arXiv subjects

Pietro Liò

Publications and source records attributed to Pietro Liò.

At least 55 records · Page 3Linked to original sources

arXiv2026

Communicability-Inspired Positional Encoding (CIPE)

Positional encodings (PEs) are essential for Transformers. Yet designing effective PEs for non-Euclidean graphs remains challenging. Such encodings should ideally induce an Attention-Compatible Geometry for self-attention: not merely describing graph structure, but defining a geometry whose inner products reflect meaningful structural relatedness. To realize this geometry, we propose Communicability-Inspired Positional Encoding (CIPE), built from communicability, a measure between pairs of nodes that aggregates contributions from paths of all lengths. By construction, CIPE inner products recover communicability, converting global multi-path connectivity into an attention-ready similarity geometry. For practical Transformer training, we introduce dimensionality alignment, mapping graph-size-dependent CIPE representations to prescribed dimensions while faithfully preserving the induced geometry. Empirically, CIPE improves structure-agnostic Transformers by 35.5% on average across seven benchmarks, outperforming representative PEs; it also consistently improves structure-biased graph Transformers, where competing PEs often yield only marginal benefits. These results position CIPE as a principled framework for attention-compatible graph positional encodings.

cs.LG↗

arXiv2026

Hierarchical Pooling for Sheaf Neural Networks

Sheaf Neural Networks (SNNs) generalize Graph Neural Networks (GNNs) by replacing scalar node signals with stalk-valued signals and by using restriction maps to measure compatibility across edges. Unlike standard graph diffusion, which encourages neighboring node features to become similar, sheaf diffusion promotes consistency through the restriction maps and can therefore model more general relationships between neighboring nodes. However, existing sheaf neural architectures mainly operate at a fixed graph resolution and do not provide a principled pooling mechanism for building hierarchical representations. In this paper, we introduce Hierarchical Sheaf Pool (HiSP), a sheaf-aware pooling framework based on local spectral coarsening. Given a partition of the graph, HiSP constructs each coarse stalk by projecting fine stalk-valued features onto the low-frequency eigenmodes of the cluster-internal sheaf Laplacian. These local modes define a cochain-level prolongation map, which allows the fine sheaf energy to be represented on the coarse space through a Galerkin operator. We further analyze the approximation induced by coarsening by separating truncation loss, due to discarded local modes, from realization loss, due to representing the projected operator as a coarse sheaf. Finally, we implement HiSP as a GNN pooling layer compatible with SNNs and provide a PyG implementation supporting batching, lifted sheaf Laplacians, and hierarchical architectures.

cs.LG↗

arXiv2026

KAPLAN: Kolmogorov-Arnold Prognostic Learnable Activation Networks for Survival Analysis

Survival analysis aims to model how covariates and time jointly shape the time-to-event distribution under right censoring. Classical methods such as the Cox model and generalised additive models (GAMs) require interactions and time-varying effects to be manually specified, which is increasingly impractical on rich clinical datasets. We introduce KAPLAN-HR, a B-spline Kolmogorov-Arnold Network (KAN) for nonparametric estimation of the conditional hazard as a joint function of covariates and time. A single-layer KAPLAN-HR model recovers a GAM, while deeper architectures capture interactions and time-varying effects through composition. We establish a convergence rate for the nonparametric KAN hazard estimator that depends only on the smoothness of the underlying KAN representation and not on the covariate dimension, thereby mitigating the curse of dimensionality for KAN-representable targets. In evaluations over six clinical benchmark datasets, KAPLAN-HR matches or exceeds the predictive performance of established statistical and deep learning survival methods.

stat.ML↗

arXiv2026

HypeR Adaptivity: Joint $hr$-Adaptive Meshing via Hypergraph Multi-Agent Deep Reinforcement Learning

