Biology subjects

Kusmierz, L.

Publications and source records attributed to Kusmierz, L..

3 recordsLinked to original sources

bioRxiv2025

Slow Transition to Low-Dimensional Chaos in Heavy-Tailed Recurrent Neural Networks

Growing evidence suggests that synaptic weights in the brain follow heavy-tailed distributions, yet most theoretical analyses of recurrent neural networks (RNNs) assume Gaussian connectivity. We systematically study the activity of RNNs with random weights drawn from biologically plausible Levy alpha-stable distributions. While mean-field theory for the infinite system predicts that the quiescent state is always unstable--implying ubiquitous chaos--our finite-size analysis reveals a sharp transition between quiescent and chaotic dynamics. We theoretically predict the gain at which the finite system transitions from quiescent to chaotic dynamics, and validate it through simulations. Compared to Gaussian networks, finite heavy-tailed RNNs exhibit a broader gain regime near the edge of chaos, namely, a slow transition to chaos. However, this robustness comes with a tradeoff: heavier tails reduce the Lyapunov dimension of the attractor, indicating lower effective dimensionality. Our results reveal a biologically aligned tradeoff between the robustness of dynamics near the edge of chaos and the richness of high-dimensional neural activity. By analytically characterizing the transition point in finite-size networks-- where mean-field theory breaks down--we provide a tractable framework for understanding dynamics in realistically sized, heavy-tailed neural circuits.*

neuroscience↗

bioRxiv2024

Transition to chaos separates learning regimes and relates to measure of consciousness in recurrent neural networks

AbstractRecurrent neural networks exhibit chaotic dynamics when the variance in their connection strengths exceed a critical value. Recent work indicates connection variance also modulates learning strategies; networks learn "rich" representations when initialized with low coupling and "lazier"solutions with larger variance. Using Watts-Strogatz networks of varying sparsity, structure, and hidden weight variance, we find that the critical coupling strength dividing chaotic from ordered dynamics also differentiates rich and lazy learning strategies. Training moves both stable and chaotic networks closer to the edge of chaos, with networks learning richer representations before the transition to chaos. In contrast, biologically realistic connectivity structures foster stability over a wide range of variances. The transition to chaos is also reflected in a measure that clinically discriminates levels of consciousness, the perturbational complexity index (PCIst). Networks with high values of PCIst exhibit stable dynamics and rich learning, suggesting a consciousness prior may promote rich learning. The results suggest a clear relationship between critical dynamics, learning regimes and complexity-based measures of consciousness.

neuroscience↗

bioRxiv2024

"Bayesian anchoring" and the fourfold pattern of risk attitudes

Experiments on decision making under uncertainty are known to display a classical pattern of risk aversion and risk seeking referred to as "fourfold pattern" (or "reflection effect"), but recent experiments varying the speed and order of mental processing have brought to light a more nuanced phenomenology. We model experiments though a Bayesian formalization of the anchor-and-adjust heuristic observed in empirical studies on cognitive bias. Using only elementary assumptions on constrained information processing, we are able to infer three separate effects found in recent observations: (1) the reported enhancement of the fourfold pattern for quicker decision processes; (2) the observed decrease of fluctuations for slower decision-making trials; (3) the reported dependence of the outcome on the order in which options are processed. The application of Bayesian modeling offers a solution to recent empirical riddles by bridging two heretofore separate domains of experimental inquiry on bounded rationality.

neuroscience↗