arXiv:2603.03337v1 Announce Type: new Abstract: Experimental neuroscience has long established that human motor control, specifically in hand movements, adheres to the "Two-Thirds Power Law," relating velocity to curvature ($v \propto \kappa^{-1/3}$). Geometrically, this implies that trajectories are geodesics of an equi-affine metric. However, in the standard framework of differential geometry, this metric is not intrinsic because its definition relies on acceleration, which is not a tensorial quantity under the full group of diffeomorphisms of $\mathbf{R}^2$. In this note, we propose a change in perspective: we model the brain's internal geometry not as the standard plane $\mathbf{R}^2$, but as the "Wire Plane" -- ~$\mathbf{R}^2$ equipped with the "wire diffeology" generated by smooth curves. We prove that the equi-affine metric is founded upon a covariant 3-tensor which, in this specific diffeological context, becomes a natural and intrinsic object defined on the plots of the space. This mathematical result suggests a neuro-geometric hypothesis: the brain perceives and plans space through 1-dimensional paths rather than 2-dimensional charts.

arXiv:2603.03343v1 Announce Type: new Abstract: We propose NEURONA, a neuro-symbolic framework for fMRI decoding and concept grounding in neural activity. Leveraging image- and video-based fMRI question-answering datasets, NEURONA learns to decode interacting concepts from visual stimuli based on patterns of fMRI responses, integrating symbolic reasoning and compositional execution with fMRI grounding across brain regions. We demonstrate that incorporating structural priors (e.g., compositional predicate-argument dependencies between concepts) into the decoding process significantly improves both decoding accuracy over precise queries, and notably, generalization to unseen queries at test time. With NEURONA, we highlight neuro-symbolic frameworks as promising tools for understanding neural activity.

arXiv:2603.03345v1 Announce Type: new Abstract: In this work we analyze the emergence of phase transitions in a quantum brain model inspired by the Lipkin-Meshkov-Glick framework, where biologically motivated synaptic feedback modulates the collective interaction in a nonlinear and state-dependent manner. We demonstrate that incorporating this retroactive mechanism substantially reshapes the phase structure, yielding an expansion of the paramagnetic phase at the expense of the ferromagnetic phases relative to the feedback-free scenario. This effect is markedly enhanced in the presence of a longitudinal field, as the feedback couples directly to the longitudinal magnetization, leading to an appreciable displacement of the critical boundaries. We characterize the ensuing transitions from a phase-space perspective by means of the ground-state Husimi distribution and the Wehrl entropy, which provide a robust diagnosis of qualitative changes in localization and enable a quantitative assessment of feedback-induced deformations of the phase diagram. Additionally, we perform an explicit dynamical analysis based on mean-field equations for the collective-spin orientation self-consistently coupled to the synaptic dynamics, which reproduces with high fidelity the quantum time evolution of collective observables for the protocols considered. Overall, these findings substantiate the suitability of this quantum brain model as a controlled theoretical framework for elucidating how synaptic plasticity mechanisms can parametrically tune and reshape collective criticality.

arXiv:2603.03347v1 Announce Type: new Abstract: Synapses are efficient in the sense that their natural conductance values convey as many bits per Joule as possible, but efficiency falls rapidly if the conductance is forced to deviate from its natural value (Harris et al, 2015). However, the exact manner in which efficiency falls as conductance deviates from its natural value remains unexplained. Here, we express the minimal energy boundary proposed in Malkin et al (2026) in terms of Shannon's information theory (Shannon, 1949) to derive a biophysically motivated model that accurately predicts the decrease in efficiency values observed in Harris et al (2015) across a wide range of synaptic conductances.

arXiv:2603.03354v1 Announce Type: new Abstract: Although obtaining deep brain activity from non-invasive scalp electroencephalography (sEEG) is crucial for neuroscience and clinical diagnosis, directly generating high-fidelity intracranial electroencephalography (iEEG) signals remains a largely unexplored field, limiting our understanding of deep brain dynamics. Current research primarily focuses on traditional signal processing or source localization methods, which struggle to capture the complex waveforms and random characteristics of iEEG. To address this critical challenge, this paper introduces NeuroFlowNet, a novel cross-modal generative framework whose core contribution lies in the first-ever reconstruction of iEEG signals from the entire deep temporal lobe region using sEEG signals. NeuroFlowNet is built on Conditional Normalizing Flow (CNF), which directly models complex conditional probability distributions through reversible transformations, thereby explicitly capturing the randomness of brain signals and fundamentally avoiding the pattern collapse issues common in existing generative models. Additionally, the model integrates a multi-scale architecture and self-attention mechanisms to robustly capture fine-grained temporal details and long-range dependencies. Validation results on a publicly available synchronized sEEG-iEEG dataset demonstrate NeuroFlowNet's effectiveness in terms of temporal waveform fidelity, spectral feature reproduction, and functional connectivity restoration. This study establishes a more reliable and scalable new paradigm for non-invasive analysis of deep brain dynamics. The code of this study is available in https://github.com/hdy6438/NeuroFlowNet