Adaptive mesh refinement is central to the efficient solution of partial differential equations (PDEs) via the finite element method (FEM). Classical $r$-adaptivity optimizes vertex positions but requires solving expensive auxiliary PDEs such as the Monge-Ampère equation, while classical $h$-adaptivity modifies topology through element subdivision but suffers from expensive error indicator computation and is constrained by isotropic refinement patterns that impose accuracy ceilings. Combined $hr$-adaptive techniques naturally outperform single-modality approaches, yet inherit both computational bottlenecks and the restricted cost-accuracy trade-off. Emerging machine learning methods for adaptive mesh refinement seek to overcome these limitations, but existing approaches address $h$-adaptivity or $r$-adaptivity in isolation. We present HypeR, a deep reinforcement learning framework that jointly optimizes mesh relocation and refinement. HypeR casts the joint adaptation problem using tools from hypergraph neural networks and multi-agent reinforcement learning. Refinement is formulated as a heterogeneous multi-agent Markov decision process (MDP) where element agents decide discrete refinement actions, while relocation follows an anisotropic diffusion-based policy on vertex agents with provable prevention of mesh tangling. The reward function combines local and global error reduction to promote general accuracy. Across benchmark PDEs, HypeR reduces approximation error by up to 6--10$\times$ versus state-of-art $h$-adaptive baselines at comparable element counts, breaking through the uniform refinement accuracy ceiling that constrains subdivision-only methods. The framework produces meshes with improved shape metrics and alignment to solution anisotropy, demonstrating that jointly learned $hr$-adaptivity strategies can substantially enhance the capabilities of automated mesh generation.

cs.CE↗

arXiv2026

The Path Matters: Learning a Token-Commitment Policy for Diffusion Language Models

Diffusion large language models promise faster generation by refining many token positions in parallel, but this parallelism introduces a hidden control problem: which proposed tokens should be transferred into the partially decoded sequence at each step? We refer to this decision as token commitment. Existing frozen-generator decoders largely rely on hand-designed confidence rules or block-specific acceptance filters. We argue that token commitment can instead be learned as a reusable trace-state policy. We introduce TraceLock, a lightweight plug-in controller that instantiates this policy for a frozen diffusion language model. Since oracle commitment times are unavailable, TraceLock derives self-supervision from future stability: at decoding step t, a proposed token for position i is labeled stable if it matches the final token at position i after the full decoding trace completes. The controller scores variable-length trace states and decides which active token proposals should be committed to the partially decoded sequence. Once trained for a given frozen backbone, the controller can be deployed across local-window widths, generation lengths, and step budgets without retraining or per-setting calibration. Experiments on question answering, mathematical reasoning, and code generation show that TraceLock improves the quality-step tradeoff over heuristic and learned baselines, with particularly stable behavior under cross-setting deployment. Diagnostic analyses show that its decisions are not reducible to scalar confidence, suggesting that frozen diffusion language models expose a learnable space of commitment trajectories beyond confidence-based decoding. Code is available at https://github.com/BobSun98/TraceLock.

cs.CL↗

arXiv2026

Algebraic Priors for Approximately Equivariant Networks

Equivariant neural networks incorporate symmetries through group actions, embedding them as an inductive bias to improve performance. Existing methods learn an equivariant action on the latent space, or design architectures that are equivariant by construction. These approaches often deliver strong empirical results but can involve architecture-specific constraints, large parameter counts, and high computational cost. We challenge the paradigm of complex equivariant architectures with a parameter-free approach grounded in group representation theory. We prove that for an equivariant encoder over a finite group, the latent space must almost surely contain one copy of its regular representation for each linearly independent data orbit, which we explore with a number of empirical studies. Leveraging this foundational algebraic insight, we impose the group's regular representation as an inductive bias via an auxiliary loss, adding no learnable parameters. Our extensive evaluation shows that this method matches or outperforms specialized models in several cases, even those for infinite groups. We further validate our choice of the regular representation through an ablation study, showing it consistently outperforms defining and trivial group representation baselines.

cs.LG↗

arXiv2026

ContextFlow: Context-Aware Flow Matching For Trajectory Inference From Spatial Omics Data

Inferring trajectories from longitudinal spatially-resolved omics data is fundamental to understanding the dynamics of structural and functional tissue changes in development, regeneration and repair, disease progression, and response to treatment. We propose ContextFlow, a novel context-aware flow matching framework that incorporates prior knowledge to guide the inference of structural tissue dynamics from spatially resolved omics data. Specifically, ContextFlow integrates local tissue organization and ligand-receptor communication patterns into a transition plausibility matrix that regularizes the optimal transport objective. By embedding these contextual constraints, ContextFlow generates trajectories that are not only statistically consistent but also biologically meaningful, making it a generalizable framework for modeling spatiotemporal dynamics from longitudinal, spatially resolved omics data. Evaluated on three datasets, ContextFlow consistently outperforms state-of-the-art flow matching methods across multiple quantitative and qualitative metrics of inference accuracy and biological coherence. Our code is available at: \href{https://github.com/santanurathod/ContextFlow}{ContextFlow}

