arXiv subjects

Mauricio Barahona

Publications and source records attributed to Mauricio Barahona.

At least 19 recordsLinked to original sources

arXiv2026

Graph-theoretic design of lasing networks for physical vision

Physical neural networks perform learning through the intrinsic nonlinear dynamics of matter. Optimising their design presents a considerable challenge: complex many-body physics can provide powerful computation, but are expensive to simulate and large experimental optimisation runs are impractical to fabricate. Hence, the high-dimensional space of possible network topologies cannot be effectively directly searched. Here, we show that this search can be efficiently performed in an abstract graph space that is vastly cheaper to explore. Using random lasing networks -- composed of interconnected nanoscale waveguides and hosting strongly coupled lasing modes -- as an exemplar physical vision system, we establish a quantitative three-layer link: simple graph-theoretic metrics predict the nonlinear lasing physics, which in turn predicts vision performance. After validating this relationship using physical simulations, we exploit it to drive an evolutionary algorithm using graph metrics, producing network topologies that outperform random designs at a fraction of the computational cost (3000$\times$ speed-up compared to physical simulation). On simulated image-classification tasks, graph-optimised networks substantially improve classification accuracy. As our framework operates on network topology rather than substrate-specific physics, we anticipate it can transfer to other network-based physical learning systems, providing an efficient route for the directed design and optimisation of complex, strongly-interacting physical neural networks.

cond-mat.dis-nn↗

arXiv2026

A Martingale Kernel Independence Test

The Hilbert-Schmidt Independence Criterion (HSIC) and its joint-independence extension $d\mathrm{HSIC}$ are degenerate $V$-statistics whose data-dependent weighted-$χ^2$ null limits force a permutation calibration that multiplies the per-test cost by the number of permutations, in practice two orders of magnitude. Adapting the recent martingale MMD construction for two-sample testing to the (joint) independence problem, we introduce two studentised statistics whose null distributions are standard normal regardless of the data law, so that a single normal-quantile lookup replaces the permutation step entirely. The first, $m\mathrm{HSIC}$, is a self-normalised lower-triangular sum of the Hadamard product of two empirically centred Gram matrices. Under independence and bounded-fourth-moment kernels it converges to a standard normal. It is consistent against every fixed alternative, and runs at quadratic cost in the sample size without any sample split, matching the biased HSIC $V$-statistic. Our second statistic, $md\mathrm{HSIC}$, achieves finite-sample consistency with a single half-sample split: the centring is estimated on one half and the lower-triangular self-normalised martingale is run on the other, shrinking the conditional-mean residual to a quantity that is exponentially small in $d$, so the statistic is asymptotically standard normal at every fixed number of jointly tested variables, with a per-test cost that grows only linearly in $d$. On synthetic data with per-variable input dimension from $1$ to $500$ and between $2$ and $10$ jointly tested variables, both statistics match the empirical type-I error rate and test power of permutation-calibrated baselines while running $25$ to $60\times$ faster.

stat.ML↗

arXiv2026

Root-to-Leaf Path Random Walks, Normalized Hodge Laplacians, and Cheeger Inequalities on Simplicial Complexes

We introduce root-to-leaf path random walks on double covers of graded signed graphs and analyze their behavior in a general setting. Viewing simplicial complexes within this framework, we show that these walks induce the natural normalization of the coboundary operator and of the Hodge Laplacians while preserving the basic structural features of combinatorial Hodge theory. We then derive Cheeger inequalities for the upper side of the normalized Hodge spectrum, identify the coherent structures governing these bounds, and combine the up- and down-cases into sharper estimates.

math.CO↗

arXiv2026

Information-theoretic signatures of causality in Bayesian networks and hypergraphs

