arXiv subjects

Dai Akita

Publications and source records attributed to Dai Akita.

9 recordsLinked to original sources

arXiv2026

Bridging integrated information theory and the free-energy principle in living neuronal networks

Integrated Information Theory (IIT) links consciousness to integrated causal structure, whereas the Free-Energy Principle (FEP) explains self-organization through variational free-energy minimization. Their relationship in living neural systems remains unclear. We analyzed dissociated neuronal cultures learning to infer hidden signal sources. Across repeated stimulation, variational free energy decreased, while inference accuracy and Bayesian surprise, defined as the divergence between prior and posterior beliefs, increased. An IIT-inspired integrated-information proxy and main-complex size followed a non-monotonic, hill-shaped trajectory. The proxy correlated most strongly with Bayesian surprise and more weakly with accuracy and variational free energy. An Ising-model analysis indicated that Bayesian surprise and integrated information can be jointly amplified near shared positive critical modes and suggested how early connectivity development followed by response stabilization could generate the observed trajectory. These results link belief updating to integrated information in living neuronal networks and provide an empirical point of contact between IIT and the FEP.

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arXiv2026

Dynamic sampling of non-stationary spontaneous activity in dissociated neuronal networks

Objective. To develop and evaluate an adaptive electrode-selection method for tracking non-stationary spontaneous activity during long-term high-density microelectrode array (HD-MEA) recordings under a fixed channel budget. Approach. We formulated electrode allocation as a sequential subset-selection problem and used a discounted Poisson-Gamma model with Thompson sampling. The method updated electrode-specific activity estimates from observed spike counts and reallocated a fixed channel budget over time. We evaluated it by offline replay of nine 34 h HD-MEA recordings, selecting 100 electrodes from 529 densely routed candidates, and in a representative online recording using 1,024 routed electrodes. Main results. Across offline recordings, the top 100 active-electrode set changed substantially, reaching 47.8% turnover at 34 h. The Bayesian method captured the largest fraction of the spikes available to an oracle selector among the tested strategies and exceeded static selection by 17.2 percentage points at the final time point. In the online recording, adaptive selection captured the first synchronized burst and supported center-of-activity trajectory analysis. Significance. Uncertainty-aware exploration and temporal discounting can improve HD-MEA recording efficiency under fixed readout constraints, providing a basis for adaptive sensing of evolving neural activity.

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arXiv2026

Finite-state enumeration of adjacency-constrained 132-avoiding permutations

For a fixed integer $m\ge 1$, let $\mathcal{A}_n^{(m)}$ be the set of permutations $π\in S_n$ that avoid the pattern $132$ and satisfy the adjacency bound $|π_{i+1}-π_i|\le m$ for all $i$. Here, a pattern $132$ means three indices $i<j<k$ such that $π_i<π_k<π_j$. A recent study initiated the enumeration of these constrained 132-avoiding permutations, treating the case $m=2$ by deriving a rational ordinary generating function and asking for finite-state decompositions, rational generating functions, and explicit rational formulas for larger fixed $m$. We introduce a two-sided endpoint-state decomposition that works uniformly for every fixed $m$. The state variables impose threshold bounds on the endpoint deficiencies $n-π_1$ and $n-π_n$, with thresholds in $\{0,1,\ldots,m-1,\infty\}$. This gives at most $(m+1)^2$ states and proves that, for every fixed $m$, the ordinary generating function $A^{(m)}(x)$ is rational and can be computed effectively by exact linear algebra. We also identify cyclic strongly connected components of the dependency graph in the finite-state system to give an explicit upper bound for the order of an eventual constant-coefficient recurrence satisfied by the sequence $a_n^{(m)}=|\mathcal{A}_n^{(m)}|$. We then recover the known case $m=2$ from this state system and work out the case $m=3$ explicitly. On the asymptotic side, we prove that the exponential growth constant exists for every $m$; for $m\ge2$ it is obtained from the spectral radii of the two cyclic components with more than one vertex in the state system. We determine the simple-pole asymptotics for $m=2$ and $m=3$, and we prove that the growth constants are nondecreasing in $m$, strictly smaller than the Catalan growth constant $4$ for every finite $m$, and converge to $4$ as $m\to\infty$.

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arXiv2025

Emergence of Deviance Detection in Cortical Cultures through Maturation, Criticality, and Early Experience

Mismatch negativity (MMN) in humans reflects deviance detection (DD), a core neural mechanism of predictive processing. However, the fundamental principles by which DD emerges and matures during early cortical development-potentially providing a neuronal scaffold for MMN-remain unclear. Here, we tracked the development of DD in dissociated cortical cultures grown on high-density CMOS microelectrode arrays from 10 to 35 days in vitro (DIV). Cultures were stimulated with oddball and many-standards control paradigms while spontaneous and evoked activity were recorded longitudinally. At early stages, stimulus-evoked responses were confined to fast components reflecting direct activation. From DIV15-20 onward, robust late responses appeared, and deviant stimuli progressively evoked stronger responses than frequent and control stimuli, marking the onset of DD. By DIV30, responses became stronger, faster, and more temporally precise. Neuronal avalanche analysis revealed a gradual transition from subcritical to near-critical dynamics, with cultures exhibiting power-law statistics showing the strongest deviant responses. Nonetheless, DD was also present in non-critical networks, indicating that criticality is not required for its emergence but instead stabilizes and amplifies predictive processing as networks mature. Early oddball experience reinforces the deviant pathway, resulting in faster conduction along those circuits. However, as frequent and deviant pathways become less distinct, the deviance detection index is reduced. Together, these findings demonstrate that DD arises intrinsically through local circuit maturation, while self-organization toward criticality and early experience further refine its strength and timing, providing mechanistic insight into predictive coding in simplified cortical networks and informing the design of adaptive, prediction-sensitive artificial systems.

