arXiv subjects

Nikita Pospelov

Publications and source records attributed to Nikita Pospelov.

9 recordsLinked to original sources

arXiv2026

XLOG: A CUDA-Native Engine for Neurosymbolic Integration

xlog is a CUDA-native logic programming engine integrating neural perception with deterministic Datalog, probabilistic inference, and epistemic world views through a typed frontend and provider-owned CUDA runtime. Its reasoning modes share device data planes, but their execution boundaries differ: ordinary Datalog and exact inference are host-orchestrated, while certified resident recursive and Monte Carlo sampled cores record zero tracked host-device transfers before a bounded terminal receipt. The probabilistic path supports end-to-end gradients through GPU knowledge compilation from provenance to CNF to Decision-DNNF, exact weighted model counting, and backward gradients. A final smoothed circuit is certified against its source formula before caching or evaluation. Circuit caching yields a 2.74x MNIST-addition training speedup; a worst-case-optimal join subsystem yields a 27.96x geometric-mean gain over xlog's binary-join baseline. MNIST-addition accuracy matches Scallop's (0.9561 versus 0.9468), but no per-epoch speed claim is made because baseline epoch time varies with CPU quota. In five hub-skewed triangle-counting cases, the Souffle-to-fused-xlog execution-time ratio rises from 0.88x at 150k edges, where Souffle is faster, to 5.54x at 1.2M; fused peak device allocations are 85-1,033 MB versus 3,287-44,979 MB for the materializing arm. Exact inference is correctness-equivalent to but slower than ProbLog2. On a public video benchmark, a proximity predicate trained only through symbolic credit replaces hand-set geometry at unchanged held-out accuracy; within Event-Calculus rule search it fails ten-fold cross-validation and does not transfer on a leak-free split. On a maritime corpus, weighted clauses beat crisp selection by 0.065 F1, with the result reproduced by one chronological training pass.

cs.AI↗

arXiv2026

DRIADA: A Python Toolkit for Cross-Scale Analysis of Single-Neuron Selectivity and Population Dynamics

Brain activity spans single-neuron, population, and network levels, and core questions in neural coding require moving between them. Yet current tools target a single paradigm and incompatible data formats, leaving cross-level questions hard to address. We present DRIADA, an open-source Python framework that unifies neural signals and time-aligned behavior in a shared data model, so selectivity testing, dimensionality reduction, and network analysis operate within a unified workflow. We evaluate it on synthetic data with known ground truth, hippocampal calcium imaging from 13~mice in an open field, and a simulated toroidal attractor network. In the hippocampal data, selectivity-based filtering restored a two-dimensional spatial embedding from a collapsed all-neuron embedding, while reverse analysis showed that ${\sim}57\%$ of neurons informative about leading manifold dimensions were not selective to any of the 11 measured behavioral features. On the toroidal benchmark, four independent modules recovered the expected topology. DRIADA makes cross-scale analysis routine across calcium imaging, spike trains, and simulated networks.

q-bio.NC↗

arXiv2026

INTENSE: Detecting and disentangling neuronal selectivity in calcium imaging data

Neurons encode information about the environment through their activity. As animals explore the environment, neurons rapidly acquire selectivity for distinct features of the external world; characterizing how these selectivity patterns emerge, reorganize, and overlap is key to linking neural activity to behavior and cognition. Calcium imaging in freely behaving animals can record large neuronal populations, but quantifying neuron-behavior selectivity directly from continuous fluorescence is challenging because both signals are temporally autocorrelated and calcium kinetics introduce time lags. Here we present INTENSE (INformation-Theoretic Evaluation of Neuronal SElectivity), an open-source framework that uses mutual information to detect neuron-behavior associations from raw calcium fluorescence data. INTENSE controls false discoveries using circular-shift permutation testing that preserves temporal structure and optimizes temporal delays to account for indicator kinetics and prospective/retrospective encoding. To separate genuine mixed selectivity from associations driven by behavioral covariance, INTENSE applies conditional mutual information-based disentanglement. We validated INTENSE on synthetic datasets, demonstrating robust detection across diverse signal-to-noise ratios and reliability conditions, whereas methods lacking temporal controls show poor performance. Applied to CA1 miniscope recordings in mice freely exploring an open field, INTENSE reveals robust selectivity to multiple variables (place, head direction, object interaction, locomotion) and refines mixed-selectivity estimates by distinguishing redundant from genuinely multi-variable encoding. Together, INTENSE enables high-throughput, information-theoretic selectivity mapping with principled control of temporal structure and behavioral covariance, bridging large-scale recordings to circuit-level hypotheses.

q-bio.NC↗

arXiv2024

Fast gradient-free activation maximization for neurons in spiking neural networks

Elements of neural networks, both biological and artificial, can be described by their selectivity for specific cognitive features. Understanding these features is important for understanding the inner workings of neural networks. For a living system, such as a neuron, whose response to a stimulus is unknown and not differentiable, the only way to reveal these features is through a feedback loop that exposes it to a large set of different stimuli. The properties of these stimuli should be varied iteratively in order to maximize the neuronal response. To utilize this feedback loop for a biological neural network, it is important to run it quickly and efficiently in order to reach the stimuli that maximizes certain neurons' activation with the least number of iterations possible. Here we present a framework with an efficient design for such a loop. We successfully tested it on an artificial spiking neural network (SNN), which is a model that simulates the asynchronous spiking activity of neurons in living brains. Our optimization method for activation maximization is based on the low-rank Tensor Train decomposition of the discrete activation function. The optimization space is the latent parameter space of images generated by SN-GAN or VQ-VAE generative models. To our knowledge, this is the first time that effective AM has been applied to SNNs. We track changes in the optimal stimuli for artificial neurons during training and show that highly selective neurons can form already in the early epochs of training and in the early layers of a convolutional spiking network. This formation of refined optimal stimuli is associated with an increase in classification accuracy. Some neurons, especially in the deeper layers, may gradually change the concepts they are selective for during learning, potentially explaining their importance for model performance.