Analyzing causality in multivariate systems involves establishing how information is generated, distributed and combined. Traditional causal discovery frameworks are capable of multivariate reasoning but their intrinsic pairwise graph topology restricts them to do so only indirectly by integrating multivariate information across pairwise edges. Higher-order information theory provides direct tools that can explicitly model higher-order interactions. In particular, Partial Information Decomposition (PID) allows the decomposition of the information that a set of sources provides about a target into redundant, unique, and synergistic components. Yet the mathematical connection between such higher-order information-theoretic measures and causal structure remains undeveloped. Here we establish the first theoretical correspondence between PID components and causal structure in both Bayesian networks and hypergraphs. We first show that in Bayesian networks unique information precisely characterizes direct causal neighbors, while synergy identifies collider relationships. This establishes a localist causal discovery paradigm in which the structure surrounding each variable can be recovered from its immediate informational footprint, eliminating the need for global search over graph space. Extending these results to more expressive causal representation, we prove that PID signatures in Bayesian hypergraphs differentiate parents, children, co-heads, and co-tails, revealing a novel collider effect unique to multi-tail hyperedges. Our results position PID as a rigorous, model-agnostic foundation for inferring both pairwise and higher-order causal structure, and introduce a fundamentally local information-theoretic viewpoint on causal discovery.

cs.IT↗

arXiv2026

MCbiF: Measuring Topological Autocorrelation in Multiscale Clusterings via 2-Parameter Persistent Homology

Datasets often possess an intrinsic multiscale structure with meaningful descriptions at different levels of coarseness. Such datasets are naturally described as multi-resolution clusterings, i.e., not necessarily hierarchical sequences of partitions across scales. To analyse and compare such sequences, we use tools from topological data analysis and define the Multiscale Clustering Bifiltration (MCbiF), a 2-parameter filtration of abstract simplicial complexes that encodes cluster intersection patterns across scales. The MCbiF is a complete invariant of (non-hierarchical) sequences of partitions and can be interpreted as a higher-order extension of Sankey diagrams, which reduce to dendrograms for hierarchical sequences. We show that the multiparameter persistent homology (MPH) of the MCbiF yields a finitely presented and block decomposable module, and its stable Hilbert functions characterise the topological autocorrelation of the sequence of partitions. In particular, at dimension zero, the MPH captures violations of the refinement order of partitions, whereas at dimension one, the MPH captures higher-order inconsistencies between clusters across scales. We then demonstrate through experiments the use of MCbiF Hilbert functions as interpretable topological feature maps for downstream machine learning tasks, and show that MCbiF feature maps outperform both baseline features and representation learning methods on regression and classification tasks for non-hierarchical sequences of partitions. We also showcase an application of MCbiF to real-world data of non-hierarchical wild mice social grouping patterns across time.

math.AT↗

arXiv2026

Few-Shot Neuromorphic Vision in a Nonlinear Photonic Network Laser

With the growing prevalence of AI, demand increases for hardware that mimics the brain's ability to extract structure from limited data. In the retina, ganglion cells detect features from sparse inputs via lateral inhibition, where neurons antagonistically suppress activity of neighbouring cells. Biological neurons exhibit diverse heterogeneous nonlinear responses, linked to robust learning and strong performance in low-data regimes. Here, we introduce a retinally-inspired photonic computing system where spatially-competing lasing modes in a random network laser act as heterogeneous, inhibitively-coupled neurons - enabling feature detection, few-shot classification, and segmentation. This silicon-compatible scheme harnesses heterogeneous excitatory and inhibitory nonlinear physical dynamics which give rise to emergent photonic computing behaviour, including parallel feature detection and strong performance when training data is scarce. We report 98.05% and 87.85% accuracy on MNIST and Fashion-MNIST, and 90.12% on BreaKHis cancer diagnosis - outperforming software CNNs including EfficientNetV2 and the vision transformer ViT in few-shot and class-imbalanced regimes with training sets of up to several hundred images. We demonstrate combined segmentation and classification on the HAM10k skin lesion dataset, achieving DICE and Jaccard scores of 84.49% and 74.80%. These results demonstrate the potential of random lasing networks as nonlinear photonic learning systems, and highlight the ability of heterogeneous nonlinear dynamics to support strong learning in challenging low-data scenarios.

cond-mat.dis-nn↗

arXiv2025

Integrating protein sequence embeddings with structure via graph-based deep learning for single-residue property prediction