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arXiv2025

Parity conditions for one-way rail networks

We present parity conditions under which a toy rail network is one-way, i.e., whether a direction can be assigned across the network so that all train journeys are completely consistent with it or completely consistent with its opposite. We show that this problem is equivalent to determining the balance of a signed graph obtained from the network, whose edges are assigned positive or negative signs. Using signed-graph theory, we derive two equivalent parity conditions for one-wayness: (i) every cycle must contain an even number of edges that join the same sides of switches, and (ii) every cycle must contain an even number of angles at switches. Signed-graph theory also offers an analytical criterion: A connected network is one-way if and only if the smallest eigenvalue of its signed Laplacian matrix is zero, suggesting a computational tool for evaluating one-wayness.

math.CO↗

arXiv2025

Emergent functions of noise-driven spontaneous activity: Homeostatic maintenance of criticality and memory consolidation

Unlike digital computers, the brain exhibits spontaneous activity even during complete rest, despite the evolutionary pressure for energy efficiency. Inspired by the critical brain hypothesis, which proposes that the brain operates optimally near a critical point of phase transition in the dynamics of neural networks to improve computational efficiency, we postulate that spontaneous activity plays a homeostatic role in the development and maintenance of criticality. Criticality in the brain is associated with the balance between excitatory and inhibitory synaptic inputs (EI balance), which is essential for maintaining neural computation performance. Here, we hypothesize that both criticality and EI balance are stabilized by appropriate noise levels and spike-timing-dependent plasticity (STDP) windows. Using spiking neural network (SNN) simulations and in vitro experiments with dissociated neuronal cultures, we demonstrated that while repetitive stimuli transiently disrupt both criticality and EI balance, spontaneous activity can develop and maintain these properties and prolong the fading memory of past stimuli. Our findings suggest that the brain may achieve self-optimization and memory consolidation as emergent functions of noise-driven spontaneous activity. This noise-harnessing mechanism provides insights for designing energy-efficient neural networks, and may explain the critical function of sleep in maintaining homeostasis and consolidating memory.

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arXiv2025

An Unbiased Variance Estimator with Denominator $N$

Standard practice obtains an unbiased variance estimator by dividing by $N-1$ rather than $N$. Yet if only half the data are used to compute the mean, dividing by $N$ can still yield an unbiased estimator. We show that an alternative mean estimator $\hat{X} = \sum c_n X_n$ can produce such an unbiased variance estimator with denominator $N$. These average-adjusted unbiased variance (AAUV) permit infinitely many unbiased forms, though each has larger variance than the usual sample variance. Moreover, permuting and symmetrizing any AAUV recovers the classical formula with denominator $N-1$. We further demonstrate a continuum of unbiased variances by interpolating between the standard and AAUV-based means. Extending this average-adjusting method to higher-order moments remains a topic for future work.

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arXiv2025

Deviance Detection and Regularity Sensitivity in Dissociated Neuronal Cultures

Understanding how neural networks process complex patterns of information is crucial for advancing both neuroscience and artificial intelligence. To investigate fundamental principles of neural computation, we studied dissociated neuronal cultures, one of the most primitive living neural networks, on high-resolution CMOS microelectrode arrays and tested whether the dissociated culture exhibits regularity sensitivity beyond mere stimulus-specific adaptation and deviance detection. In oddball electrical stimulation paradigms, we confirmed that the neuronal culture produced mismatch responses (MMRs) with true deviance detection beyond mere adaptation. These MMRs were dependent on the N-methyl-D-aspartate (NMDA) receptors, similar to mismatch negativity (MMN) in humans, which is known to have true deviance detection properties. Crucially, we also showed sensitivity to the statistical regularity of stimuli, a phenomenon previously observed only in intact brains: the MMRs in a predictable, periodic sequence were smaller than those in a commonly used sequence in which the appearance of the deviant stimulus was random and unpredictable. These results challenge the traditional view that a hierarchically structured neural network is required to process complex temporal patterns, suggesting instead that deviant detection and regularity sensitivity are inherent properties arising from the primitive neural network. They also suggest new directions for the development of neuro-inspired artificial intelligence systems, emphasizing the importance of incorporating adaptive mechanisms and temporal dynamics in the design of neural networks.

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arXiv2025

Dissociated Neuronal Cultures as Model Systems for Self-Organized Prediction

Dissociated neuronal cultures provide a simplified yet effective model system for investigating self-organized prediction and information processing in neural networks. This review consolidates current research demonstrating that these in vitro networks display fundamental computational capabilities, including predictive coding, adaptive learning, goal-directed behavior, and deviance detection. We examine how these cultures develop critical dynamics optimized for information processing, detail the mechanisms underlying learning and memory formation, and explore the relevance of the free energy principle within these systems. Building on these insights, we discuss how findings from dissociated neuronal cultures inform the design of neuromorphic and reservoir computing architectures, with the potential to enhance energy efficiency and adaptive functionality in artificial intelligence. The reduced complexity of neuronal cultures allows for precise manipulation and systematic investigation, bridging theoretical frameworks with practical implementations in bio-inspired computing. Finally, we highlight promising future directions, emphasizing advancements in three-dimensional culture techniques, multi-compartment models, and brain organoids that deepen our understanding of hierarchical and predictive processes in both biological and artificial systems. This review aims to provide a comprehensive overview of how dissociated neuronal cultures contribute to neuroscience and artificial intelligence, ultimately paving the way for biologically inspired computing solutions.

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