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Pietro Liò

Publications and source records attributed to Pietro Liò.

At least 19 recordsLinked to original sources
arXiv2026

Non-Zero Radius: The Missing Component of Neural Networks

Inspired by the analogy between the all-or-none activation of biological neurons and the true-false of logic circuits, McCulloch and Pitts proposed a mathematical model of the biological neuron in 1943 with the aim of simulating logical reasoning. Although Norbert Wiener considered the model overly simplistic at the time, it later became a building block of modern neural networks, including large language models. Despite their remarkable empirical success, however, conventional neural networks remain largely black-box systems and struggle with reliable symbolic reasoning. Viewing vectors as spheres of zero radius, we relax the zero-radius constraint and represent concepts as spheres with non-zero radii. We argue that sphere-based representations can capture additional features of biological cognition, including representing spatial concepts as regions and reasoning through model construction and inspection. Building on sphere embeddings, we introduce Sphere Neural Networks (SphNNs), which use a transition map to achieve symbolic-level Aristotelian syllogistic reasoning without training data, thereby taking an initial step toward the original goal of McCulloch and Pitts. We suggest that the zero-radius constraint may reflect an aspect of the oversimplification identified by Wiener and may limit conventional neural networks' capacity for symbolic-level logical reasoning.

cs.AI↗
arXiv2026

TDLM: Adaptive Temporal Integration for Diffusion Language Models

Masked diffusion language models repeatedly compute representations for unresolved tokens, but conventional denoisers do not explicitly retain these representations for reuse across steps. We introduce Temporal Self-Conditioning Diffusion Language Model (TDLM), which lets each unresolved position attend to its own history of hidden representations within a frozen denoiser. This gives later predictions access to computation already performed. Training uses self-generated trajectories and a simple cross-entropy objective for tokens revealed between consecutively sampled decoding steps, while causal temporal attention permits parallel evaluation during training. On LLaDA, the temporal modules add only approximately 0.84% trainable parameters. Across LLaDA and Dream, the main comparison shows up to 7.15$\times$ faster generation than the corresponding original diffusion language model, with competitive answer quality on the evaluated tasks. These results motivate temporal memory as a practical way to make more effective use of repeated denoising computation.

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

On the Token Collapse Phenomenon in Textual Graph Soft Prompting

Recent methods for injecting graph structure into LLM prompts include graph soft prompting, in which a graph neural network (GNN) learns graph-specific tokens that capture relational information among entities in textual prompts. G-Retriever combines graph soft prompts with a verbalized description of the same graph to strengthen the textual prompt signal. We conduct an in-depth analysis of G-Retriever and uncover a pathological behavior we term token collapse. Across three benchmarks, three graph encoders, two LLM families, and both frozen and LoRA-adapted models, G-Retriever's graph tokens become almost indistinguishable across inputs. We provide evidence that the same failure is inherited by subsequent methods, even with multi-token pooling. Under the standard setup, swapping a token with the dataset mean, a token from another example, or one derived from a corrupted graph produces no resolved answer-level effect in accuracy. Moreover, a learned constant prompt that never accesses the graph matches or surpasses G-Retriever on all three benchmarks. These findings indicate that, rather than conveying graph content as intended, the collapsed token functions primarily as a generic soft prompt. We also examine conditions linked to this collapse and propose a two-stage procedure that yields non-collapsed tokens while maintaining competitive performance in most cases. However, token variability alone does not prove that the model uses graph information: via interventions and decoding probes, we show that depending on the configuration, a token can reflect the question, an answer prior, or graph-derived content that the LLM may or may not use. Overall, our results offer a practical approach to evaluating graph-token alignment rather than inferring it from task accuracy alone. Code to reproduce our experiments is available at https://github.com/difra100/Token_Collapse_KGQA.

cs.LG↗
arXiv2026

The Stepwise Informativeness Assumption: When Do Entropy Dynamics Track Reasoning Correctness in LLMs?

Recent work uses entropy-based signals at multiple representation levels to study reasoning in large language models, but the field remains largely empirical. From a theoretical perspective, reductions in model uncertainty do not necessarily reflect progress toward correctness. In this work, we characterize when such alignment can be expected through the Stepwise Informativeness Assumption (SIA), which requires entropy-reducing reasoning-prefix extensions increase the probability assigned to valid answers in expectation. We show that next-token prediction can transfer answer-relevant information from training data to the model, but does not, by itself, guarantee alignment with correctness. Instead, we propose that this alignment depends on how the training regime couples reasoning traces to correct answers. Furthermore, we hypothesize observable signatures of this phenomenon and characterize its expected failure regimes. We empirically investigate how entropy dynamics relate to correctness across four reasoning benchmarks (GSM8K, ARC, SVAMP, MATH) and diverse open-weight language models spanning base, instruction-tuned, and RL-trained regimes. Our results show that entropy-correctness alignment strengthens with post-training but can weaken when task difficulty exceeds model capabilities.