cs.LG↗

arXiv2026

Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheaves

Sheaf Neural Networks equip graph structures with a cellular sheaf: a geometric structure which assigns local vector spaces (stalks) and a linear learnable restriction/transport maps to nodes and edges, yielding an edge-aware inductive bias that handles heterophily and limits oversmoothing. However, common Neural Sheaf Diffusion implementations rely on SVD-based sheaf normalization and dense per-edge restriction maps, which scale with stalk dimension, require frequent Laplacian rebuilds, and yield brittle gradients. To address these limitations, we introduce Polynomial Neural Sheaf Diffusion (PolyNSD), a new sheaf diffusion approach whose propagation operator is a degree-K polynomial in a normalised sheaf Laplacian, evaluated via a stable three-term recurrence on a spectrally rescaled operator. This provides an explicit K-hop receptive field in a single layer (independently of the stalk dimension), with a trainable spectral response obtained as a convex mixture of K+1 orthogonal polynomial basis responses. PolyNSD enforces stability via convex mixtures, spectral rescaling, and residual/gated paths, reaching new state-of-the-art results on both homophilic and heterophilic benchmarks, inverting the Neural Sheaf Diffusion trend by obtaining these results with just diagonal restriction maps, decoupling performance from large stalk dimension, while reducing runtime and memory requirements.

cs.LG↗

arXiv2026

SplineFlow: Flow Matching for Dynamical Systems with B-Spline Interpolants

Flow matching is a scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, current state-of-the-art methods are not well-suited for modeling dynamical systems, as they construct conditional paths using linear interpolants that may not capture the underlying state evolution, especially when learning higher-order dynamics from irregular sampled observations. Constructing unified paths that satisfy multi-marginal constraints across observations is challenging, since naïve higher-order polynomials tend to be unstable and oscillatory. We introduce SplineFlow, a theoretically grounded flow matching algorithm that jointly models conditional paths across observations via B-spline interpolation. Specifically, SplineFlow exploits the smoothness and stability of B-spline bases to learn the complex underlying dynamics in a structured manner while ensuring the multi-marginal requirements are met. Comprehensive experiments across various deterministic and stochastic dynamical systems of varying complexity, as well as on cellular trajectory inference tasks, demonstrate the strong improvement of SplineFlow over existing baselines. Our code is available at: https://github.com/santanurathod/SplineFlow.

cs.LG↗

arXiv2026

Many Needles in a Haystack: Active Hit Discovery for Perturbation Experiments

High-throughput gene perturbation experiments can test several genetic interventions in parallel, yet experimental budgets remain limited. A central goal is hit discovery: identifying as many perturbations as possible whose phenotypic effect exceeds a predefined threshold. Pure exploration strategies are statistically inefficient, wasting budget on low-value regions. Bayesian optimization methods offer a principled alternative but target a single global optimum, over-exploiting dominant modes while neglecting other high-value regions. We formalize hit discovery as a sequential experimental design problem and propose Probability-of-Hit, an acquisition function that directly targets threshold exceedance by ranking candidates according to their posterior probability of being a hit. We prove asymptotic optimality of this approach and demonstrate strong empirical performance on both synthetic benchmarks and real biological immunology datasets, including up to 6.4% improvement over baselines on the Schmidt IL-2 dataset.

cs.LG↗

arXiv2026

HeterSEED: Semantics-Structure Decoupling for Heterogeneous Graph Learning under Heterophily

