplored. This paper makes a contribution towards filling this gap, by providing a quantitative characterization of the personalization degree on the tradeoff. The results further offer theoretical insights for choosing the personalization degree. As a side contribution, we establish the minimax optimality in terms of statistical accuracy for a widely studied PFL formulation. The theoretical result is validated on both synthetic and real-world datasets and its generalizability is verified in a non-convex setting.

Neural network minima are often connected by curves along which train and test loss remain nearly constant, a phenomenon known as mode connectivity. While this property has enabled applications such as model merging and fine-tuning, its theoretical explanation remains unclear. We propose a new approach to exploring the connectedness of minima using parameter space symmetry. By linking the topology of symmetry groups to that of the minima, we derive the number of connected components of the minima of linear networks and show that skip connections reduce this number. We then examine when mode connectivity and linear mode connectivity hold or fail, using parameter symmetries which account for a significant part of the minimum. Finally, we provide explicit expressions for connecting curves in the minima induced by symmetry. Using the curvature of these curves, we derive conditions under which linear mode connectivity approximately holds. Our findings highlight the role of continuous symmetries in understanding the neural network loss landscape.

In-context learning based on attention models is examined for data with categorical outcomes, with inference in such models viewed from the perspective of functional gradient descent (GD). We develop a network composed of attention blocks, with each block employing a self-attention layer followed by a cross-attention layer, with associated skip connections. This model can exactly perform multi-step functional GD inference for in-context inference with categorical observations. We perform a theoretical analysis of this setup, generalizing many prior assumptions in this line of work, including the class of attention mechanisms for which it is appropriate. We demonstrate the framework empirically on synthetic data, image classification and language generation.

Deep tabular models have demonstrated remarkable success on i.i.d. data, excelling in a variety of structured data tasks. However, their performance often deteriorates under temporal distribution shifts, where trends and periodic patterns are present in the evolving data distribution over time. In this paper, we explore the underlying reasons for this failure in capturing temporal dependencies. We begin by investigating the training protocol, revealing a key issue in how the data is split for model training and validation. While existing approaches typically use temporal ordering for splitting, we show that even a random split significantly improves model performance. By accounting for reducing training lag and validation bias to achieve better generalization ability, our proposed splitting protocol offers substantial improvements across a variety of methods. Furthermore, we analyses how temporal data affects deep tabular representations, uncovering that these models often fail to capture crucial periodic and trend information. To address this gap, we introduce a plug-and-play temporal embedding based on Fourier series expansion to learn and incorporate temporal patterns, offering an adaptive approach to handle temporal shifts. Our experiments demonstrate that this temporal embedding, combined with the improved splitting strategy, provides a more effective and robust framework for learning from temporal tabular data.

We study the computational model where we can access a matrix $\mathbf{A}$ only by computing matrix-vector products $\mathbf{A}\mathrm{x}$ for vectors of the form $\mathrm{x} = \mathrm{x}_1 \otimes \cdots \otimes \mathrm{x}_q$. We prove exponential lower bounds on the number of queries needed to estimate various properties, including the trace and the top eigenvalue of $\mathbf{A}$. Our proofs hold for all adaptive algorithms, modulo a mild conditioning assumption on the algorithm's queries. We further prove that algorithms whose queries come from a small alphabet (e.g., $\mathrm{x}_i \in \\{\pm1\\}^n$) cannot test if $\mathbf{A}$ is identically zero with polynomial complexity, despite the fact that a single query using Gaussian vectors solves the problem with probability 1. In steep contrast to the non-Kronecker case, this shows that sketching $\mathbf{A}$ with different distributions of the same subguassian norm can yield exponentially different query complexities. Our proofs follow from the observation that random vectors with Kronecker structure have exponentially smaller inner products than their non-Kronecker counterparts.

One explanation for the strong generalization ability of neural networks is implicit bias. Yet, the definition and mechanism of implicit bias in non-linear contexts remains little understood. In this work, we propose to characterize implicit bias by the count of connected regions in the input space with the same predicted label. Compared with parameter-dependent metrics (e.g., norm or normalized margin), region count can be better adapted to nonlinear, overparameterized models, because it is determined by the function mapping and is invariant to reparametrization. Empirically, we found that small region counts align with geometrically simple decision boundaries and correlate well with good generalization performance. We also observe that good hyper-parameter choices such as larger learning rates and smaller batch sizes can induce small region counts. We further establish the theoretical connections and explain how larger learning rate can induce small region counts in neural networks.