cs.CL↗
arXiv2026

A Bochner Weitzenböck Decomposition for Cellular Sheaf Laplacians, Curvature and Neural Sheaf Diffusion

We extend the Bochner-Weitzenböck decomposition to cellular sheaf Laplacians, splitting it into a positive semidefinite term, the Bochner sheaf Laplacian, and a block diagonal term, the Forman curvature. We show that the Bochner Laplacians form a class of cellular sheaves that extends both connection and matrix-weighted Laplacians, and generalizes signed graphs to $d$ dimensions. We give a holonomy characterization of their kernel, prove the related Cheeger inequalities, and attach to them a random walk that generalizes the Gremban expansion. For the Forman term, we prove a discrete Bochner theorem, which bounds the first cohomology of a cellular sheaf with nonnegative curvature, and we read the whole decomposition as an opinion-dynamics model. We then apply this machinery to Sheaf Neural Networks, whose learnt Laplacian is otherwise unobserved. The Bochner interpretation yields a node-level conviction score that acts as an operational importance measure under frozen-model interventions, while the Forman profile provides a local descriptor of the learnt operator.

cs.CG↗
arXiv2026

LocaLeJEPA: Maximum Entropy Representations under Geometric Priors

Joint-Embedding Predictive Architectures (JEPA) offer an appealing approach to self-supervised learning, but are typically prone to representation collapse. LeJEPA resolves this by introducing a theoretically grounded distribution-matching objective that drives the embedding towards an isotropic Gaussian. However, this approach is fundamentally tied to Euclidean assumptions, and its global target does not reflect domain-specific geometric priors, such as the use of non-Euclidean embedding geometries, e.g., equivariant CNNs or hyperbolic ViTs. We thus introduce LocaLeJEPA, a framework motivated by a manifold-theoretic reformulation of LeJEPA's entropy-maximization property. The accompanying LocaLeReg, a novel locally Euclidean distribution-matching regularizer, enables a stable and scalable implementation of the LocaLeJEPA framework. We then perform extensive experiments in the vision setting on models trained on ImageNet-1K. LocaLeJEPA significantly outperforms LeJEPA when paired with hyperbolic ViT-S/8 and equivariant ResNet-50 backbones, and also with ordinary Euclidean ViT-S/8 and ViT-L/14 backbones. This holds both in terms of linear and k-NN classification performance on ImageNet and on a series of downstream tasks tested. We view the LocaLeJEPA formalism as a principled approach to the JEPA paradigm that better respects intrinsic data geometry while also accommodating generalizations to exotic embedding geometries. Code available at https://github.com/alessioborgi/LocaLeJEPA.

cs.LG↗
arXiv2026

Heterogeneous Sheaf Neural Networks

Heterogeneous graphs, whose nodes and edges can belong to different types and feature spaces, arise in many real-world domains, including biology, recommendation, social networks, and computer systems. Existing heterogeneous graph neural networks typically handle this heterogeneity at the architectural level through relation-specific modules, meta-path machinery or type-aware attention, which often leads to increasingly specialised parameter-heavy designs. In this work, we propose HetSheaf, a framework for learning heterogeneous graphs through cellular sheaves. Instead of encoding heterogeneity solely in the architecture, HetSheaf represents it directly in the underlying data structure by assigning type-aware local feature spaces and learning restriction maps conditioned on node features, node types, and edge types. To support graph-level prediction, we further introduce SheafPool, a universal stalk-space readout that aggregates node representations while being invariant to local changes of basis, thereby making graph classification with sheaf networks well-defined and achieving an F1 Score up to 42 percentage points higher than mean pooling. Across a diverse suite of benchmarks (node classification, link prediction and graph classification). HetSheaf consistently achieves up to 2 percentage points higher performance (up to 94.97% Macro F1 Score on node classification and up to 99.62% on link prediction) on the Heterogeneous Graph Benchmark (HGB) framework against homogeneous (GCN, GAT, GIN, GraphSAGE), heterogeneous (R-GCN, HAT, HGT) and type-agnostic sheaf baselines, while reducing the number of parameters by up to 10$\times$.

cs.LG↗
arXiv2026

Graph Transductive Sharpening: Leveraging Unlabeled Predictions in Node Classification