arXiv:2603.03355v1 Announce Type: new Abstract: We present a memory-augmented transformer in which attention serves simultaneously as a retrieval, consolidation, and write-back operator. The core update, $A^\top A V W$, re-grounds retrieved values into persistent memory slots via the Gram matrix $A^\top A$, providing a principled tripartite projection: observation space $\to$ latent memory $\to$ supervised transformation. We partition the memory into lateralized left and right banks coupled through a sign-controlled cross-talk matrix $W_s$, and show that the sign of this coupling is decisive for specialization. Excitatory cross-talk ($s=+1$) causes bank-dominance collapse: one bank monopolises all inputs and $\mathcal{P}_{ct} \to 0.5$, despite lowering task loss. Inhibitory cross-talk ($s=-1$), motivated by the net inhibitory effect of callosal projections in human cortex, actively suppresses contralateral bank activation and achieves saturated specialization ($\mathcal{D}_{sep} = \pm 1.00$, $\mathcal{P}_{ct} \approx 0$). On a controlled symbolic benchmark combining an episodic bijection cipher (requiring associative recall) with a strict arithmetic progression (requiring rule extraction), the inhibitory model reduces cipher-domain loss by $124{\times}$ over the baseline while matching it on the arithmetic domain, confirming that persistent lateralized memory is necessary for episodic recall but not for rule-based prediction.

arXiv:2603.03358v1 Announce Type: new Abstract: Over the past two decades, quantum-like modeling (QLM) has emerged as a powerful framework for describing non-classical features of cognition and decision-making. Rather than assuming physical quantum processes in the brain, QLM employs the Hilbert space formalism to model contextuality, incompatibility of mental observables, and entanglement-like correlations. In this paper, we develop a quantum-informational model of mental markers within the broader I-field (information field) approach. We propose that, under conditions of information overload and limited cognitive resources, individuals primarily respond not to detailed semantic content but to compact content labels - mental markers - carrying cognitive and affective components. We formalize mental markers as structured quantum-like states and analyze the nonclassical correlations between their cognitive and affective components using the Contextuality-Incompatibility-Entanglement triad. Special attention is given to intra-system entanglement between rational (cognitive) evaluation and emotional (affective) coloring, accounting for context-dependent judgments, order effects, and affect-driven decision shifts. Illustrative examples with psychological interpretation and experimental perspectives are provided. An Appendix briefly discusses neurobiological analogues of information overload in neural networks, highlighting structural parallels with the proposed marker-based framework; coupling to the origin and diagnostics of neurological diseases is analyzed. The paper contributes to QLM by distinguishing inter-system and intra-system entanglement and by demonstrating that cognitive - affective entanglement constitutes a fundamental structural feature of mental markers in socially mediated information environments.

arXiv:2603.03362v1 Announce Type: new Abstract: The brain achieves stability and plasticity in a topologically complex, shifting world through Metric-Topology Factorization (MTF), separating discrete topological indexing for context selection from continuous metric condensation for local inference. Semantically rich environments defy single globally contractive geometries, causing obstructions under shifts, so intelligence factorizes these: the hippocampus provides sparse signatures indexing manifold identity, while the neocortex untangles geometry hierarchically. In the ventral stream, a dynamic-programming-like process quotients symmetries (e.g., translation, scale), transforming non-convex sensory mazes into separable bowls. Offline replay and consolidation amortize transformations for rapid task switching. Dreaming in REM involves stochastic hippocampal traversal to expose and regularize latent structures. Consciousness arises from resolving topological uncertainty into stable embeddings, with awareness for unamortized states. Evolutionarily, transitions like sensorimotor control to language expand topological complexity, demanding advanced indexing-metric separation. Intelligence emerges via recalibrating context-specific geometries, converting global navigation into local dynamics, not deeper search.

