2026-11-04

We present a non-equilibrium theory of sensory perception and the mesoscale of sensory cortex. We propose that local neuron assemblies (cortical columns) toggle spontaneously between activity states (on and off) and that small populations of columns are coupled within and between areas of sensory cortex. The resulting network generates sudden, large-scale fluctuations and represents sensory inputs and perceptions by characteristic patterns of activity flows. The non-equilibrium dynamic is governed by the variational principle of maximal path entropy, or Maximum Caliber. Many current theories, by contrast, posit equilibrium dynamics and representation with activity states Our minimal model of sensory cortex describes populations of columns from two cortical areas and is fully constrained by empirical observations of `reversals' in perceived appearance, which occur spontaneously for visual, auditory, and tactile stimulation. We formalize representation by activity flows with dynamic Hamiltonian functions. Surprisingly, effective representation requires small-number fluctuations of toggling columns, as larger numbers would be dominated by hysteresis. Finally, we detail predictions for the microscale of spiking neurons that follow from on-off toggling and non-equilibrium dynamics. We conclude that the neural levels underlying perception are functionally organized in terms of activity flows. The inherent instability of non-equilibrium ensures active updating and renders all perceptions open to immediate revision. We conjecture that current theories of brain function (such as the Free Energy Principle) could be reformulated in terms of the variational principle of non-equilibrium, Maximum Caliber.

In cellular automata, localized activity patterns called gliders propagate and interact to carry and transform information. Whether neuronal networks can harness this computational power remains unclear. Here, we demonstrate that a cortical network model with separate excitatory and inhibitory populations, graded cellular activity and uniform local connectivity spontaneously generates diverse, interacting gliders. An analytical reduction identifies the cellular conditions sustaining propagation of the dominant G-glider. Distinct gliders can assemble into growing structures that emit other glider types. Near excitation/inhibition balance, sparse glider dynamics coexist with high computational capacity, measured by input differentiation and generalization, with local capacity varying across space and time. Strong mutual inhibition between interneurons instead permits metastatic proliferation with low computational capacity. These findings connect cellular automata to neuronal information processing and identify interacting gliders as a candidate mechanism for dynamic plasticity: the reorganization of computation within an unchanged synaptic architecture.

Multielectrode-array recordings of the retina reveal neural population activity at cellular resolution, but relating recurring population states to stimulus timing and single-unit responses requires several linked analysis steps. We present PHASOR (Population HMM Analysis of Stimulus-locked Output in the Retina), a pipeline that combines stimulus-clock alignment, Fourier-based response classification, hidden Markov modeling with Chow-Liu tree emissions, model-order selection, and state visualization. We evaluated the workflow with synthetic populations and demonstrated its use in ten ex vivo recordings from three wild-type retinas (two male, one female) and one male rd1 retina, including 2 Hz full-field sinusoidal stimulation. Across ten synthetic datasets containing seven generative states, selected model orders ranged from seven to nine, with a mean of 7.9, matching the generative count exactly in three of the ten datasets. A representative confusion matrix showed a near one-to-one correspondence between generative and decoded states, with a single additional low-occupancy state, illustrating the distinction between recovering temporal structure and recovering the exact state count. In a representative retinal recording, response classes differed in stimulus phase and contrast dependence, and decoded states differed in occupancy, dwell time, and active-unit composition. Recordings during L-AP4 application, without projected stimulation, and in a photoreceptor-degenerate rd1 retina illustrated changes in the resulting population-state descriptions. PHASOR integrates established analysis methods into a reusable workflow for relating stimulus-associated population activity to functional response classes. The selected states provide a descriptive model of population activity; their number and correspondence to biological assemblies require separate validation.

A network of spiking neurons is said to operate in the rate coding regime if its dynamics can be accurately described by a continuous rate network. But how can discrete spike-based communication between neurons give rise to continuous rate-based dynamics? Computational studies showing that heterogeneous spiking networks can approximate the dynamics of recurrent neural networks (RNNs), a special case of rate network, assume that spikes are approximately Poisson or that network dynamics are slow. Here, we show that neither assumption is necessary: heterogeneous networks of non-Poisson neurons can produce fast rate-based dynamics. To demonstrate this, we show that signal transmission in feedforward networks of integrate-and-fire-type neurons can be described by a history-dependent rate network that is asymptotically exact as network size grows, even if heterogeneity persists, while linear-nonlinear rate networks fail. By providing a constructive model of fast rate coding in heterogeneous networks, this work lays the foundation for extending rate-based analyses of neural recordings beyond the assumption of slow dynamics or Poisson rate codes.

Understanding the connectivity of neuronal networks is essential for understanding brain function. Current anatomical mapping techniques, such as serial section microscopy and viral tracing, are resource-intensive and cannot capture the efficacy of connectivity. A complementary approach is to infer effective connectivity from single-neuron-resolution population activity. We developed a graph neural network (GNN)-based tool, CircuitGNN, that accurately infers neural effective connectivity from population activity. CircuitGNN accurately inferred the connectivity of several small circuits and detected both the strengthening and weakening of connections, such as those that occur during learning. CircuitGNN outperformed other methods when applied to simulated population activity generated by an invertebrate central pattern-generating circuit and a cortical microcircuit. CircuitGNN was evaluated on networks of varying size, recording duration, and proportion of hidden neurons. Although performance improved with longer recordings, CircuitGNN achieved high precision with recordings as short as 4 min, scaled to large circuits of up to ~750 neurons, and remained robust when 20% or 40% of neurons were hidden. These results establish CircuitGNN as an accurate and robust technique for inferring neural connectivity from activity.

Real-time phase estimation on stimulus-aligned transient EEG is critical for closed-loop neuromodulation systems targeting the theta-band, yet most real-time phase estimation methods have been developed and validated on resting-state, high-fidelity signals in the alpha band. Recent work has pursued deep learning architectures, while individualized classical bandpass filter tuning remains underexplored. This study characterizes the spectral and temporal properties of non-anticipative bandpass filtering and demonstrates the performance gains achieved through individualized tuning. We present a Bayesian-Optimized Biquad Filter-Burg (BOB) model evaluated on EEG recorded during peripheral vibrotactile stimulation of the left median nerve (theta, N=20 healthy subjects) and on resting-state recordings from the Max Planck Institute's LEMON dataset (alpha, N=20 healthy subjects). BOB was benchmarked against the Deep Dual-Branch Complex Neural Network (DBCNN), EEG Phase Prediction Network (EPN), Phastimate, and Phase Estimation with Autoregressive Padding (PEAP) under matched testing conditions: channel selection, individualized optimization, evaluation time points, and an offline reference phase obtained through zero-phase filtering and the Hilbert transform. Under these testing conditions, BOB achieved matched or better performance than these models at a fraction of the calibration time.