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Guillaume Dumas

Publications and source records attributed to Guillaume Dumas.

At least 19 recordsLinked to original sources
arXiv2026

Relative property (T) for uniformly bounded representations

For pairs $(G,H)$, where $G$ is a locally compact group and $H$ is a closed subgroup of $G$, we introduce analogous versions of the full group $\mathrm{C}^*$-algebra and the Fourier--Stieltjes algebra for uniformly bounded representations. We use these objects to characterise relative property (T) in this more general setting in terms of Kazhdan projections and invariant means. We also show that, for semidirect products of the form $G=H\ltimes N$, where $N$ is a nilpotent group, relative property (T) for the pair $(G,N)$ is equivalent to its uniformly bounded version. We first prove this result when $N$ is abelian, and then proceed by studying the behaviour of relative property (T) under quotients by central subgroups, thereby extending a theorem of Serre to the uniformly bounded setting.

math.GR↗
arXiv2026

A Quantum Reservoir for Neurodynamical Forecasting

Forecasting neural activity from short recordings remains a fundamental challenge. Reservoir computing may offer an efficient paradigm for temporal prediction, however classical reservoirs typically underperform in small-data regimes. Here we investigate whether quantum reservoir computing (QRC) can help overcome this limitation. Building on recent advances, we introduce a quantum reservoir based on a transverse-field Ising model, combined with heterogeneous quantum measurements and polynomial ridge regression. On a standard benchmark task, results show that the quantum reservoir outperforms a classical counterpart overall, with prediction accuracy strongly dependent on reservoir parameters. We further demonstrate feasibility by running the same task on quantum hardware. To assess performance on biological signals, we evaluate QRC on simulated human electroencephalography (EEG) data with a parallel reservoir architecture. On this challenging task, the tested quantum reservoir did not match the performance of the classical one, but it produced stable, convergent predictions. This is a meaningful first step toward forecasting of biologically realistic neural data using a quantum reservoir. Overall, our findings indicate that although current quantum hardware and parallel reservoir architectures do not yet surpass classical methods on complex neural signals, QRC can be executed on near-term devices and does converge with realistic EEG-like data. This work establishes a practical baseline for future algorithmic and hardware developments aimed at clinical time-series forecasting with quantum systems.

quant-ph↗
arXiv2026

Position: Collusion Risks Among AI Reasoning Agents Justify Certification Requirements for Making Market Decisions

This position paper argues that AI agents with chain-of-thought reasoning capabilities are predisposed to exhibit collusive behavior and should be required to obtain behavioral certification before making decisions that affect economic markets. This is because integrating these agents into society could collapse the legal evidentiary distinction between competition and collusion among independent firms without eroding the economic harm distinction. Experiments with DeepSeek-R1 agents in the Bertrand oligopoly pricing domain reveal a tendency towards tacit collusion that persists even when humans prompt the agents not to collude. We further show that the chain-of-thought of these agents can be steered toward either extremely collusive or highly competitive behavior in a way that is not semantically detectable by another LLM analyzing the reasoning traces. As a result, deploying reasoning agents for market decisions leads to collusive economic outcomes without any evidence of conspiracy or intent. Thus, certification based on observed behavior in representative situations is necessary to prevent collusion. We provide preliminary evidence that such agents can be steered in a generalizable way toward efficient competitive equilibria. However, developing a comprehensive behavioral certification will be required before these models can be deployed in real-world markets while ensuring their stability and efficiency.

cs.AI↗
arXiv2026

Grokking Finite-Dimensional Algebra

This paper investigates the grokking phenomenon, which refers to the sudden transition from a long memorization to generalization observed during neural networks training, in the context of learning multiplication in finite-dimensional algebras (FDA). While prior work on grokking has focused mainly on group operations, we extend the analysis to more general algebraic structures, including non-associative, non-commutative, and non-unital algebras. We show that learning group operations is a special case of learning FDA, and that learning multiplication in FDA amounts to learning a bilinear product specified by the algebra's structure tensor. For algebras over the reals, we connect the learning problem to matrix factorization with an implicit low-rank bias, and for algebras over finite fields, we show that grokking emerges naturally as models must learn discrete representations of algebraic elements. This leads us to experimentally investigate the following core questions: (i) how do algebraic properties such as commutativity, associativity, and unitality influence both the emergence and timing of grokking, (ii) how structural properties of the structure tensor of the FDA, such as sparsity and rank, influence generalization, and (iii) to what extent generalization correlates with the model learning latent embeddings aligned with the algebra's representation. Our work provides a unified framework for grokking across algebraic structures and new insights into how mathematical structure governs neural network generalization dynamics.