arXiv:2603.03414v1 Announce Type: new Abstract: We propose that the jagged intelligence landscape of modern AI systems arises from a missing training signal that we call "cognitive dark matter" (CDM): brain functions that meaningfully shape behavior yet are hard to infer from behavior alone. We identify key CDM domains-metacognition, cognitive flexibility, episodic memory, lifelong learning, abductive reasoning, social and common-sense reasoning, and emotional intelligence-and present evidence that current AI benchmarks and large-scale neuroscience datasets are both heavily skewed toward already-mastered capabilities, with CDM-loaded functions largely unmeasured. We then outline a research program centered on three complementary data types designed to surface CDM for model training: (i) latent variables from large-scale cognitive models, (ii) process-tracing data such as eye-tracking and think-aloud protocols, and (iii) paired neural-behavioral data. These data will enable AI training on cognitive process rather than behavioral outcome alone, producing models with more general, less jagged intelligence. As a dual benefit, the same data will advance our understanding of human intelligence itself.

arXiv:2603.03476v1 Announce Type: new Abstract: We propose a novel computational framework for analyzing electroencephalography (EEG) time series using methods from stringology, the study of efficient algorithms for string processing, to systematically identify and characterize recurrent temporal patterns in neural signals. The primary aim is to introduce quantitative measures to understand neural signal dynamics, with the present findings serving as a proof-of-concept. The framework adapts order-preserving matching (OPM) and Cartesian tree matching (CTM) to detect temporal motifs that preserve relative ordering and hierarchical structure while remaining invariant to amplitude scaling. This approach provides a temporally precise representation of EEG dynamics that complements traditional spectral and global complexity analyses. To evaluate its utility, we applied the framework to multichannel EEG recordings from individuals with attention-deficit/hyperactivity disorder (ADHD) and matched controls using a publicly available dataset. Highly recurrent, group-specific motifs were extracted and quantified using both OPM and CTM. The ADHD group exhibited significantly higher motif frequencies, suggesting increased repetitiveness in neural activity. OPM analysis revealed shorter motif lengths and greater gradient instability in ADHD, reflected in larger mean and maximal inter-sample amplitude changes. CTM analysis further demonstrated reduced hierarchical complexity in ADHD, characterized by shallower tree structures and fewer hierarchical levels despite comparable motif lengths. These findings suggest that ADHD-related EEG alterations involve systematic differences in the structure, stability, and hierarchical organization of recurrent temporal patterns. The proposed stringology-based motif framework provides a complementary computational tool with potential applications for objective biomarker development in neurodevelopmental disorders.

arXiv:2603.03864v1 Announce Type: new Abstract: While EEG features differentiate Major Depressive Disorder (MDD) from healthy controls (HC), their clinical utility as biomarkers depends on a monotonic trajectory across the disease spectrum, from the acute (AC) phase to the maintenance (MA) phase and finally to the healthy baseline. However, the progression of the MA phase remains poorly understood in traditional marker analysis. Analyzing EEG data from 74 individuals (24 AC, 23 MA, and 27 HC), this study provides a comprehensive evaluation of classic ERP and resting-state indices across AC, MA, and HC groups. Our results demonstrate that almost no conventional metrics strictly satisfy the criterion of monotonic progression, likely due to profound inter-individual heterogeneity. These findings highlight the inherent limitations of group-level feature extraction and provide critical insights for developing future paradigms and algorithms to identify neurobiological markers with genuine clinical utility.

arXiv:2603.03870v1 Announce Type: new Abstract: We introduce a two-phase quadratic integrate-and-fire (QIF) neuron whose membrane potential evolves according to two alternating Riccati equations within finite bounds. This simple extension removes the unphysical voltage divergence of the standard QIF model while producing realistic spike waveforms. Despite this modification, the system retains an exact low-dimensional description in the thermodynamic limit, governed by a single complex Riccati equation. Expressions for collective quantities such as the firing rate and mean voltage remain compact and analytically tractable. Because the formalism preserves the mathematical structure of the standard QIF ensemble, it inherits its many generalizations and can serve as a drop-in replacement in existing mean-field frameworks, providing a more biologically plausible yet still exactly solvable neuronal model.

