In personalized federated learning, each member of a potentially large set of agents aims to train a model minimizing its loss function averaged over its local data distribution. We study this problem under the lens of stochastic optimization, focusing on a scenario with a large number of agents, that each possess very few data samples from their local data distribution. Specifically, we prove novel matching lower and upper bounds on the number of samples required from all agents to approximately minimize the generalization error of a fixed agent. We provide strategies matching these lower bounds, based on a gradient filtering approach: given prior knowledge on some notion of distance between local data distributions, agents filter and aggregate stochastic gradients received from other agents, in order to achieve an optimal bias-variance trade-off. Finally, we quantify the impact of using rough estimations of the distances between local distributions of agents, based on a very small number of local samples.

A major challenge in designing efficient statistical supervised learning algorithms is finding representations that perform well not only on available training samples but also on unseen data. While the study of representation learning has spurred much interest, most existing such approaches are heuristic; and very little is known about theoretical generalization guarantees. For example, the information bottleneck method seeks a good generalization by finding a minimal description of the input that is maximally informative about the label variable, where minimality and informativeness are both measured by Shannon's mutual information. In this paper, we establish a compressibility framework that allows us to derive upper bounds on the generalization error of a representation learning algorithm in terms of the "Minimum Description Length" (MDL) of the labels or the latent variables (representations). Rather than the mutual information between the encoder's input and the representation, which is often believed to reflect the algorithm's generalization capability in the related literature but in fact, falls short of doing so, our new bounds involve the "multi-letter" relative entropy between the distribution of the representations (or labels) of the training and test sets and a fixed prior.

How do brain circuits learn to generate behaviour? While significant strides have been made in understanding learning in artificial neural networks, applying this knowledge to biological networks remains challenging. For instance, while backpropagation is known to perform accurate credit assignment of error in artificial neural networks, how a similarly powerful process can be realized within the constraints of biological circuits remains largely unclear. One of the major challenges is that the brain's extensive recurrent connectivity requires the propagation of error through both space and time, a problem that is notoriously difficult to solve in vanilla recurrent neural networks. Moreover, the extensive feedback connections in the brain are known to influence forward network activity, but the interaction between feedback-driven activity changes and local, synaptic plasticity-based learning is not fully understood. Building on our previous work modelling motor learning, this work investigates the mechanistic properties of pre-trained networks with feedback control on a standard motor task. We show that feedback control of the ongoing recurrent network dynamics approximates the optimal first-order gradient with respect to the network activities, allowing for rapid, ongoing movement correction. Moreover, we show that trial-by-trial adaptation to a persistent perturbation using a local, biologically plausible learning rule that integrates recent activity and error feedback is both more accurate and more efficient with feedback control during learning, due to the decoupling of the recurrent network dynamics and the injection of an adaptive, second-order gradient into the network dynamics. Thus, our results suggest that feedback control may guide credit assignment in biological recurrent neural networks, enabling both rapid and efficient learning in the brain.

A.1 Detailed Re-alignment Task Formulation and Training Setup In Figure A1, we show the procedure for converting the data samples in the alignment datasets into training data of AEM (negative samples used in AIL are generated similarly). In DP-inferred chain-of-edits (CoEs), we use a few special tokens to mark the editing operations (with their position and content). Then our decipher module will translate these special tokens into natural language. As the final step, we add a special token [SEP] between Context + Source and the ground truth Chain-of-Edits (CoEs) and Target, as a boundary signal similar to the settings in text-to-text training. During inference, we input a certain Context + Source, and the LM trained by SECONDTHOUGHTS can generate CoEs and the corresponding Target.

Reconstruction of 3D neural fields from posed images has emerged as a promising method for self-supervised representation learning. The key challenge preventing the deployment of these 3D scene learners on large-scale video data is their dependence on precise camera poses from structure-from-motion, which is prohibitively expensive to run at scale. We propose a method that jointly reconstructs camera poses and 3D neural scene representations online and in a single forward pass. We estimate poses by first lifting frame-to-frame optical flow to 3D scene flow via differentiable rendering, preserving locality and shift-equivariance of the image processing backbone. SE(3) camera pose estimation is then performed via a weighted least-squares fit to the scene flow field. This formulation enables us to jointly supervise pose estimation and a generalizable neural scene representation via re-rendering the input video, and thus, train end-to-end and fully self-supervised on real-world video datasets. We demonstrate that our method performs robustly on diverse, real-world video, notably on sequences traditionally challenging to optimization-based pose estimation techniques.

Molecular Representation Learning (MRL) has emerged as a powerful tool for drug and materials discovery in a variety of tasks such as virtual screening and inverse design. While there has been a surge of interest in advancing modelcentric techniques, the influence of both data quantity and quality on molecular representations is not yet clearly understood within this field.