Understanding the intertwined contributions of amino acid sequence and spatial structure is essential to explain protein behaviour. Here, we introduce INFUSSE (Integrated Network Framework Unifying Structure and Sequence Embeddings), a deep learning framework for the prediction of single-residue properties that combines fine-tuning of sequence embeddings derived from a Large Language Model with the inclusion of graph-based representations of protein structures via a diffusive Graph Convolutional Network. To illustrate the benefits of jointly leveraging sequence and structure, we apply INFUSSE to the prediction of B-factors in antibodies, a residue property that reflects the local flexibility shaped by biochemical and structural constraints in these highly variable and dynamic proteins. Using a dataset of 1510 antibody and antibody-antigen complexes from the database SAbDab, we show that INFUSSE improves performance over current machine learning (ML) methods based on sequence or structure alone, and allows for the systematic disentanglement of sequence and structure contributions to the performance. Our results show that adding structural information via geometric graphs enhances predictions especially for intrinsically disordered regions, protein-protein interaction sites, and highly variable amino acid positions -- all key structural features for antibody function which are not well captured by purely sequence-based ML descriptions.

q-bio.QM↗

arXiv2025

Machine learning approaches for interpretable antibody property prediction using structural data

Understanding the relationship between antibody sequence, structure and function is essential for the design of antibody-based therapeutics and research tools. Recently, machine learning (ML) models mostly based on the application of large language models to sequence information have been developed to predict antibody properties. Yet there are open directions to incorporate structural information, not only to enhance prediction but also to offer insights into the underlying molecular mechanisms. This chapter provides an overview of these approaches and describes two ML frameworks that integrate structural data (via graph representations) with neural networks to predict properties of antibodies: ANTIPASTI predicts binding affinity (a global property) whereas INFUSSE predicts residue flexibility (a local property). We survey the principles underpinning these models; the ways in which they encode structural knowledge; and the strategies that can be used to extract biologically relevant statistical signals that can help discover and disentangle molecular determinants of the properties of interest.

q-bio.QM↗

arXiv2025

Protein generation with embedding learning for motif diversification

A fundamental challenge in protein design is the trade-off between generating structural diversity while preserving motif biological function. Current state-of-the-art methods, such as partial diffusion in RFdiffusion, often fail to resolve this trade-off: small perturbations yield motifs nearly identical to the native structure, whereas larger perturbations violate the geometric constraints necessary for biological function. We introduce Protein Generation with Embedding Learning (PGEL), a general framework that learns high-dimensional embeddings encoding sequence and structural features of a target motif in the representation space of a diffusion model's frozen denoiser, and then enhances motif diversity by introducing controlled perturbations in the embedding space. PGEL is thus able to loosen geometric constraints while satisfying typical design metrics, leading to more diverse yet viable structures. We demonstrate PGEL on three representative cases: a monomer, a protein-protein interface, and a cancer-related transcription factor complex. In all cases, PGEL achieves greater structural diversity, better designability, and improved self-consistency, as compared to partial diffusion. Our results establish PGEL as a general strategy for embedding-driven protein generation allowing for systematic, viable diversification of functional motifs.

q-bio.QM↗

arXiv2025

Multiscale mobility patterns and the restriction of human movement

From the perspective of human mobility, the COVID-19 pandemic constituted a natural experiment of enormous reach in space and time. Here, we analyse the inherent multiple scales of human mobility using Facebook Movement Maps collected before and during the first UK lockdown. First, we obtain the pre-lockdown UK mobility graph, and employ multiscale community detection to extract, in an unsupervised manner, a set of robust partitions into flow communities at different levels of coarseness. The partitions so obtained capture intrinsic mobility scales with better coverage than NUTS regions, which suffer from mismatches between human mobility and administrative divisions. Furthermore, the flow communities in the fine scale partition match well the UK Travel to Work Areas (TTWAs) but also capture mobility patterns beyond commuting to work. We also examine the evolution of mobility under lockdown, and show that mobility first reverted towards fine scale flow communities already found in the pre-lockdown data, and then expanded back towards coarser flow communities as restrictions were lifted. The improved coverage induced by lockdown is well captured by a linear decay shock model, which allows us to quantify regional differences both in the strength of the effect and the recovery time from the lockdown shock.

