Deep neural networks are parametric models able to learn complex non-linear functions from few training instances and thus can be deployed to solve many tasks. Their overparameterized architecture, characterized by a number of parameters far larger than that of training data points, enables them to retain entire datasets even with random labels [84]. Even more, this overparameterized regime makes neural network approximations of a given function not unique in the sense that multiple configurations of weights might lead to the same function. Indeed, the output of a feed forward neural network given some fixed input remains unchanged under a set of transformations. For instance, certain weight permutations and sign flips in MLPs leave the output unchanged [9].

The invariance principle from causality is at the heart of notable approaches such as invariant risk minimization (IRM) that seek to address out-of-distribution (OOD) generalization failures. Despite the promising theory, invariance principle-based approaches fail in common classification tasks, where invariant (causal) features capture all the information about the label. Are these failures due to the methods failing to capture the invariance? Or is the invariance principle itself insufficient? To answer these questions, we revisit the fundamental assumptions in linear regression tasks, where invariance-based approaches were shown to provably generalize OOD. In contrast to the linear regression tasks, we show that for linear classification tasks we need much stronger restrictions on the distribution shifts, or otherwise OOD generalization is impossible. Furthermore, even with appropriate restrictions on distribution shifts in place, we show that the invariance principle alone is insufficient. We prove that a form of the information bottleneck constraint along with invariance helps address key failures when invariant features capture all the information about the label and also retains the existing success when they do not. We propose an approach that incorporates both of these principles and demonstrate its effectiveness in several experiments.

In this paper, we introduce spatiotemporal joint filter decomposition to decouple spatial and temporal learning, while preserving spatiotemporal dependency in a video. A 3D convolutional filter is now jointly decomposed over a set of spatial and temporal filter atoms respectively. In this way, a 3D convolutional layer becomes three: a temporal atom layer, a spatial atom layer, and a joint coefficient layer, all three remaining convolutional. One obvious arithmetic manipulation allowed in our joint decomposition is to swap spatial or temporal atoms with a set of atoms that have the same number but different sizes, while keeping the remaining unchanged. For example, as shown later, we can now achieve tempo-invariance by simply dilating temporal atoms only. To illustrate this useful atom-swapping property, we further demonstrate how such a decomposition permits the direct learning of 3DCNNs with full-size videos through iterations of two consecutive sub-stages of learning: In the temporal stage, full-temporal downsampled-spatial data are used to learn temporal atoms and joint coefficients while fixing spatial atoms. In the spatial stage, full-spatial downsampled-temporal data are used for spatial atoms and joint coefficients while fixing temporal atoms. We show empirically on multiple action recognition datasets that, the decoupled spatiotemporal learning significantly reduces the model memory footprints, and allows deep 3DCNNs to model high-spatial long-temporal dependency with limited computational resources while delivering comparable performance.

We consider the problem of model compression for deep neural networks (DNNs) in the challenging one-shot/post-training setting, in which we are given an accurate trained model, and must compress it without any retraining, based only on a small amount of calibration input data. This problem has become popular in view of the emerging software and hardware support for executing models compressed via pruning and/or quantization with speedup, and well-performing solutions have been proposed independently for both compression approaches. In this paper, we introduce a new compression framework which covers both weight pruning and quantization in a unified setting, is time-and space-efficient, and considerably improves upon the practical performance of existing post-training methods. At the technical level, our approach is based on an exact and efficient realization of the classical Optimal Brain Surgeon (OBS) framework of [LeCun, Denker, and Solla, 1990] extended to also cover weight quantization at the scale of modern DNNs. From the practical perspective, our experimental results show that it can improve significantly upon the compression-accuracy trade-offs of existing post-training methods, and that it can enable the accurate compound application of both pruning and quantization in a post-training setting.