arXiv:2603.04149v1 Announce Type: new Abstract: Structural and functional heterogeneity are hallmarks of cortical circuits, from broad degree distributions in the mouse connectome to diverse intrinsic neuronal timescales. Yet a mechanistic link between connectivity heterogeneity and functional diversity is lacking. To bridge this gap, we introduce a random recurrent network in which connectivity is generated by a configuration model with tunable degree heterogeneity and synaptic weights exhibiting varying levels of correlation. Using generating-functional methods, we derive a heterogeneous dynamical mean-field theory (hDMFT) with degree-conditioned stochastic dynamics. The theory shows that the interaction of partial symmetry in the weights and degree heterogeneity induces a non-Markovian memory term in the form of an emergent self-coupling whose strength scales with degree and produces a broad distribution of activity timescales. We obtain analytic stability criteria demonstrating that degree heterogeneity lowers the critical gain and localizes unstable modes onto hubs. The resulting rich dynamical landscape includes silent, chaotic, and multistable regimes, which we uncover via spectral, replica, and Lyapunov exponent analyses. We highlight the computational benefits of the observed timescale heterogeneity by revealing that, under an external input drive featuring a broadband spectrum, slow hub neurons act as integrators, demixing slow input components. Finally, instantiating the model with the empirically measured topology from the MICrONS cubic-millimeter mouse connectome explains the broad range of single-neuron timescales and their positive correlation with in-degree observed in resting-state recordings. Our results provide a mechanistic link between connectome topology, neural dynamics, and computation, identifying hubs in partially symmetric networks as a natural substrate for multiplexed processing across timescales.

arXiv:2603.03312v1 Announce Type: cross Abstract: Decoding natural language from non-invasive EEG signals is a promising yet challenging task. However, current state-of-the-art models remain constrained by three fundamental limitations: Semantic Bias (mode collapse into generic templates), Signal Neglect (hallucination based on linguistic priors rather than neural inputs), and the BLEU Trap, where evaluation metrics are artificially inflated by high-frequency stopwords, masking a lack of true semantic fidelity. To address these challenges, we propose SemKey, a novel multi-stage framework that enforces signal-grounded generation through four decoupled semantic objectives: sentiment, topic, length, and surprisal. We redesign the interaction between the neural encoder and the Large Language Model (LLM) by injecting semantic prompts as Queries and EEG embeddings as Key-Value pairs, strictly forcing the model to attend to neural inputs. Furthermore, we move beyond standard translation metrics by adopting N-way Retrieval Accuracy and Fr\'echet Distance to rigorously assess diversity and alignment. Extensive experiments demonstrate that our approach effectively eliminates hallucinations on noise inputs and achieves SOTA performance on these robust protocols. Code will be released upon acceptance at https://github.com/xmed-lab/SemKey.

arXiv:2603.03507v1 Announce Type: cross Abstract: Adversarial attacks - input perturbations imperceptible to humans that fool neural networks - remain both a persistent failure mode in machine learning, and a phenomenon with mysterious origins. To shed light, we define and analyze a network's perceptual manifold (PM) for a class concept as the space of all inputs confidently assigned to that class by the network. We find, strikingly, that the dimensionalities of neural network PMs are orders of magnitude higher than those of natural human concepts. Since volume typically grows exponentially with dimension, this suggests exponential misalignment between machines and humans, with exponentially many inputs confidently assigned to concepts by machines but not humans. Furthermore, this provides a natural geometric hypothesis for the origin of adversarial examples: because a network's PM fills such a large region of input space, any input will be very close to any class concept's PM. Our hypothesis thus suggests that adversarial robustness cannot be attained without dimensional alignment of machine and human PMs, and therefore makes strong predictions: both robust accuracy and distance to any PM should be negatively correlated with the PM dimension. We confirmed these predictions across 18 different networks of varying robust accuracy. Crucially, we find even the most robust networks are still exponentially misaligned, and only the few PMs whose dimensionality approaches that of human concepts exhibit alignment to human perception. Our results connect the fields of alignment and adversarial examples, and suggest the curse of high dimensionality of machine PMs is a major impediment to adversarial robustness.

arXiv:2511.14555v3 Announce Type: replace Abstract: Decoded Neurofeedback (DecNef) is a flourishing non-invasive approach to brain modulation with wide-ranging applications in neuromedicine and cognitive neuroscience. However, progress in DecNef research remains constrained by subject-dependent learning variability, reliance on indirect measures to quantify progress, and the high cost and time demands of experimentation. We present DecNefSimulator, a modular and interpretable simulation framework that formalizes DecNef as a machine learning problem. Beyond providing a virtual laboratory, DecNefSimulator enables researchers to model, analyze and understand neurofeedback dynamics. Using latent variable generative models as simulated participants, DecNefSimulator allows direct observation of internal cognitive states and systematic evaluation of how different protocol designs and subject characteristics influence learning. We demonstrate how this approach can (i) reproduce empirical phenomena of DecNef learning, (ii) identify conditions under which DecNef feedback fails to induce learning, and (iii) guide the design of more robust and reliable DecNef protocols in silico before human implementation. In summary, DecNefSimulator bridges computational modeling and cognitive neuroscience, offering a principled foundation for methodological innovation, robust protocol design, and ultimately, a deeper understanding of DecNef-based brain modulation.

