Despite extensive studies, the underlying reason as to why overparameterized neural networks can generalize remains elusive. Existing theory shows that common stochastic optimizers prefer flatter minimizers of the training loss, and thus a natural potential explanation is that flatness implies generalization. This work critically examines this explanation. Through theoretical and empirical investigation, we identify the following three scenarios for two-layer ReLU networks: (1) flatness provably implies generalization; (2) there exist non-generalizing flattest models and sharpness minimization algorithms fail to generalize poorly, and (3) perhaps most strikingly, there exist non-generalizing flattest models, but sharpness minimization algorithms still generalize. Our results suggest that the relationship between sharpness and generalization subtly depends on the data distributions and the model architectures and sharpness minimization algorithms do not only minimize sharpness to achieve better generalization. This calls for the search for other explanations for the generalization of over-parameterized neural networks.

This paper presents new projection-free algorithms for Online Convex Optimization (OCO) over a convex domain K Rd. Classical OCO algorithms (such as Online Gradient Descent) typically need to perform Euclidean projections onto the convex set K to ensure feasibility of their iterates. Alternative algorithms, such as those based on the Frank-Wolfe method, swap potentially-expensive Euclidean projections onto Kfor linear optimization over K. However, such algorithms have a sub-optimal regret in OCO compared to projection-based algorithms. In this paper, we look at a third type of algorithms that output approximate Newton iterates using a self-concordant barrier for the set of interest. The use of a self-concordant barrier automatically ensures feasibility without the need of projections. However, the computation of the Newton iterates requires a matrix inverse, which can still be expensive. As our main contribution, we show how the stability of the Newton iterates can be leveraged to only compute the inverse Hessian a vanishing fractions of the rounds, leading to a new efficient projection-free OCO algorithm with a state-of-the-art regret bound.

Most recurrent neural networks (RNNs) do not include a fundamental constraint of real neural circuits: Dale's Law, which implies that neurons must be excitatory (E) or inhibitory (I). Dale's Law is generally absent from RNNs because simply partitioning a standard network's units into E and I populations impairs learning. However, here we extend a recent feedforward bio-inspired EI network architecture, named Dale's ANNs, to recurrent networks, and demonstrate that good performance is possible while respecting Dale's Law. This begs the question: What makes some forms of EI network learn poorly and others learn well? And, why does the simple approach of incorporating Dale's Law impair learning? Historically the answer was thought to be the sign constraints on EI network parameters, and this was a motivation behind Dale's ANNs. However, here we show the spectral properties of the recurrent weight matrix at initialisation are more impactful on network performance than sign constraints. We find that simple EI partitioning results in a singular value distribution that is multimodal and dispersed, whereas standard RNNs have an unimodal, more clustered singular value distribution, as do recurrent Dale's ANNs. We also show that the spectral properties and performance of partitioned EI networks are worse for small networks with fewer I units, and we present normalised SVD entropy as a measure of spectrum pathology that correlates with performance.

In the rapidly evolving landscape of smart home automation, the potential of IoT devices is vast. In this realm, rules are the main tool utilized for this automation, which are predefined conditions or triggers that establish connections between devices, enabling seamless automation of specific processes. However, one significant challenge researchers face is the lack of comprehensive datasets to explore and advance the field of smart home rule recommendations. These datasets are essential for developing and evaluating intelligent algorithms that can effectively recommend rules for automating processes while preserving the privacy of the users, as it involves personal information about users' daily lives. To bridge this gap, we present the Wyze Rule Dataset, a large-scale dataset designed specifically for smart home rule recommendation research. Wyze Rule encompasses over 1 million rules gathered from a diverse user base of 300,000 individuals from Wyze Labs, offering an extensive and varied collection of real-world data. With a focus on federated learning, our dataset is tailored to address the unique challenges of a cross-device federated learning setting in the recommendation domain, featuring a large-scale number of clients with widely heterogeneous data. To establish a benchmark for comparison and evaluation, we have meticulously implemented multiple baselines in both centralized and federated settings. Researchers can leverage these baselines to gauge the performance and effectiveness of their rule recommendation systems, driving advancements in the domain.