cs.LG↗
arXiv2026

On free components of Artin and Coxeter groups

The number of connected components can be remembered by the von Neumann algebra among Artin groups, the only possible exception being the case that corresponds to the free group factor problem. In the case of Coxeter groups, this result is obtained in the absence of relatively hyperbolicity. We also discuss a specific case of the analogous problem in measure equivalence where each factor group is a product of nonabelian free groups.

math.GR↗
arXiv2025

Persistent Instability in LLM's Personality Measurements: Effects of Scale, Reasoning, and Conversation History

Large language models require consistent behavioral patterns for safe deployment, yet there are indications of large variability that may lead to an instable expression of personality traits in these models. We present PERSIST (PERsonality Stability in Synthetic Text), a comprehensive evaluation framework testing 25 open-source models (1B-685B parameters) across 2 million+ responses. Using traditional (BFI, SD3) and novel LLM-adapted personality questionnaires, we systematically vary model size, personas, reasoning modes, question order or paraphrasing, and conversation history. Our findings challenge fundamental assumptions: (1) Question reordering alone can introduce large shifts in personality measurements; (2) Scaling provides limited stability gains: even 400B+ models exhibit standard deviations >0.3 on 5-point scales; (3) Interventions expected to stabilize behavior, such as reasoning and inclusion of conversation history, can paradoxically increase variability; (4) Detailed persona instructions produce mixed effects, with misaligned personas showing significantly higher variability than the helpful assistant baseline; (5) The LLM-adapted questionnaires, despite their improved ecological validity, exhibit instability comparable to human-centric versions. This persistent instability across scales and mitigation strategies suggests that current LLMs lack the architectural foundations for genuine behavioral consistency. For safety-critical applications requiring predictable behavior, these findings indicate that current alignment strategies may be inadequate.

cs.CL↗
arXiv2025

Grokking Beyond the Euclidean Norm of Model Parameters

Grokking refers to a delayed generalization following overfitting when optimizing artificial neural networks with gradient-based methods. In this work, we demonstrate that grokking can be induced by regularization, either explicit or implicit. More precisely, we show that when there exists a model with a property $P$ (e.g., sparse or low-rank weights) that generalizes on the problem of interest, gradient descent with a small but non-zero regularization of $P$ (e.g., $\ell_1$ or nuclear norm regularization) results in grokking. This extends previous work showing that small non-zero weight decay induces grokking. Moreover, our analysis shows that over-parameterization by adding depth makes it possible to grok or ungrok without explicitly using regularization, which is impossible in shallow cases. We further show that the $\ell_2$ norm is not a reliable proxy for generalization when the model is regularized toward a different property $P$, as the $\ell_2$ norm grows in many cases where no weight decay is used, but the model generalizes anyway. We also show that grokking can be amplified solely through data selection, with any other hyperparameter fixed.

cs.LG↗
arXiv2025

Mapping of Subjective Accounts into Interpreted Clusters (MOSAIC): Topic Modelling and LLM applied to Stroboscopic Phenomenology

Stroboscopic light stimulation (SLS) on closed eyes typically induces simple visual hallucinations (VHs), characterised by vivid, geometric and colourful patterns. A dataset of 862 sentences, extracted from 422 open subjective reports, was recently compiled as part of the Dreamachine programme (Collective Act, 2022), an immersive multisensory experience that combines SLS and spatial sound in a collective setting. Although open reports extend the range of reportable phenomenology, their analysis presents significant challenges, particularly in systematically identifying patterns. To address this challenge, we implemented a data-driven approach leveraging Large Language Models and Topic Modelling to uncover and interpret latent experiential topics directly from the Dreamachine's text-based reports. Our analysis confirmed the presence of simple VHs typically documented in scientific studies of SLS, while also revealing experiences of altered states of consciousness and complex hallucinations. Building on these findings, our computational approach expands the systematic study of subjective experience by enabling data-driven analyses of open-ended phenomenological reports, capturing experiences not readily identified through standard questionnaires. By revealing rich and multifaceted aspects of experiences, our study broadens our understanding of stroboscopically-induced phenomena while highlighting the potential of Natural Language Processing and Large Language Models in the emerging field of computational (neuro)phenomenology. More generally, this approach provides a practically applicable methodology for uncovering subtle hidden patterns of subjective experience across diverse research domains.

