A central question in the theory of machine learning concerns the identification of classes of data distributions for which one can provide computationally efficient learning algorithms with provable statistical learning guarantees. Indeed, in the context of probably approximately correct (PAC) learning, there has been much interest in exploring intermediate PAC learning models that, unlike the realizable PAC learning setting, allow for some stochasticity in the labels, and unlike the fully agnostic PAC learning setting, also admit computationally efficient learning algorithms with finite sample complexity bounds. Some examples of such models include random classification noise (RCN), probabilistic concepts, Massart noise, and generalized linear models (GLMs); in general, most of this work has focused on binary classification problems. In this paper, we study what we call realizable-statistic models (RSMs), wherein we allow stochastic labels but assume that some vector-valued statistic of the conditional label distribution comes from some known function class. RSMs are a flexible class of models that interpolate between the realizable and fully agnostic settings, and that also recover several previously studied models as special cases.

What representation do deep neural networks learn? How similar are images to each other for neural networks? Despite the overwhelming success of deep learning methods key questions about their internal workings still remain largely unanswered, due to their internal high dimensionality and complexity. To address this, one approach is to measure the similarity of activation responses to various inputs.Representational Similarity Matrices (RSMs) distill this similarity into scalar values for each input pair.These matrices encapsulate the entire similarity structure of a system, indicating which input lead to similar responses.While the similarity between images is ambiguous, we argue that the spatial location of semantic objects does neither influence human perception nor deep learning classifiers. Thus this should be reflected in the definition of similarity between image responses for computer vision systems. Revisiting the established similarity calculations for RSMs we expose their sensitivity to spatial alignment. In this paper we propose to solve this through, which are invariant to spatial permutation.

However, achieving this capability necessitates not only an effective scene representation but also an understanding of the mechanisms governing interactions among object subsets. Recent studies have made significant progress in representing scenes using object slots.

However, achieving this capability necessitates not only an effective scene representation but also an understanding of the mechanisms governing interactions among object subsets. Recent studies have made significant progress in representing scenes using object slots.

Agents with the ability to comprehend and reason about the dynamics of objects would be expected to exhibit improved robustness and generalization in novel scenarios. However, achieving this capability necessitates not only an effective scene representation but also an understanding of the mechanisms governing interactions among object subsets. Recent studies have made significant progress in representing scenes using object slots. In this work, we introduce Reusable Slotwise Mechanisms, or RSM, a framework that models object dynamics by leveraging communication among slots along with a modular architecture capable of dynamically selecting reusable mechanisms for predicting the future states of each object slot. Crucially, RSM leverages the Central Contextual Information (CCI), enabling selected mechanisms to access the remaining slots through a bottleneck, effectively allowing for modeling of higher order and complex interactions that might require a sparse subset of objects. Experimental results demonstrate the superior performance of RSM compared to state-of-the-art methods across various future prediction and related downstream tasks, including Visual Question Answering and action planning. Furthermore, we showcase RSM's Out-of-Distribution generalization ability to handle scenes in intricate scenarios.

Agents with the ability to comprehend and reason about the dynamics of objects would be expected to exhibit improved robustness and generalization in novel scenarios. However, achieving this capability necessitates not only an effective scene representation but also an understanding of the mechanisms governing interactions among object subsets. Recent studies have made significant progress in representing scenes using object slots. In this work, we introduce Reusable Slotwise Mechanisms, or RSM, a framework that models object dynamics by leveraging communication among slots along with a modular architecture capable of dynamically selecting reusable mechanisms for predicting the future states of each object slot. Crucially, RSM leverages the Central Contextual Information (CCI), enabling selected mechanisms to access the remaining slots through a bottleneck, effectively allowing for modeling of higher order and complex interactions that might require a sparse subset of objects.