Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties. In short, the barycenter task is to take the average of a collection of probability distributions w.r.t.

We take an unorthodox view of voting by expanding the design space to include both the elicitation rule, whereby voters map their (cardinal) preferences to votes, and the aggregation rule, which transforms the reported votes into collective decisions. Intuitively, there is a tradeoff between the communication requirements of the elicitation rule (i.e., the number of bits of information that voters need to provide about their preferences) and the efficiency of the outcome of the aggregation rule, which we measure through distortion (i.e., how well the utilitarian social welfare of the outcome approximates the maximum social welfare in the worst case). Our results chart the Pareto frontier of the communication-distortion tradeoff.

Depth-wise Separable Convolution (DSConv) has a powerful representation even with fewer parameters and computation, leading to its adoption by almost all of the state-of-the-art CNN models. DSConv models are already compact making it hard to apply pruning, and there are few previous pruning techniques that target depth-wise convolution (DW-conv). In this paper, we present Depth-wise Separable Convolution Pruning (DEPrune), a novel pruning method applied to both point-wise and depth-wise convolutions. DEPrune is optimized by analyzing the computation of DSConv on GPUs. DEPrune employs a fine-grained pruning approach, yet it achieves the structured sparsity typically absent in fine-grained pruning, enabling practical hardware acceleration. Moreover, this method maintains a high pruning ratio without causing any accuracy drop. We additionally represent techniques that further enhance DEPrune performance: 1) balanced workload tuning (BWT), and 2) hardware-aware sparsity recalibration (HSR). Experiment results show that DEPrune achieves up to 3.74 practical speedup in DSConv inference on GPUs while maintaining the accuracy of EfficientNet-B0 on ImageNet.

Stochastic gradient descent with a large initial learning rate is widely used for training modern neural net architectures. Although a small initial learning rate allows for faster training and better test performance initially, the large learning rate achieves better generalization soon after the learning rate is annealed. Towards explaining this phenomenon, we devise a setting in which we can prove that a two layer network trained with large initial learning rate and annealing provably generalizes better than the same network trained with a small learning rate from the start. The key insight in our analysis is that the order of learning different types of patterns is crucial: because the small learning rate model first memorizes easy-to-generalize, hard-to-fit patterns, it generalizes worse on hard-to-generalize, easier-to-fit patterns than its large learning rate counterpart. This concept translates to a larger-scale setting: we demonstrate that one can add a small patch to CIFAR-10 images that is immediately memorizable by a model with small initial learning rate, but ignored by the model with large learning rate until after annealing. Our experiments show that this causes the small learning rate model's accuracy on unmodified images to suffer, as it relies too much on the patch early on.

Spike Timing-Dependent Plasticity (STDP) is a promising substitute to backpropagation for local training of Spiking Neural Networks (SNNs) on neuromorphic hardware. STDP allows SNNs to address classification tasks by combining unsupervised STDP for feature extraction and supervised STDP for classification. Unsupervised STDP is usually employed with Winner-Takes-All (WTA) competition to learn distinct patterns. However, WTA for supervised STDP classification faces unbalanced competition challenges. In this paper, we propose a method to effectively implement WTA competition in a spiking classification layer employing first-spike coding and supervised STDP training.

We consider the task of active geo-localization (AGL) in which an agent uses a sequence of visual cues observed during aerial navigation to find a target specified through multiple possible modalities. This could emulate a UAV involved in a search-and-rescue operation navigating through an area, observing a stream of aerial images as it goes. The AGL task is associated with two important challenges. Firstly, an agent must deal with a goal specification in one of multiple modalities (e.g., through a natural language description) while the search cues are provided in other modalities (aerial imagery). The second challenge is limited localization time (e.g., limited battery life, urgency) so that the goal must be localized as efficiently as possible, i.e. the agent must effectively leverage its sequentially observed aerial views when searching for the goal. To address these challenges, we propose GOMAA-Geo - a goal modality agnostic active geo-localization agent - for zeroshot generalization between different goal modalities. Our approach combines cross-modality contrastive learning to align representations across modalities with supervised foundation model pretraining and reinforcement learning to obtain highly effective navigation and localization policies. Through extensive evaluations, we show that GOMAA-Geo outperforms alternative learnable approaches and that it generalizes across datasets - e.g., to disaster-hit areas without seeing a single disaster scenario during training - and goal modalities - e.g., to ground-level imagery or textual descriptions, despite only being trained with goals specified as aerial views. Our code is available at: https://github.com/mvrl/GOMAA-Geo.

Knowledge Distillation is the mechanism by which the insights gained from a larger teacher model are transferred to a smaller student model. However, the transfer suffers when the teacher model is significantly larger than the student. To overcome this, prior works have proposed training intermediately sized models, Teacher Assistants (TAs) to help the transfer process. However, training TAs is expensive, as training these models is a knowledge transfer task in itself. Further, these TAs are larger than the student model and training them especially in large data settings can be computationally intensive.

Recently, there has been growing evidence that if the width and depth of a neural network are scaled toward the so-called rich feature learning limit (µP and its depth extension), then some hyperparameters -- such as the learning rate -- exhibit transfer from small to very large models. From an optimization perspective, this phenomenon is puzzling, as it implies that the loss landscape is consistently similar across very different model sizes. In this work, we study the landscape through the lens of the loss Hessian, with a focus on its largest eigenvalue (i.e. the sharpness), and find that certain spectral properties under µP are largely independent of the size of the network, and remain consistent as training progresses. We name this property Super Consistency of the landscape. On the other hand, we show that in the Neural Tangent Kernel (NTK) and other scaling regimes, the sharpness exhibits very different dynamics at different scales.

Certified defenses against adversarial attacks offer formal guarantees on the robustness of a model, making them more reliable than empirical methods such as adversarial training, whose effectiveness is often later reduced by unseen attacks. Still, the limited certified robustness that is currently achievable has been a bottleneck for their practical adoption. Gowal et al. and Wang et al. have shown that generating additional training data using state-of-the-art diffusion models can considerably improve the robustness of adversarial training. In this work, we demonstrate that a similar approach can substantially improve deterministic certified defenses but also reveal notable differences in the scaling behavior between certified and empirical methods. In addition, we provide a list of recommendations to scale the robustness of certified training approaches.

We present an optimal method for encoding cluster assignments of arbitrary data sets. Our method, Random Cycle Coding (RCC), encodes data sequentially and sends assignment information as cycles of the permutation defined by the order of encoded elements. RCC does not require any training and its worst-case complexity scales quasi-linearly with the size of the largest cluster. We characterize the achievable bit rates as a function of cluster sizes and number of elements, showing RCC consistently outperforms previous methods while requiring less compute and memory resources. Experiments show RCC can save up to 2 bytes per element when applied to vector databases, and removes the need for assigning integer ids to identify vectors, translating to savings of up to 70% in vector database systems for similarity search applications.