physics.soc-ph↗

arXiv2025

PyGenStability: Multiscale community detection with generalized Markov Stability

We present PyGenStability, a general-use Python software package that provides a suite of analysis and visualisation tools for unsupervised multiscale community detection in graphs. PyGenStability finds optimized partitions of a graph at different levels of resolution by maximizing the generalized Markov Stability quality function with the Louvain or Leiden algorithms. The package includes automatic detection of robust graph partitions and allows the flexibility to choose quality functions for weighted undirected, directed and signed graphs, and to include other user-defined quality functions.

cs.SI↗

arXiv2025

LGDE: Local Graph-based Dictionary Expansion

We present Local Graph-based Dictionary Expansion (LGDE), a method for data-driven discovery of the semantic neighbourhood of words using tools from manifold learning and network science. At the heart of LGDE lies the creation of a word similarity graph from the geometry of word embeddings followed by local community detection based on graph diffusion. The diffusion in the local graph manifold allows the exploration of the complex nonlinear geometry of word embeddings to capture word similarities based on paths of semantic association, over and above direct pairwise similarities. Exploiting such semantic neighbourhoods enables the expansion of dictionaries of pre-selected keywords, an important step for tasks in information retrieval, such as database queries and online data collection. We validate LGDE on two user-generated English-language corpora and show that LGDE enriches the list of keywords with improved performance relative to methods based on direct word similarities or co-occurrences. We further demonstrate our method through a real-world use case from communication science, where LGDE is evaluated quantitatively on the expansion of a conspiracy-related dictionary from online data collected and analysed by domain experts. Our empirical results and expert user assessment indicate that LGDE expands the seed dictionary with more useful keywords due to the manifold-learning-based similarity network.

cs.CL↗

arXiv2025

Permutation-Free High-Order Interaction Tests

Kernel-based hypothesis tests offer a flexible, non-parametric tool to detect high-order interactions in multivariate data, beyond pairwise relationships. Yet the scalability of such tests is limited by the computationally demanding permutation schemes used to generate null approximations. Here we introduce a family of permutation-free high-order tests for joint independence and partial factorisations of $d$ variables. Our tests eliminate the need for permutation-based approximations by leveraging V-statistics and a novel cross-centring technique to yield test statistics with a standard normal limiting distribution under the null. We present implementations of the tests and showcase their efficacy and scalability through synthetic datasets. We also show applications inspired by causal discovery and feature selection, which highlight both the importance of high-order interactions in data and the need for efficient computational methods.

stat.ME↗

arXiv2025

Analysing Multiscale Clusterings with Persistent Homology

In data clustering, it is often desirable to find not just a single partition into clusters but a sequence of partitions that describes the data at different scales (or levels of coarseness). A natural problem then is to analyse and compare the (not necessarily hierarchical) sequences of partitions that underpin such multiscale descriptions. Here, we use tools from topological data analysis and introduce the Multiscale Clustering Filtration (MCF), a well-defined and stable filtration of abstract simplicial complexes that encodes arbitrary cluster assignments in a sequence of partitions across scales of increasing coarseness. We show that the zero-dimensional persistent homology of the MCF measures the degree of hierarchy of this sequence, and the higher-dimensional persistent homology tracks the emergence and resolution of conflicts between cluster assignments across the sequence of partitions. To broaden the theoretical foundations of the MCF, we provide an equivalent construction via a nerve complex filtration, and we show that, in the hierarchical case, the MCF reduces to a Vietoris-Rips filtration of an ultrametric space. Using synthetic data, we then illustrate how the persistence diagram of the MCF provides a feature map that can serve to characterise and classify multiscale clusterings.