arXiv:2603.01387v2 Announce Type: replace Abstract: The Bayesian brain hypothesis has been a leading theory in understanding perceptual decision-making under uncertainty. While extensive psychophysical evidence supports the notion of the brain performing Bayesian computations, how uncertainty information is encoded in sensory neural populations remains elusive. Specifically, two competing hypotheses propose that early sensory populations encode either the likelihood function (exemplified by probabilistic population codes) or the posterior distribution (exemplified by neural sampling codes) over the stimulus, with the key distinction lying in whether stimulus priors would modulate the neural responses. However, experimentally differentiating these two hypotheses has remained challenging, as it is unclear what task design would effectively distinguish the two. In this work, we present an information-theoretic framework for optimizing the task stimulus distribution that would maximally differentiate competing probabilistic neural codes. To quantify how distinguishable the two probabilistic coding hypotheses are under a given task design, we derive the information gap--the expected performance difference when likelihood versus posterior decoders are applied to neural populations--by evaluating the Kullback-Leibler divergence between the true posterior and a task-marginalized surrogate posterior. Through extensive simulations, we demonstrate that the information gap accurately predicts decoder performance differences across diverse task settings. Critically, maximizing the information gap yields stimulus distributions that optimally differentiate likelihood and posterior coding hypotheses. Our framework enables principled, theory-driven experimental designs with maximal discriminative power to differentiate probabilistic neural codes, advancing our understanding of how neural populations represent and process sensory uncertainty.

arXiv:2603.02491v1 Announce Type: cross Abstract: As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world models, but not that such representations are required. We prove quantitative "selection theorems" showing that low *average-case regret* on structured families of action-conditioned prediction tasks forces an agent to implement a predictive, structured internal state. Our results cover stochastic policies, partial observability, and evaluation under task distributions, without assuming optimality, determinism, or access to an explicit model. Technically, we reduce predictive modeling to binary "betting" decisions and show that regret bounds limit probability mass on suboptimal bets, enforcing the predictive distinctions needed to separate high-margin outcomes. In fully observed settings, this yields approximate recovery of the interventional transition kernel; under partial observability, it implies necessity of belief-like memory and predictive state, addressing an open question in prior world-model recovery work.

arXiv:2603.03037v1 Announce Type: cross Abstract: We use topological data analysis to study neural population activity in the Sensorium 2023 dataset, which records responses from thousands of mouse visual cortex neurons to diverse video stimuli. For each video, we build frame-by-frame cubical complexes from neuronal activity and apply zigzag persistent homology to capture how topological structure evolves over time. These dynamics are summarized with persistence landscapes, providing a compact vectorized representation of temporal features. We focus on one-dimensional topological features-loops in the data-that reflect coordinated, cyclical patterns of neural co-activation. To test their informativeness, we compare repeated trials of different videos by clustering their resulting topological neural representations. Our results show that these topological descriptors reliably distinguish neural responses to distinct stimuli. This work highlights a connection between evolving neuronal activity and interpretable topological signatures, advancing the use of topological data analysis for uncovering neural coding in complex dynamical systems.

arXiv:2603.03201v1 Announce Type: cross Abstract: Reasoning is the ability to integrate internal states and external inputs in a meaningful and semantically consistent flow. Contemporary machine learning (ML) systems increasingly rely on such sequential reasoning, from language understanding to multi-modal generation, often operating over dictionaries of prototypical patterns reminiscent of associative memory models. Understanding retrieval and sequentiality in associative memory models provides a powerful bridge to gain insight into ML reasoning. While the static retrieval properties of associative memory models are well understood, the theoretical foundations of sequential retrieval and multi-memory integration remain limited, with existing studies largely relying on numerical evidence. This work develops a dynamical theory of sequential reasoning in Hopfield networks. We consider the recently proposed input-driven plasticity (IDP) Hopfield network and analyze a two-timescale architecture coupling fast associative retrieval with slow reasoning dynamics. We derive explicit conditions for self-sustained memory transitions, including gain thresholds, escape times, and collapse regimes. Together, these results provide a principled mathematical account of sequentiality in associative memory models, bridging classical Hopfield dynamics and modern reasoning architectures.