arXiv subjects

Anupam Chaudhuri

Publications and source records attributed to Anupam Chaudhuri.

5 recordsLinked to original sources

arXiv2024

Minimising changes to audit when updating decision trees

Interpretable models are important, but what happens when the model is updated on new training data? We propose an algorithm for updating a decision tree while minimising the number of changes to the tree that a human would need to audit. We achieve this via a greedy approach that incorporates the number of changes to the tree as part of the objective function. We compare our algorithm to existing methods and show that it sits in a sweet spot between final accuracy and number of changes to audit.

cs.LG↗

arXiv2024

Detecting out-of-distribution text using topological features of transformer-based language models

To safeguard machine learning systems that operate on textual data against out-of-distribution (OOD) inputs that could cause unpredictable behaviour, we explore the use of topological features of self-attention maps from transformer-based language models to detect when input text is out of distribution. Self-attention forms the core of transformer-based language models, dynamically assigning vectors to words based on context, thus in theory our methodology is applicable to any transformer-based language model with multihead self-attention. We evaluate our approach on BERT and compare it to a traditional OOD approach using CLS embeddings. Our results show that our approach outperforms CLS embeddings in distinguishing in-distribution samples from far-out-of-domain samples, but struggles with near or same-domain datasets.

cs.CL↗

arXiv2024

Quantifying Manifolds: Do the manifolds learned by Generative Adversarial Networks converge to the real data manifold

This paper presents our experiments to quantify the manifolds learned by ML models (in our experiment, we use a GAN model) as they train. We compare the manifolds learned at each epoch to the real manifolds representing the real data. To quantify a manifold, we study the intrinsic dimensions and topological features of the manifold learned by the ML model, how these metrics change as we continue to train the model, and whether these metrics convergence over the course of training to the metrics of the real data manifold.

cs.LG↗

arXiv2019

Local topological recursion governs the enumeration of lattice points in $\overline{\mathcal M}_{g,n}$

The second author and Norbury initiated the enumeration of lattice points in the Deligne-Mumford compactifications of moduli spaces of curves. They showed that the enumeration may be expressed in terms of polynomials, whose top and bottom degree coefficients store psi-class intersection numbers and orbifold Euler characteristics of $\overline{\mathcal M}_{g,n}$, respectively. Furthermore, they ask whether the enumeration is governed by the topological recursion and whether the intermediate coefficients also store algebro-geometric information. In this paper, we prove that the enumeration does indeed satisfy the topological recursion, although with a modification to the initial spectral curve data. Thus, one can consider this to be one of the first known instances of a natural enumerative problem governed by the so-called local topological recursion. Combining the present work with the known relation between local topological recursion and cohomological field theory should uncover the geometric meaning of the intermediate coefficients of the aforementioned polynomials.

math.GT↗

arXiv2018

Generalisations of the Harer-Zagier recursion for 1-point functions

Harer and Zagier proved a recursion to enumerate gluings of a $2d$-gon that result in an orientable genus $g$ surface, in their work on Euler characteristics of moduli spaces of curves. Analogous results have been discovered for other enumerative problems, so it is natural to pose the following question: how large is the family of problems for which these so-called 1-point recursions exist? In this paper, we prove the existence of 1-point recursions for a class of enumerative problems that have Schur function expansions. In particular, we recover the Harer-Zagier recursion, but our methodology also applies to the enumeration of dessins d'enfant, to Bousquet-Mélou-Schaeffer numbers, to monotone Hurwitz numbers, and more. On the other hand, we prove that there is no 1-point recursion that governs simple Hurwitz numbers. Our results are effective in the sense that one can explicitly compute particular instances of 1-point recursions, and we provide several examples. We conclude the paper with a brief discussion and a conjecture relating 1-point recursions to the theory of topological recursion.

math-ph↗