Many real-world heterogeneous graphs exhibit pronounced heterophily, where connected nodes often have dissimilar labels or play different semantic roles. In such settings, standard heterogeneous graph neural networks that aggregate messages along metapaths or meta-relations primarily based on feature similarity can propagate misleading information, since feature similarity may be misaligned with underlying relational semantics. In this paper, we propose HeterSEED, a semantics-structure decoupling framework for heterogeneous graph learning under heterophily. HeterSEED decouples representation learning into a heterogeneous semantic channel that captures type- and relation-aware local semantics and a structure-aware heterophily channel that separates homophilic and heterophilic neighborhoods via pseudo-label-guided partitioning and aggregates them using metapath-based structural weights. A node-level adaptive fusion mechanism then combines the two channels to produce context-dependent node representations. Theoretically, we establish that, on heterogeneous graphs under heterophily, HeterSEED is strictly more expressive than standard heterogeneous graph neural networks that rely primarily on feature similarity and provably reduces the prediction bias introduced by heterophilic neighbors. Experiments on five real-world heterogeneous graphs, including two large-scale networks at the million-node and hundred-million-edge scale, demonstrate that HeterSEED consistently outperforms representative heterogeneous graph neural networks and recent heterophily-aware baselines, especially in strongly heterophilic regimes.

cs.LG↗

arXiv2026

GEM-FI: Gated Evidential Mixtures with Fisher Modulation

Evidential Deep Learning (EDL) enables single-pass uncertainty estimation by predicting Dirichlet evidence, but it can remain overconfident and poorly calibrated, and it often fails to represent multi-modal epistemic uncertainty. We introduce Gated Evidential Mixtures (GEM), a family of models that learns an in-model energy signal and uses it to gate evidential outputs end-to-end in a distance-informed manner. GEM-CORE learns a feature-level energy and maps it to a bounded gate that smoothly suppresses evidence when support is low. To capture epistemic multi-modality without multi-pass ensembling, GEM-MIX adds a lightweight mixture of evidential heads with learned routing weights while preserving single-pass inference. Finally, GEM-FI stabilizes mixture allocations via a Fisher-informed regularizer, reducing head collapse and producing smoother boundary uncertainty. Across image classification and OOD detection benchmarks, GEM improves calibration and ID/OOD separation with single-pass inference. On CIFAR-10, GEM-FI vs. DAEDL improves accuracy from 91.11 to 93.75 (+2.64 pp), reduces Brier x100 from 14.27 to 6.81 (-7.46), and also improves misclassification-detection AUPR from 99.08 to 99.94 (+0.86). For epistemic OOD detection, GEM-FI achieves AUPR/AUROC of 92.59/95.09 on CIFAR-10 to SVHN and 90.20/89.06 on CIFAR-10 to CIFAR-100, compared with 85.54/89.30 and 88.19/86.10 for DAEDL.

cs.LG↗

arXiv2026

GeoCert: Certified Geometric AI for Reliable Forecasting

Forecasting systems in science must be accurate, physically consistent, and certifiably reliable. Most existing models address prediction, constraint enforcement, and verification separately, limiting scalability and interpretability. We introduce GeoCert, a geometric AI framework that unifies forecasting, physical reasoning, and formal verification within a single differentiable computation. GeoCert formulates forecasting as evolution along a hyperbolic manifold, where negative curvature induces contraction dynamics, intrinsic robustness, and logarithmic-time certification. A hierarchical constraint architecture separates universal physical laws from domain-specific dynamics, enabling certified generalization across energy, climate, finance, and transportation systems. GeoCert achieves state-of-the-art accuracy while reducing computational cost by 97.5% and maintaining better certification rates. By embedding verification into the geometry of learning, GeoCert transforms forecasting from empirical approximation to formally verified inference, offering a scalable foundation for trustworthy, reproducible, and physically grounded scientific AI.

cs.LG↗

arXiv2026

When Numbers Start Talking: Implicit Numerical Coordination Among LLM-Based Agents

LLMs-based agents increasingly operate in multi-agent environments where strategic interaction and coordination are required. While existing work has largely focused on individual agents or on interacting agents sharing explicit communication, less is known about how interacting agents coordinate implicitly. In particular, agents may engage in covert communication, relying on indirect or non-linguistic signals embedded in their actions rather than on explicit messages. This paper presents a game-theoretic study of covert communication in LLM-driven multi-agent systems. We analyse interactions across four canonical game-theoretic settings under different communication regimes, including explicit, restricted, and absent communication. Considering heterogeneous agent personalities and both one-shot and repeated games, we characterise when covert signals emerge and how they shape coordination and strategic outcomes.

