Related papers: Characteristic classes as obstructions to local ho…
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…
Self-training is a competitive approach in domain adaptive segmentation, which trains the network with the pseudo labels on the target domain. However inevitably, the pseudo labels are noisy and the target features are dispersed due to the…
In this paper, we explore connections between interpretable machine learning and learning theory through the lens of local approximation explanations. First, we tackle the traditional problem of performance generalization and bound the…
These notes are based on a series of five lectures given during the summer school ``Interactions between Homotopy Theory and Algebra'' held at the University of Chicago in 2004.
We consider locally checkable labeling LCL problems in the LOCAL model of distributed computing. Since 2016, there has been a substantial body of work examining the possible complexities of LCL problems. For example, it has been established…
Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how…
The paper relates character value of an irreducible representation of a compact connected Lie group at certain elements of finite order with the dimension of a representation on another group, up to some precise constants, which all have…
Adversarial attacks have been widely studied for general classification tasks, but remain unexplored in the context of fine-grained recognition, where the inter-class similarities facilitate the attacker's task. In this paper, we identify…
The antinuclear antibody detection with human epithelial cells is a popular approach for autoimmune diseases diagnosis. The manual evaluation demands time, effort and capital, and automation in screening can greatly aid the physicians in…
Sometimes, it is very important to consider what type of setting is assumed when studying a mathematical object. For example, in Galois theory, properties can completely change if we study a field extension over $F_p$ instead of a field…
The fact that deep neural networks are susceptible to crafted perturbations severely impacts the use of deep learning in certain domains of application. Among many developed defense models against such attacks, adversarial training emerges…
In this article, we show and discuss our experience in applying the flipped classroom method for teaching Conditional Random Fields in a Natural Language Processing course. We present the activities that we developed together with their…
We study pattern formation for a variational model displaying competition between a local term penalizing interfaces and a non-local term favoring oscillations. By means of a $\Gamma$--convergence analysis, we show that as the parameter J…
Distance-based anomaly detection methods rely on compact in-distribution (ID) embeddings that are well separated from anomalies. However, conventional contrastive learning strategies often struggle to achieve this balance, either promoting…
Those notes rest on the Samuel Eilenberg Lectures I gave at Columbia University, NY, in the fall 2022. I thank all the mathematicians who participated in their elaboration, directly or indirectly. They are meant to be published as a…
Learning representations unaffected by superficial characteristics is important to ensure that shifts in these characteristics at test time do not compromise downstream prediction performance. For instance, in healthcare applications, we…
Unsupervised learning of latent variable models (LVMs) is widely used to represent data in machine learning. When such models reflect the ground truth factors and the mechanisms mapping them to observations, there is reason to expect that…
We introduce refined variants of the Local Learning Coefficient (LLC), a measure of model complexity grounded in singular learning theory, to study the development of internal structure in transformer language models during training. By…
These are my notes for a talk at the The Tate Conjecture workshop at the American Institute of Mathematics in Palo Alto, CA, July 23--July 27, 2007, somewhat revised and expanded. The intent of the talk was to review what is known and to…
Various natural language processing tasks are structured prediction problems where outputs are constructed with multiple interdependent decisions. Past work has shown that domain knowledge, framed as constraints over the output space, can…