We study tropical circuits with scalar multiplication gates, that is, algebraic circuits whose gates implement $\max$, $+$, or multiplication with a positive constant. For such circuits, we prove exponential size lower bounds for computing maximum weight directed spanning trees and maximum weight bipartite perfect matchings. As a corollary, we obtain an exponential size separation between monotone and non-monotone maxout neural networks, which generalize the popularly used ReLU neural networks. One conclusion from this is that neural network models with enforced convexity constraints, such as input-convex neural networks (ICNNs), sometimes need to be exponentially larger than their unrestricted counterparts in order to express the same functions.
A central design principle in modern machine learning and artificial intelligence is to align a model's inductive bias with the structure of its input data. For matrix-valued inputs, relevant matrix-level relationships can be characterised through spectral values and spectral sub…
Automating theoretical research is constrained not only by the generation of candidate results, but also by their reliable evaluation. A common approach is to close the research loop with a large language model (LLM) reviewer. However, such reviewers remain empirically unreliable…
Singular value soft-thresholding can be computed via a reduction to the matrix polar decomposition, which allows one to exploit GPU-friendly algorithms for computing the polar decomposition. Empirically, there is a significant speed-up on GPUs compared to the standard approach us…
In this paper, we propose a new solution for addressing the content cold-start problem in industry-scale search and recommender systems. Compared to prior approaches, we have made the following new contributions: 1) our solution spans the entire multi-stage funnel and generalizes…
Dysphagia is a debilitating late effect of head and neck cancer (HNC) treatment, yet timely identification of at-risk patients remains challenging in survivorship care. Definitive assessment relies on videofluoroscopic imaging, as captured by the Dynamic Imaging Grade of Swallowi…
Electroencephalography (EEG) is widely used to diagnose neurological conditions, but its analysis usually relies on either predefined spectral features or deep neural networks. Predefined features carry a strong bias, since they fix in advance what counts as informative, while de…