cs.MA↗

arXiv2026

Fast and Interpretable Protein Substructure Alignment via Optimal Transport

Proteins are essential biological macromolecules that execute life functions. Local structural motifs, such as active sites, are the most critical components for linking structure to function and are key to understanding protein evolution and enabling protein engineering. Existing computational methods struggle to identify and compare these local structures, which leaves a significant gap in understanding protein structures and harnessing their functions. This study presents PLASMA, a deep-learning-based framework for efficient and interpretable residue-level local structural alignment. We reformulate the problem as a regularized optimal transport task and leverage differentiable Sinkhorn iterations. For a pair of input protein structures, PLASMA outputs a clear alignment matrix with an interpretable overall similarity score. Through extensive quantitative evaluations and three biological case studies, we demonstrate that PLASMA achieves accurate, lightweight, and interpretable residue-level alignment. Additionally, we introduce PLASMA-PF, a training-free variant that provides a practical alternative when training data are unavailable. Our method addresses a critical gap in protein structure analysis tools and offers new opportunities for functional annotation, evolutionary studies, and structure-based drug design. Reproducibility is ensured via our official implementation at https://github.com/ZW471/PLASMA-Protein-Local-Alignment.git.

q-bio.QM↗

arXiv2026

FAIRGAME: a Framework for AI Agents Bias Recognition using Game Theory

Letting AI agents interact in multi-agent applications adds a layer of complexity to the interpretability and prediction of AI outcomes, with profound implications for their trustworthy adoption in research and society. Game theory offers powerful models to capture and interpret strategic interaction among agents, but requires the support of reproducible, standardized and user-friendly IT frameworks to enable comparison and interpretation of results. To this end, we present FAIRGAME, a Framework for AI Agents Bias Recognition using Game Theory. We describe its implementation and usage, and we employ it to uncover biased outcomes in popular games among AI agents, depending on the employed Large Language Model (LLM) and used language, as well as on the personality trait or strategic knowledge of the agents. Overall, FAIRGAME allows users to reliably and easily simulate their desired games and scenarios and compare the results across simulation campaigns and with game-theoretic predictions, enabling the systematic discovery of biases, the anticipation of emerging behavior out of strategic interplays, and empowering further research into strategic decision-making using LLM agents.

cs.AI↗

arXiv2026

A Standardized Framework For Evaluating Gene Expression Generative Models

The rapid development of generative models for single-cell gene expression data has created an urgent need for standardised evaluation frameworks. Current evaluation practices suffer from inconsistent metric implementations, incomparable hyperparameter choices, and a lack of biologically-grounded metrics. We present Generated Genetic Expression Evaluator (GGE), an open-source Python framework that addresses these challenges by providing a comprehensive suite of distributional metrics with explicit computation space options and biologically-motivated evaluation through differentially expressed gene (DEG)-focused analysis and perturbation-effect correlation, enabling standardized reporting and reproducible benchmarking. Through extensive analysis of the single-cell generative modeling literature, we identify that no standardized evaluation protocol exists. Methods report incomparable metrics computed in different spaces with different hyperparameters. We demonstrate that metric values vary substantially depending on implementation choices, highlighting the critical need for standardization. GGE enables fair comparison across generative approaches and accelerates progress in perturbation response prediction, cellular identity modeling, and counterfactual inference.

q-bio.GN↗

arXiv2026

On the Necessity of Learnable Sheaf Laplacians

Sheaf Neural Networks (SNNs) were introduced as an extension of Graph Convolutional Networks to address oversmoothing on heterophilous graphs by attaching a sheaf to the input graph and replacing the adjacency-based operator with a sheaf Laplacian defined by (learnable) restriction maps. Prior work motivates this design through theoretical properties of sheaf diffusion and the kernel of the sheaf Laplacian, suggesting that suitable non-identity restriction maps can avoid representations converging to constants across connected components. Since oversmoothing can also be mitigated through residual connections and normalization, we revisit a trivial sheaf construction to ask whether the additional complexity of learning restriction maps is necessary. We introduce an Identity Sheaf Network baseline, where all restriction maps are fixed to the identity, and use it to ablate the empirical improvements reported by sheaf-learning architectures. Across five popular heterophilic benchmarks, the identity baseline achieves comparable performance to a range of SNN variants. Finally, we introduce the Rayleigh quotient as a normalized measure for comparing oversmoothing across models and show that, in trained networks, the behavior predicted by the diffusion-based analysis of SNNs is not reflected empirically. In particular, Identity Sheaf Networks do not appear to suffer more significant oversmoothing than their SNN counterparts.

cs.LG↗