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Autumn Semester 2026

Date / Time Speaker Title Location
* 8 October 2026
13:45-15:00 		Yatin Dandi
EPFL
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DACO Seminar

Title Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning
Speaker, Affiliation Yatin Dandi, EPFL
Date, Time 8 October 2026, 13:45-15:00
Location HG D 3.3
Abstract Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based training in which hierarchical feature learning becomes an explicit iterative spectral procedure. In this limit, the dynamics at each layer decouple: given the current representation, the next layer selects directions with maximal accessible low-degree correlation to the label. This yields a tractable surrogate mechanism for deep learning, together with a natural kernel-space interpretation. Neural LoFi provides a mathematically explicit framework for studying multi-layer feature learning beyond the lazy regime. It predicts how representations are selected layer by layer, explains how emergence of concepts arises with given sample complexity, and gives a concrete mechanism by which depth progressively constructs new features from old ones through low-degree compositionality. We complement the theory with mechanistic experiments on fully connected and convolutional architectures, showing that Neural LoFi improves over lazy random-feature baselines, recovers meaningful structured filters, and predicts representations aligned with early gradient-descent feature discovery with real datasets. The talk is based on joint work with Matteo Vilucchio, Luca Arnaboldi, Hugo Tabanelli, and Florent Krzakala (https://arxiv.org/abs/2605.13612).
Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learningread_more
HG D 3.3
* 22 October 2026
14:00-15:00 		Enli Chen
TU Delft
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DACO Seminar

Title Strongly convergent random matrix models for q-Gaussian variables
Speaker, Affiliation Enli Chen, TU Delft
Date, Time 22 October 2026, 14:00-15:00
Location HG E 41
Abstract q-Gaussian variables form a family of noncommutative random variables interpolating between free and classical Gaussian behavior. A natural question is whether they admit finite-dimensional random matrix models that converge not only in moments, but also strongly, meaning that the operator norms of all noncommutative polynomials converge. I will explain our construction of strongly convergent random matrix models for finite families of q-Gaussian variables. The construction proceeds in two stages. First, normalized sums of graph-product (Γ-independent) semicircular variables converge strongly to finite q-Gaussian families. Second, the corresponding graph-product semicircular systems are realized as strong limits of finite-dimensional tensor-GUE random matrices. Both steps admit matrix-coefficient versions, and the resulting random-matrix convergence is uniform for growing coefficient dimensions that may even exceed the dimension of the random matrices themselves. Our current arXiv version treats the range |q| < √2 − 1, and we have recently extended the result to the full range |q|<1. I will conclude with a brief discussion of recent connections between our construction and q-Gaussian limits arising from Kikuchi matrices.
Strongly convergent random matrix models for q-Gaussian variablesread_more
HG E 41
* 23 October 2026
14:15-15:15 		Prof. Dr. Jorge Garza-Vargas
MIT, USA
Details

DACO Seminar

Title Strong convergence of random matrices
Speaker, Affiliation Prof. Dr. Jorge Garza-Vargas, MIT, USA
Date, Time 23 October 2026, 14:15-15:15
Location HG D 3.3
Abstract I will review the method of Chen, Tropp, van Handel, and myself for proving strong convergence of random matrices. This, roughly speaking, can be thought of as a method for obtaining a sharp control on the norm of random matrices whose randomness possess certain symmetries. I will then state some results and open problems.
Strong convergence of random matricesread_more
HG D 3.3
5 November 2026
14:00-15:00 		Dr. Tom Szwagier
IRIT, Toulouse, France
Details

DACO Seminar

Title Random Matrix Theory for Symmetric Tensor Unfolding
Speaker, Affiliation Dr. Tom Szwagier, IRIT, Toulouse, France
Date, Time 5 November 2026, 14:00-15:00
Location HG G 19.1
Abstract How can we recover a hidden low-rank signal from a noisy, high-dimensional tensor? A popular approach, known as unfolding, transforms the tensor into a matrix so that standard spectral methods can be applied. However, when the tensor is symmetric, its entries are dependent, making the theoretical analysis substantially more challenging. In this talk, I will present a random matrix analysis of symmetric tensor unfolding that directly accounts for these dependencies. We establish a sharp phase transition for signal recovery, identifying an exact signal-to-noise ratio threshold above which the signal is partially recovered, the corresponding alignment and limiting spectral distribution. Our results confirm a conjecture of Montanari and Richard (2014). They also show that, after appropriate transformation, unfolded symmetric tensors exhibit the same spectral behavior as classical random matrix models, despite their intricate dependence structure. Based on a joint work with Henrique Goulart and Xiaoyi Mai.
Random Matrix Theory for Symmetric Tensor Unfoldingread_more
HG G 19.1
19 November 2026
13:15-15:15 		Prof. Dr. Coja-Oghlan Amin
Universität Bielefeld
Details

DACO Seminar

Title The chromatic number of random graphs with $o(n^{3/2})$ edges
Speaker, Affiliation Prof. Dr. Coja-Oghlan Amin, Universität Bielefeld
Date, Time 19 November 2026, 13:15-15:15
Location HG G 19.1
Abstract Let $G(n,m)$ be the Erdős-Rényi random graph with $n$ vertices and $m$ edges. Using the L\'ovasz local lemma, Alon and Krivelevich [Combinatorica 1997] proved that for $m=o(n^{3/2})$ there \emph{exists} $q=q(n,m)$ such that the chromatic number of $G(n,m)$ equals either $q$ or $q+1$ with probability tending to one as $n\to\infty$. In this talk we determine $q$ explicitly. We also show that for `most' $m$ in a certain precise sense the chromatic number of the random graph equals $q$, i.e., concentrates on just a single explicit value. The talk is based on joint work with Michael Isaev, Mihyun Kang and Pavel Zakharov.
The chromatic number of random graphs with $o(n^{3/2})$ edgesread_more
HG G 19.1
26 November 2026
13:45-14:45 		Gaia Carenini
University of Cambridge
Details

DACO Seminar

Title A proof of the satisfiability conjecture
Speaker, Affiliation Gaia Carenini, University of Cambridge
Date, Time 26 November 2026, 13:45-14:45
Location HG G 19.1
Abstract We prove that the scaling window of random k-SAT has width O(n^1/2+1/k), a polynomial improvement over our previous bound of O(n/ log n). Combined with a result of Abbe and Montanari, this establishes the satisfiability conjecture for every fixed k ≥ 3: there exists a constant αk such that a random k-SAT formula on n variables with ⌊αn⌋ clauses is satisfiable with high probability if α<αk.
A proof of the satisfiability conjectureread_more
HG G 19.1
* 9 December 2026
13:45-15:00 		Prof. Dr. Cristopher Moore
Santa Fe Institute
Details

DACO Seminar

Title Title TBD (talk on how to build puzzles)
Speaker, Affiliation Prof. Dr. Cristopher Moore, Santa Fe Institute
Date, Time 9 December 2026, 13:45-15:00
Location HG D 3.1
Abstract TBD
Title TBD (talk on how to build puzzles)read_more
HG D 3.1

Notes: the highlighted event marks the next occurring event and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

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