We show how large-deviation statistics allows one to obtain reliable estimates of the multiplicity of stable fixed-points in a model of neural ordinary differential equations previously employed in computational tasks. The result is obtained by developing a suitable perturbative method in the amplitude of the disorder. It turns out that for not-too-large coupling strengths there are no qualitative differences between the symmetric case, when the dynamics is a purely gradient evolution, and the asymmetric case, when limit cycles and chaos can, in principle, arise. The selection of this specific model is dictated by pedagogical reasons, but we are confident that the approach can be extended to other many-degree-of-freedom dynamical models characterized by different classes of random coupling matrices.
Optimizing modern recommender models still depends heavily on engineers manually iterating over architectural, objective, and training-strategy changes. While LLM-based agents can automate this trial-and-error process, allowing the LLM to both select modification directions and g…
Motivated by challenging modelling issues in the life sciences, we investigate the relationship between logic programming semantics and the eventual states of causal processes compatible with those logic programs. More precisely, we show that while stable models of positive logic…
Due to the complexity of neural network loss landscapes, optimization theory is forced to rely on idealized models, and there is generally a tradeoff between how theoretically tractable the model is, and how accurately it describes the true optimization dynamics. In this work, we…
Numerous studies have analyzed the use of hybrid quantum-classical convolutional neural networks as a promising alternative to classical deep learning. However, network components on quantum hardware impose fundamental limitations, while the scalability of quantum circuits leads…
High-complexity operational environments require methods that detect and anticipate temporally distributed patterns rather than classify isolated events. This paper introduces TRACTA (Temporal Reasoning and Capability-Trajectory Analysis), a controlled synthetic benchmark for tem…
Large Language Models (LLMs) excel at natural language understanding and generation but remain unreliable for multi-step logical reasoning, especially in safety-critical or compliance-sensitive domains. Recent neuro-symbolic approaches address this gap by coupling neural models w…