cs.NE↗

arXiv2024

Metric structural human connectomes: localization and multifractality of eigenmodes

In this study, we explore the fundamental principles behind the architecture of the human brain's structural connectome, from the perspective of spectral analysis of Laplacian and adjacency matrices. Building on the idea that the brain strikes a balance between efficient information processing and minimizing wiring costs, we aim to understand the impact of the metric properties of the connectome and how they relate to the existence of an inherent scale. We demonstrate that a simple generative model, combining nonlinear preferential attachment with an exponential penalty for spatial distance between nodes, can effectively reproduce several key characteristics of the human connectome, including spectral density, edge length distribution, eigenmode localization and local clustering properties. We also delve into the finer spectral properties of the human structural connectomes by evaluating the inverse participation ratios ($\text{IPR}_q$) across various parts of the spectrum. Our analysis reveals that the level statistics in the soft cluster region of the Laplacian spectrum deviate from a purely Poisson distribution due to interactions between clusters. Additionally, we identified scar-like localized modes with large IPR values in the continuum spectrum. We identify multiple fractal eigenmodes distributed across different parts of the spectrum, evaluate their fractal dimensions and find a power-law relationship in the return probability, which is a hallmark of critical behavior. We discuss the conjectures that a brain operates in the Griffiths or multifractal phases.

q-bio.NC↗

arXiv2024

Multiple Neuronal Specializations Elicited By Socially Driven Recognition Of Food Odors

This study investigates the dynamics of non-spatial specializations in hippocampal place cells during exposure to novel environments. Hippocampal place cells, known for their role in spatial mapping, exhibit multi-modal responses to sensory cues. The research focuses on understanding how these cells adapt their specialization in response to novel stimuli, specifically examining non-spatial determinants such as odors and social interactions. Using a social-driven food odor recognition model in mice, the study records CA1 hippocampal neuron activity through miniscope imaging. The experimental design involves demonstrations of novel odors to mice, followed by observation sessions with food options. The analysis employs deep neural network tools for behavior tracking and the custom-developed INTENS software package for identifying neural specializations. Results indicate multiple specializations, particularly those related to odor, with differences observed between training and testing sessions. The findings suggest a temporal aspect to the formation of these specializations in novel conditions, necessitating further investigation for precise tracking.

q-bio.NC↗

arXiv2023

Largest eigenvalue statistics of sparse random adjacency matrices

We investigate the statistics of the largest eigenvalue, $λ_{\rm max}$, in an ensemble of $N\times N$ large ($N\gg 1$) sparse adjacency matrices, $A_N$. The most attention is paid to the distribution and typical fluctuations of $λ_{\rm max}$ in the vicinity of the percolation threshold, $p_c=\frac{1}{N}$. The overwhelming majority of subgraphs representing $A_N$ near $p_c$ are exponentially distributed linear subchains, for which the statistics of the normalized largest eigenvalue can be analytically connected with the Gumbel distribution. For the ensemble of {\rm all} subgraphs near $p_c$ we suggest that under an appropriate modification of the normalization constant the Gumbel distribution provides a reasonably good approximation. Using numerical simulations we demonstrate that the proposed transformation of $λ_{\rm max}$ is indeed Gumbel-distributed and the leading finite-size corrections in the vicinity of $p_c$ scale with $N$ as $\sim \ln^{-2}N$. All together, our results reveal a previously unknown universality in eigenvalue statistics of sparse matrices close to the percolation threshold.

cond-mat.stat-mech↗

arXiv2022

From steady-state TASEP model with open boundaries to 1D Ising model at negative fugacity

We demonstrate here a series of exact mappings between particular cases of four statistical physics models: equilibrium 1-dimensional lattice gas with nearest-neighbor repulsion, $(1+1)$-dimensional combinatorial heap of pieces, random walks on half-plane and totally asymmetric simple exclusion process (TASEP) in one dimension (1D). In particular, we show that generating function of a steady state of one-dimensional TASEP with open boundaries can be interpreted as a quotient of partition functions of 1D hard-core lattice gases with one adsorbing lattice site and negative fugacity. This result is based on the combination of (i) a representation of the steady-state TASEP configurations in terms of $(1+1)$-dimensional heaps of pieces and (ii) a theorem connecting the partition function of $(1+1)$-dimensional heaps of pieces with that of a single layer of pieces, which in this case is a 1D hard-core lattice gas.

cond-mat.stat-mech↗

arXiv2021

α-Indirect Control in Onion-like Networks

Tens of thousands of parent companies control millions of subsidiaries through long chains of intermediary entities in global corporate networks. Conversely, tens of millions of entities are directly held by sole owners. We propose an algorithm for identification of ultimate controlling entities in such networks that unifies direct and indirect control and allows for continuous interpolation between the two concepts via a factor damping long paths. By exploiting onion-like properties of ownership networks the algorithm scales linearly with the network size and handles circular ownership by design. We apply it to the universe of 4.2 mln UK companies and 4 mln of their holders to understand the distribution of control in the country. Furthermore, we provide the first independent evaluation of the control identification results. We reveal that the proposed $α$-ICON algorithm identifies more than 96% of beneficiary entities from the evaluation set and supersedes the existing approaches reported in the literature. We refer the superiority of $α$-ICON algorithm to its ability to correctly identify the parents long away from their subsidiaries in the network.

physics.soc-ph↗