Correlation flow governs learning at criticality

The initialization of deep neural networks determines whether information and gradients can propagate across depth, yet a unified theory connecting these properties to learning dynamics remains elusive. Combining mean-field theory and random matrix theory, we establish a direct link between correlation propagation and the Neural Tangent Kernel (NTK) that governs learning in the sequential limit of infinitely wide, infinitely deep networks. Correlation propagation to infinite depth is possible only at a single, critical point in the weight-bias variance plane. At this point, we leverage the algebraic decay of the end-to-end Jacobian with depth to prove that the NTK becomes exactly proportional to the output correlation at infinite depth, tying together information propagation and learning dynamics. We further show that orthogonal initialization suppresses the leading finite-size corrections present under Gaussian initialization, clarifying the respective roles of the two initialization ensembles in this limit. These theoretical predictions are validated quantitatively on finite-width, finite-depth networks. Together, these results demonstrate that orthogonal initialization and criticality are required to control the asymptotic dynamics of deep learning.

Sleep EEG Signal Criticality as a Non-Invasive Predictor of Cognitive Decline in Dementia

Early detection of neurodegeneration remains a critical clinical challenge. This study investigates whether sleep EEG signal criticality, quantified via Multifractal Detrended Fluctuation Analysis (MFDFA), serves as a non-invasive biomarker for future cognitive decline. We analyzed longitudinal data from the National Sleep Research Resource (NSRR) Study of Osteoporotic Fractures (SOF) cohort, comparing baseline sleep EEG dynamics between women who remained cognitively normal and those who later progressed to dementia-related impairment ($3MS < 78$).Our results reveal significant group-level differences in Hurst exponent $H(q)$ distributions, particularly during non-REM stages N2 and N3. Cognitively healthy individuals exhibited signal dynamics significantly closer to an optimally critical state across all electrode locations ($p \leqslant 0.001$), supporting the Brain Criticality Hypothesis. Supervised UMAP projections confirmed clear spatial separation between groups throughout the overnight sleep architecture.The dementia group demonstrated a shift in DFA exponents toward $1.0$, suggesting that a reconfiguration of scale-free neural dynamics during sleep precedes clinical symptoms. These findings highlight the potential for MFDFA-derived measures to be integrated into automated, sleep-based screening tools, enabling earlier preventative interventions during the prodromal window of dementia.

Towards Critical Branching Mechanism in Recurrent Neural Networks

Criticality has been proposed as a key organizing principle in biological neural systems, yet its origin and relevance in artificial neural networks remain unclear. We analyze hidden-state dynamics in trained long short-term memory (LSTM) networks and show that small networks near their optimal training epochs (steps) exhibit scale-free avalanche statistics and branching parameters close to unity, indicative of near-critical dynamics, while larger models remain subcritical. To explain the coexistence of subcritical branching with robust $1/f^β$ noise, we introduce a mixture branching process framework that links heterogeneous branching dynamics to long-range temporal correlations. These results identify critical-like behavior in LSTMs as an emergent, capacity-dependent dynamical regime.