Online learning with graph-structured feedback against adaptive adversaries

We derive upper and lower bounds for the policy regret of $T$-round online learning problems with graph-structured feedback, where the adversary is nonoblivious but assumed to have a bounded memory. We obtain upper bounds of $\widetilde O(T^{2/3})$ and $\widetilde O(T^{3/4})$ for strongly-observable and weakly-observable graphs, respectively, based on analyzing a variant of the Exp3 algorithm. When the adversary is allowed a bounded memory of size 1, we show that a matching lower bound of $\widetilde\Omega(T^{2/3})$ is achieved in the case of full-information feedback. We also study the particular loss structure of an oblivious adversary with switching costs, and show that in such a setting, non-revealing strongly-observable feedback graphs achieve a lower bound of $\widetilde\Omega(T^{2/3})$, as well.Comment: This paper has been accepted to ISIT 201

On the Neural Tangent Kernel of Equilibrium Models

This work studies the neural tangent kernel (NTK) of the deep equilibrium (DEQ) model, a practical ``infinite-depth'' architecture which directly computes the infinite-depth limit of a weight-tied network via root-finding. Even though the NTK of a fully-connected neural network can be stochastic if its width and depth both tend to infinity simultaneously, we show that contrarily a DEQ model still enjoys a deterministic NTK despite its width and depth going to infinity at the same time under mild conditions. Moreover, this deterministic NTK can be found efficiently via root-finding

Leveraging Multiple Descriptive Features for Robust Few-shot Image Learning

Modern image classification is based upon directly predicting model classes via large discriminative networks, making it difficult to assess the intuitive visual ``features'' that may constitute a classification decision. At the same time, recent works in joint visual language models such as CLIP provide ways to specify natural language descriptions of image classes but typically focus on providing single descriptions for each class. In this work, we demonstrate that an alternative approach, arguably more akin to our understanding of multiple ``visual features'' per class, can also provide compelling performance in the robust few-shot learning setting. In particular, we automatically enumerate multiple visual descriptions of each class -- via a large language model (LLM) -- then use a vision-image model to translate these descriptions to a set of multiple visual features of each image; we finally use sparse logistic regression to select a relevant subset of these features to classify each image. This both provides an ``intuitive'' set of relevant features for each class, and in the few-shot learning setting, outperforms standard approaches such as linear probing. When combined with finetuning, we also show that the method is able to outperform existing state-of-the-art finetuning approaches on both in-distribution and out-of-distribution performance

Monotone deep Boltzmann machines

Deep Boltzmann machines (DBMs), one of the first ``deep'' learning methods ever studied, are multi-layered probabilistic models governed by a pairwise energy function that describes the likelihood of all variables/nodes in the network. In practice, DBMs are often constrained, i.e., via the \emph{restricted} Boltzmann machine (RBM) architecture (which does not permit intra-layer connections), in order to allow for more efficient inference. In this work, we revisit the generic DBM approach, and ask the question: are there other possible restrictions to their design that would enable efficient (approximate) inference? In particular, we develop a new class of restricted model, the monotone DBM, which allows for arbitrary self-connection in each layer, but restricts the \emph{weights} in a manner that guarantees the existence and global uniqueness of a mean-field fixed point. To do this, we leverage tools from the recently-proposed monotone Deep Equilibrium model and show that a particular choice of activation results in a fixed-point iteration that gives a variational mean-field solution. While this approach is still largely conceptual, it is the first architecture that allows for efficient approximate inference in fully-general weight structures for DBMs. We apply this approach to simple deep convolutional Boltzmann architectures and demonstrate that it allows for tasks such as the joint completion and classification of images, within a single deep probabilistic setting, while avoiding the pitfalls of mean-field inference in traditional RBMs