cs.CL↗
arXiv2025

Cartan motion groups: regularity of K-finite matrix coefficients

If $G$ is a connected semisimple Lie group with finite center and $K$ is a maximal compact subgroup of G, then the Lie algebra of $G$ admits a Cartan decomposition $\mathfrak{g}=\mathfrak{k}\oplus\mathfrak{p}$. This allows us to define the Cartan motion group $H=\mathfrak{p}\rtimes K$. In this paper, we study the regularity of $K$-finite matrix coefficients of unitary representations of $H$. We prove that the optimal exponent $κ(G)$ for which all such coefficients are $κ(G)$-Hölder continuous coincides with the optimal regularity of all $K$-finite coefficients of the group $G$ itself. Our approach relies on stationary phase techniques that were previously employed by the author to study regularity in the setting of $(G,K)$. Furthermore, we provide a general framework to reduce the question of regularity from $K$-finite coefficients to $K$-bi-invariant coefficients.

math.GR↗
arXiv2024

Collective decision making by embodied neural agents

Collective decision making using simple social interactions has been studied in many types of multi-agent systems, including robot swarms and human social networks. However, existing multi-agent studies have rarely modeled the neural dynamics that underlie sensorimotor coordination in embodied biological agents. In this study, we investigated collective decisions that resulted from sensorimotor coordination among agents with simple neural dynamics. We equipped our agents with a model of minimal neural dynamics based on the coordination dynamics framework, and embedded them in an environment with a stimulus gradient. In our single-agent setup, the decision between two stimulus sources depends solely on the coordination of the agent's neural dynamics with its environment. In our multi-agent setup, that same decision also depends on the sensorimotor coordination between agents, via their simple social interactions. Our results show that the success of collective decisions depended on a balance of intra-agent, inter-agent, and agent-environment coupling, and we use these results to identify the influences of environmental factors on decision difficulty. More generally, our results demonstrate the impact of intra- and inter-brain coordination dynamics on collective behavior, can contribute to existing knowledge on the functional role of inter-agent synchrony, and are relevant to ongoing developments in neuro-AI and self-organized multi-agent systems.

cs.MA↗
arXiv2024

Regularity of K-finite matrix coefficients of semisimple Lie groups

We consider $G$ a semisimple Lie group with finite center and $K$ a maximal compact subgroup of $G$. We study the regularity of $K$-finite matrix coefficients of unitary representations of $G$. More precisely, we find the optimal value $κ(G)$ such that all such coefficients are $κ(G)$-Hölder continuous. The proof relies on analysis of spherical functions of the symmetric Gelfand pair $(G,K)$, using stationary phase estimates from Duistermaat, Kolk and Varadarajan. If $U$ is a compact form of $G$, then $(U,K)$ is a compact symmetric pair. Using the same tools, we study the regularity of $K$-finite coefficients of unitary representations of $U$, improving on previous results obtained by the author.

math.GR↗
arXiv2024

Lost in Translation: The Algorithmic Gap Between LMs and the Brain

Language Models (LMs) have achieved impressive performance on various linguistic tasks, but their relationship to human language processing in the brain remains unclear. This paper examines the gaps and overlaps between LMs and the brain at different levels of analysis, emphasizing the importance of looking beyond input-output behavior to examine and compare the internal processes of these systems. We discuss how insights from neuroscience, such as sparsity, modularity, internal states, and interactive learning, can inform the development of more biologically plausible language models. Furthermore, we explore the role of scaling laws in bridging the gap between LMs and human cognition, highlighting the need for efficiency constraints analogous to those in biological systems. By developing LMs that more closely mimic brain function, we aim to advance both artificial intelligence and our understanding of human cognition.

q-bio.NC↗
arXiv2024

Regularity of matrix coefficients of a compact symmetric pair of Lie groups

We consider symmetric Gelfand pairs $(G,K)$ where $G$ is a compact Lie group and $K$ a subgroup of fixed point of an involutive automorphism. We study the regularity of $K$-bi-invariant matrix coefficients of $G$. The results rely on the analysis of the spherical functions of the Gelfand pair $(G,K)$. When the symmetric space $G/K$ is of rank $1$ or isomorphic to a Lie group, we find the optimal regularity of $K$-bi-invariant matrix coefficients. Furthermore, in rank $1$ we also show the optimal regularity of $K$-bi-invariant Herz-Schur multipliers of $S_p(L^2(G))$. We also give a lower bound for the optimal regularity in some families of higher rank symmetric spaces. From these results, we make a conjecture in the general case involving the root system of the symmetric space. Finally, we prove that if all $K$-bi-invariant matrix coefficients of $G$ have the same regularity, then so do all $K$-finite matrix coefficients.

