Temporal prediction is inherently uncertain, but representing the ambiguity in natural image sequences is a challenging high-dimensional probabilistic inference problem. For natural scenes, the curse of dimensionality renders explicit density estimation statistically and computationally intractable. Here, we describe an implicit regression-based framework for learning and sampling the conditional density of the next frame in a video given previous observed frames. We show that sequence-to-image deep networks trained on a simple resilience-to-noise objective function extract adaptive representations for temporal prediction. Synthetic experiments demonstrate that this score-based framework can handle occlusion boundaries: unlike classical methods that average over bifurcating temporal trajectories, it chooses among likely trajectories, selecting more probable options with higher frequency. Furthermore, analysis of networks trained on natural image sequences reveals that the representation automatically weights predictive evidence by its reliability, which is a hallmark of statistical inference
Vision transformers have gained popularity recently, leading to the development of new vision backbones with improved features and consistent performance gains. However, these advancements are not solely attributable to novel feature transformation designs; certain benefits also arise from advanced network-level and block-level architectures. This paper aims to identify the real gains of popular convolution and attention operators through a detailed study. We find that the key difference among these feature transformation modules, such as attention or convolution, lies in their spatial feature aggregation approach, known as the "spatial token mixer" (STM). To facilitate an impartial comparison, we introduce a unified architecture to neutralize the impact of divergent network-level and block-level designs. Subsequently, various STMs are integrated into this unified framework for comprehensive comparative analysis. Our experiments on various tasks and an analysis of inductive bias show a significant performance boost due to advanced network-level and block-level designs, but performance differences persist among different STMs. Our detailed analysis also reveals various findings about different STMs, including effective receptive fields, invariance, and adversarial robustness tests.
Stochastic majorization-minimization (SMM) is a class of stochastic optimization algorithms that proceed by sampling new data points and minimizing a recursive average of surrogate functions of an objective function. The surrogates are required to be strongly convex and convergence rate analysis for the general non-convex setting was not available. In this paper, we propose an extension of SMM where surrogates are allowed to be only weakly convex or block multi-convex, and the averaged surrogates are approximately minimized with proximal regularization or block-minimized within diminishing radii, respectively. For the general nonconvex constrained setting with non-i.i.d. data samples, we show that the first-order optimality gap of the proposed algorithm decays at the rate $O((\log n)^{1+\epsilon}/n^{1/2})$ for the empirical loss and $O((\log n)^{1+\epsilon}/n^{1/4})$ for the expected loss, where $n$ denotes the number of data samples processed. Under some additional assumption, the latter convergence rate can be improved to $O((\log n)^{1+\epsilon}/n^{1/2})$. As a corollary, we obtain the first convergence rate bounds for various optimization methods under general nonconvex dependent data setting: Double-averaging projected gradient descent and its generalizations, proximal point empirical risk minimization, and online matrix/tensor decomposition algorithms. We also provide experimental validation of our results.