Neural network models of memory and error correction famously include the Hopfield network, which can directly store--and error-correct through its dynamics-- arbitrary N-bit patterns, but only for N such patterns. On the other end of the spectrum, Shannon's coding theory established that it is possible to represent exponentially many states ( e

We thank the reviewers for their thoughtful comments. An expander graph code allows simple, neurally plausible decoding to perform at par with BP. These expander codes can also be decoded by belief propagation (BP), but it's harder the other way around. Relevance to neuroscience (R3): We plan to follow this paper with another paper describing neuroscience applications. For space and coherence, this paper focuses on the conceptual theory without elaborating on applications.

Achieving robust 3D perception in the face of corrupted data presents an challenging hurdle within 3D vision research. Contemporary transformer-based point cloud recognition models, albeit advanced, tend to overfit to specific patterns, consequently undermining their robustness against corruption. In this work, we introduce the Target-Guided Adversarial Point Cloud Transformer, termed APCT, a novel architecture designed to augment global structure capture through an adversarial feature erasing mechanism predicated on patterns discerned at each step during training.

We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly smaller than the minimum mixing weight, much less is known when outliers may crowd out low-weight clusters - a setting we refer to as list-decodable mixture learning (LD-ML). In this case, adversarial outliers can simulate additional spurious mixture components. Hence, if all means of the mixture must be recovered up to a small error in the output list, the list size needs to be larger than the number of (true) components. We propose an algorithm that obtains order-optimal error guarantees for each mixture mean with a minimal list-size overhead, significantly improving upon list-decodable mean estimation, the only existing method that is applicable for LD-ML. Although improvements are observed even when the mixture is non-separated, our algorithm achieves particularly strong guarantees when the mixture is separated: it can leverage the mixture structure to partially cluster the samples before carefully iterating a base learner for list-decodable mean estimation at different scales.

In many environments, only a relatively small subset of the complete state space is necessary in order to accomplish a given task. We develop a simple technique using emergency stops (e-stops) to exploit this phenomenon. Using e-stops significantly improves sample complexity by reducing the amount of required exploration, while retaining a performance bound that efficiently trades off the rate of convergence with a small asymptotic sub-optimality gap. We analyze the regret behavior of e-stops and present empirical results in discrete and continuous settings demonstrating that our reset mechanism can provide order-of-magnitude speedups on top of existing reinforcement learning methods.

Deep learning approaches have been widely adopted for precipitation nowcasting in recent years. Previous studies mainly focus on proposing new model architectures to improve pixel-wise metrics. However, they frequently result in blurry predictions which provide limited utility to forecasting operations. In this work, we propose a new Fourier Amplitude and Correlation Loss (FACL) which consists of two novel loss terms: Fourier Amplitude Loss (FAL) and Fourier Correlation Loss (FCL). FAL regularizes the Fourier amplitude of the model prediction and FCL complements the missing phase information.

Feature attributions attempt to highlight what inputs drive predictive power. Good attributions or explanations are thus those that produce inputs that retain this predictive power; accordingly, evaluations of explanations score their quality of prediction. However, evaluations produce scores better than what appears possible from the values in the explanation for a class of explanations, called encoding explanations. Probing for encoding remains a challenge because there is no general characterization of what gives the extra predictive power. We develop a definition of encoding that identifies this extra predictive power via conditional dependence and show that the definition fits existing examples of encoding. This definition implies, in contrast to encoding explanations, that non-encoding explanations contain all the informative inputs used to produce the explanation, giving them a "what you see is what you get" property, which makes them transparent and simple to use.

Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning controllers. Existing methods in the literature for estimating the Lipschitz constant suffer from either lack of accuracy or poor scalability. In this paper, we present a convex optimization framework to compute guaranteed upper bounds on the Lipschitz constant of DNNs both accurately and efficiently. Our main idea is to interpret activation functions as gradients of convex potential functions. Hence, they satisfy certain properties that can be described by quadratic constraints.

We thank the reviewers for their constructive comments. We will release the code necessary to reproduce these results. This conversion implicitly handles the padding and stride hyperparameters. Therefore, we can directly use LipSDP for CNNs. Reviewer 1: Software release: We have already implemented the software necessary to reproduce our results.

Especially we appreciate your suggestion of underdamped Langevin for further consideration.