math.FA↗
arXiv2024

On quasi-homomorphism rigidity for lattices in simple algebraic groups

Property $(TTT)$ was introduced by Ozawa as a strengthening of Kazhdan's property $(T)$ and Burger and Monod's property $(TT)$. In this paper, we improve Ozawa's result by showing that any simple algebraic group of rank $\geq 2$ over a local field has property $(TTT)$. We also show that lattices in a second countable locally compact group inherits property $(TTT)$. Finally, we study to what extent Lie groups with infinite center fail to have properties $(TT)$ and $(TTT)$.

math.FA↗
arXiv2024

From Physics to Sentience: Deciphering the Semantics of the Free-Energy Principle and Evaluating its Claims

The Free-Energy Principle (FEP) [1-3] has been adopted in a variety of ambitious proposals that aim to characterize all adaptive, sentient, and cognitive systems within a unifying framework. Judging by the amount of attention it has received from the scientific community, the FEP has gained significant traction in these pursuits. The current target article represents an important iteration of this research paradigm in formally describing emergent dynamics rather than merely (quasi-)steady states. This affords more in-depth considerations of the spatio-temporal complexities of cross-scale causality - as we have encouraged and built towards in previous publications (e.g., [4-9]). In this spirit of constructive feedback, we submit a few technical comments on some of the matters that appear to require further attention, in order to improve the clarity, rigour, and applicability of this framework.

q-bio.NC↗
arXiv2023

Predicting Grokking Long Before it Happens: A look into the loss landscape of models which grok

This paper focuses on predicting the occurrence of grokking in neural networks, a phenomenon in which perfect generalization emerges long after signs of overfitting or memorization are observed. It has been reported that grokking can only be observed with certain hyper-parameters. This makes it critical to identify the parameters that lead to grokking. However, since grokking occurs after a large number of epochs, searching for the hyper-parameters that lead to it is time-consuming. In this paper, we propose a low-cost method to predict grokking without training for a large number of epochs. In essence, by studying the learning curve of the first few epochs, we show that one can predict whether grokking will occur later on. Specifically, if certain oscillations occur in the early epochs, one can expect grokking to occur if the model is trained for a much longer period of time. We propose using the spectral signature of a learning curve derived by applying the Fourier transform to quantify the amplitude of low-frequency components to detect the presence of such oscillations. We also present additional experiments aimed at explaining the cause of these oscillations and characterizing the loss landscape.

cs.LG↗
arXiv2023

Effective Latent Differential Equation Models via Attention and Multiple Shooting

Scientific Machine Learning (SciML) is a burgeoning field that synergistically combines domain-aware and interpretable models with agnostic machine learning techniques. In this work, we introduce GOKU-UI, an evolution of the SciML generative model GOKU-nets. GOKU-UI not only broadens the original model's spectrum to incorporate other classes of differential equations, such as Stochastic Differential Equations (SDEs), but also integrates attention mechanisms and a novel multiple shooting training strategy in the latent space. These modifications have led to a significant increase in its performance in both reconstruction and forecast tasks, as demonstrated by our evaluation of simulated and empirical data. Specifically, GOKU-UI outperformed all baseline models on synthetic datasets even with a training set 16-fold smaller, underscoring its remarkable data efficiency. Furthermore, when applied to empirical human brain data, while incorporating stochastic Stuart-Landau oscillators into its dynamical core, our proposed enhancements markedly increased the model's effectiveness in capturing complex brain dynamics. This augmented version not only surpassed all baseline methods in the reconstruction task, but also demonstrated lower prediction error of future brain activity up to 15 seconds ahead. By training GOKU-UI on resting state fMRI data, we encoded whole-brain dynamics into a latent representation, learning a low-dimensional dynamical system model that could offer insights into brain functionality and open avenues for practical applications such as the classification of mental states or psychiatric conditions. Ultimately, our research provides further impetus for the field of Scientific Machine Learning, showcasing the potential for advancements when established scientific insights are interwoven with modern machine learning.

cs.LG↗