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We analyze the loss landscape and expressiveness of practical deep convolutional neural networks (CNNs) with shared weights and max pooling layers. We show that such CNNs produce linearly independent features at a "wide" layer which has…

Balancing the trade-off between safety and efficiency is of significant importance for path planning under uncertainty. Many risk-aware path planners have been developed to explicitly limit the probability of collision to an acceptable…

Neural ranking models have achieved remarkable progress and are now widely deployed in real-world applications such as Retrieval-Augmented Generation (RAG). However, like other neural architectures, they remain vulnerable to adversarial…

In this paper, we investigate a new variant of neural architecture search (NAS) paradigm -- searching with random labels (RLNAS). The task sounds counter-intuitive for most existing NAS algorithms since random label provides few information…

Robustness is a crucial factor for the successful deployment of robots in unstructured environments, particularly in the domain of Simultaneous Localization and Mapping (SLAM). Simulation-based benchmarks have emerged as a highly scalable…

Large margin nearest neighbor (LMNN) is a metric learner which optimizes the performance of the popular $k$NN classifier. However, its resulting metric relies on pre-selected target neighbors. In this paper, we address the feasibility of…

We present a novel method for reliably explaining the predictions of neural networks. We consider an explanation reliable if it identifies input features relevant to the model output by considering the input and the neighboring data points.…

Evolving Neural Networks (NNs) has recently seen an increasing interest as an alternative path that might be more successful. It has many advantages compared to other approaches, such as learning the architecture of the NNs. However, the…

Recent studies on the adversarial vulnerability of neural networks have shown that models trained to be more robust to adversarial attacks exhibit more interpretable saliency maps than their non-robust counterparts. We aim to quantify this…

Combinatorial optimization problems implicitly define fitness landscapes that combine the numeric structure of the 'fitness' function to be maximized with the combinatorial structure of which assignments are 'adjacent'. Local search starts…

Experimental studies on enzyme evolution show that only a small fraction of all possible mutation trajectories are accessible to evolution. However, these experiments deal with individual enzymes and explore a tiny part of the fitness…

Marginal optima are minima or maxima of a function with many nearly flat directions. In settings with many competing optima, marginal ones tend to attract algorithms and physical dynamics. Often, the important family of marginal attractors…

Graph Neural Networks (GNNs) have improved unsupervised community detection of clustered nodes due to their ability to encode the dual dimensionality of the connectivity and feature information spaces of graphs. Identifying the latent…

We tackle the problem of robust novelty detection, where we aim to detect novelties in terms of semantic content while being invariant to changes in other, irrelevant factors. Specifically, we operate in a setup with multiple environments,…

This paper introduces new parameterizations of equilibrium neural networks, i.e. networks defined by implicit equations. This model class includes standard multilayer and residual networks as special cases. The new parameterization admits a…

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…

In this work, we consider ranking problems among a finite set of candidates: for instance, selecting the top-$k$ items among a larger list of candidates or obtaining the full ranking of all items in the set. These problems are often…

The nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rank-one factors needed to reconstruct it exactly. The problem of determining this rank and computing the corresponding nonnegative factors is difficult;…

Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of…

Neural collapse ($\mathcal{NC}$) is a phenomenon observed in classification tasks where top-layer representations collapse into their class means, which become equinorm, equiangular and aligned with the classifiers. These behaviours --…