math.AT↗

arXiv2025

Information-Theoretic Measures on Lattices for High-Order Interactions

Traditional measures based solely on pairwise associations often fail to capture the complex statistical structure of multivariate data. Existing approaches for identifying information shared among $d>3$ variables are frequently computationally intractable, asymmetric with respect to a target variable, or unable to account for all the ways in which the joint probability distribution can be factorised. Here we present a systematic framework based on lattice theory to derive higher-order information-theoretic measures for multivariate data. Our construction uses lattice and operator function pairs, whereby an operator function is applied over a lattice that represents the algebraic relationships among variables. We show that many commonly used measures can be derived within this framework, yet they fail to capture all interactions for $d>3$, either because they are defined on restricted sublattices, or because the use of the KL divergence as an operator function, a typical choice, leads to undesired disregard of groups of interactions. To fully characterise all interactions among $d$ variables, we introduce the Streitberg Information, which is defined over the full partition lattice and uses generalised divergences (beyond KL) as operator functions. We validate the Streitberg Information on synthetic data, and illustrate its application in detecting complex interactions among stocks, decoding neural signals, and performing feature selection in machine learning.

cs.IT↗

arXiv2025

Moment-based parameter inference with error guarantees for stochastic reaction networks

Inferring parameters of models of biochemical kinetics from single-cell data remains challenging because of the uncertainty arising from the intractability of the likelihood function of stochastic reaction networks. Such uncertainty falls beyond current error quantification measures, which focus on the effects of finite sample size and identifiability but lack theoretical guarantees when likelihood approximations are needed. Here, we propose a method for the inference of parameters of stochastic reaction networks that works for both steady-state and time-resolved data and is applicable to networks with non-linear and rational propensities. Our approach provides bounds on the parameters via convex optimisation over sets constrained by moment equations and moment matrices by taking observations to form moment intervals, which are then used to constrain parameters through convex sets. The bounds on the parameters contain the true parameters under the condition that the moment intervals contain the true moments, thus providing uncertainty quantification and error guarantees. Our approach does not need to predict moments and distributions for given parameters (i.e., it avoids solving or simulating the forward problem), and hence circumvents intractable likelihood computations or computationally expensive simulations. We demonstrate its use for uncertainty quantification, data integration and prediction of latent species statistics through synthetic data from common non-linear biochemical models including the Schlögl model and the toggle switch, a model of post-transcriptional regulation at steady state, and a birth-death model with time-dependent data.

q-bio.QM↗

arXiv2024

ANTIPASTI: interpretable prediction of antibody binding affinity exploiting Normal Modes and Deep Learning

The high binding affinity of antibodies towards their cognate targets is key to eliciting effective immune responses, as well as to the use of antibodies as research and therapeutic tools. Here, we propose ANTIPASTI, a Convolutional Neural Network model that achieves state-of-the-art performance in the prediction of antibody binding affinity using as input a representation of antibody-antigen structures in terms of Normal Mode correlation maps derived from Elastic Network Models. This representation captures not only structural features but energetic patterns of local and global residue fluctuations. The learnt representations are interpretable: they reveal similarities of binding patterns among antibodies targeting the same antigen type, and can be used to quantify the importance of antibody regions contributing to binding affinity. Our results show the importance of the antigen imprint in the Normal Mode landscape, and the dominance of cooperative effects and long-range correlations between antibody regions to determine binding affinity.

q-bio.QM↗

arXiv2024

Interpretable statistical representations of neural population dynamics and geometry

The dynamics of neuron populations commonly evolve on low-dimensional manifolds. Thus, we need methods that learn the dynamical processes over neural manifolds to infer interpretable and consistent latent representations. We introduce a representation learning method, MARBLE, that decomposes on-manifold dynamics into local flow fields and maps them into a common latent space using unsupervised geometric deep learning. In simulated non-linear dynamical systems, recurrent neural networks, and experimental single-neuron recordings from primates and rodents, we discover emergent low-dimensional latent representations that parametrise high-dimensional neural dynamics during gain modulation, decision-making, and changes in the internal state. These representations are consistent across neural networks and animals, enabling the robust comparison of cognitive computations. Extensive benchmarking demonstrates state-of-the-art within- and across-animal decoding accuracy of MARBLE compared with current representation learning approaches, with minimal user input. Our results suggest that manifold structure provides a powerful inductive bias to develop powerful decoding algorithms and assimilate data across experiments.

cs.LG↗