Singular Learning Theory Days 2026

Contribution List

1. Singular Learning Theory : Foundations and Future Challenges

Sumio Watanabe (Institute of Science Tokyo)

26/10/2026, 10:00

Talk

Learning models with hierarchical structures or hidden variables, such as deep neural networks, do not have a one-to-one correspondence between parameters and the functions they realize. Their likelihood functions and posterior distributions have singularities that cannot be approximated by Gaussian functions, which has made it difficult to mathematically analyze their predictive accuracy and...

3. Resolution of singularities - theory and practice

Anne Frühbis-Krüger (University of Oldenburg)

26/10/2026, 11:15

Talk

Resolution of singularities in characteristic zero has been proved non-constructively by Hironaka in the 1960s and constructive proofs have been established in the late 1980s and early 1990s filling the non-constructive steps by different variants of explicit algorithms. But these general algorithms have significant purely practical limitations, which leads to question about their...

4. Exact Algebraic Computation of Learning Coefficients for Two-Dimensional Singular Models

Jules Tsukahara (Sorbonne University)

26/10/2026, 13:30

Talk

We present an algorithm to compute local real log canonical thresholds of bivariate polynomials with rational coefficients, based on previous works of Varchenko, Phong et al. and Collins et al., using Newton polygons and Puiseux expansions. This algorithm is exact, and only requires finitely many computations over the rationals. We bound the number of iterations via a generalization of a...

5. Singular Geometry of Low-Rank Adaptation

Anthea Monod (Imperial College London)

26/10/2026, 15:00

Talk

Low-rank adaptation (LoRA) is a standard approach to parameter-efficient fine-tuning of large neural networks, including LLMs and foundation models. We study the real log canonical threshold (RLCT) of LoRA and how it depends jointly on the low-rank parametrization and the pretrained network. Under local linearization, LoRA induces a low-rank trace-regression model whose KL geometry is...

2. The Singular Bayesian Information Criterion: Rationale and Recent Applications

Mathias Drton (TU Munich)

27/10/2026, 10:00

Talk

The classical Bayesian information criterion (BIC) of Schwarz forms a trade-off between the fit and the complexity of a parametric statistical model via a penalty term that refers to the dimension of the model. The specific trade-off is derived through asymptotic analysis of Bayesian marginal likelihood. The BIC is commonly employed to address statistical model selection problems across...

6. Bernstein-Sato ideals, especially of generic arrangements

Dan Bath (KU Leuven)

27/10/2026, 11:15

Talk

I will give a brief, algebraically minded, accounting of Bernstein-Sato ideals and how they are the correct generalization of the Bernstein-Sato polynomial of a single function to that of a tuple of functions. In the positive direction, I will give a formula for the Bernstein-Sato ideal of a generic (possibly non-reduced) arrangement factored into linear forms and a formula for the zeroes for...

7. The real log-canonical threshold via jet schemes

Simon Pepin Lehalleur (University of Amsterdam)

27/10/2026, 13:30

Talk

The jet schemes $J_m(F)$ of an analytic function $F$ are geometric objects
which encode the order of vanishing of F along smooth curves. They
provide an alternative, more intrinsic way to "disentangle" the fine
structure of singularities than log-resolutions, and as such they have
been intensively studied in singularity theory (mostly in complex
algebraic geometry) and motivic...