In the transductive setting, where the full graph is observed but node labels are only partially available, progress in semi-supervised node classification has largely focused on architectural innovation. In this paper, we revisit an orthogonal axis: the training objective. We start from a simple observation: transductive models produce predictions for every node during training, including nodes without labels. These unlabeled-node predictions may contain useful training signal, but standard supervised objectives discard them because no ground-truth labels are available. Inspired by the decomposition of cross-entropy into a label-dependent alignment term and a label-independent entropy term, we propose prediction confidence as a natural way to extract this signal in the absence of labels. This motivates Transductive Sharpening (TS): a loss-level modification that minimizes prediction entropy on unlabeled nodes while counterbalancing this effect on labeled nodes. We evaluate Transductive Sharpening across a wide range of node-classification benchmarks and observe consistent performance improvements without requiring any changes to the backbone architecture. Code is available at https://github.com/transductive-sharpening/tunedGNN.

cs.LG↗
arXiv2026

Diagnosing GNN Failure Modes with Layer-Wise Probe Entropy

Graph neural networks (GNNs) are typically evaluated only at their final layer, obscuring how task-relevant information evolves during message passing. We introduce a post-hoc diagnostic that freezes a trained GNN, fits an independent linear probe to each layer, and tracks probe accuracy alongside normalized predictive entropy. Across real and synthetic graph settings, layer-wise probe entropy distinguishes beneficial, neutral, and harmful smoothing, a capability not demonstrated by existing geometric measures. Moreover, by comparing shallow and deep models, we show that the onset of entropy degradation separates the two main GNN failure modes: structural mismatch under heterophily, which appears from the earliest layers even in shallow models, and excessive-depth oversmoothing, which emerges only as propagation depth increases. These results establish probe-entropy trajectories as a tool for analyzing information flow in GNNs and motivate future work on adaptive depth selection and early-exit mechanisms.

cs.LG↗
arXiv2026

LLM-as-an-Investigator: Evidence-First Agentic Reasoning for Robust Interactive Problem Diagnosis

Large language models (LLMs) are used for technical troubleshooting, where problem descriptions are often incomplete and multiple causes can explain the same symptoms. Effective diagnosis requires acquiring discriminative evidence and selecting the explanation best supported by it. Yet reasoning or interaction alone may not prevent premature commitment to an incorrect hypothesis. We introduce LLM-as-an-Investigator, an evidence-first methodology for interactive problem diagnosis that reduces premature commitment while distinguishing competing causes. We implement it through the Solution Investigator Agent (SIA), which orchestrates three complementary reasoning behaviours through a shared investigation state: a Diagnostic Reasoner that conducts and reassesses the diagnostic interview, a Hypothesis Investigator that maintains and updates competing hypotheses, and a Counterfactual Investigator that challenges current explanations and guides discriminative follow-up questions. Final selection uses cited dialogue evidence and a separate verification step, while explicit hypothesis and evidence records make the diagnosis traceable and preserve unresolved alternatives. We construct a structured corpus from 303 technical forum threads across mechanical, electrical, and hydraulic domains. A source-grounded pipeline separates the initial problem, pre-solution clarifications, and reported outcome, while a user simulator answers diagnostic questions without access to the reference solution. We compare SIA with direct, reasoning-based, interactive, and search-based baselines, including adaptations of ReAct and Tree of Thoughts. Evaluation distinguishes final diagnostic quality from hypothesis coverage and oracle potential, while ablations and paired stress tests assess component contributions and robustness to plausible but misleading user hypotheses.

cs.AI↗
arXiv2026

Zatom-2: Multitask Pretraining on Atomistic Data for Generative Modeling across Domains

Unified atomistic modeling has the potential to accelerate discovery in chemistry, materials science, and biology by bridging data-rich chemical domains and data-scarce biological contexts. However, existing generative approaches to atomistic modeling remain highly specialized to scientific disciplines (chemistry vs. biology) or do not leverage both high-volume organic (molecule) and inorganic (material) data for general-purpose pretraining. To this end, we introduce Zatom-2, an atomistic generative model pretrained on approximately five million structures from the OMol25 and OMat24 electronic structure datasets. Zatom-2 features a multiscale Transformer architecture coupled with conditional flow matching that supports force conditioning and foundational pretraining tasks such as generation, structure prediction, and prediction of molecular and material energies and forces. Empirically, Zatom-2 achieves better molecular distribution fidelity than Zatom-1 and achieves strong performance on existing molecule and material generation benchmarks. Zatom-2 demonstrates the ability to control sample generation across low- and high-force regimes, and enhances protein generation in a low-data setting through joint generative-predictive pretraining and transfer learning, increasing protein backbone designability in a length extrapolation setting from 67.8% without pretraining to 74.8% after finetuning on 2,000 protein domains.

cs.LG↗
arXiv2026

Differentiable Retrieval-Augmented Generation for Predicting Cellular Responses to Gene Perturbation

Predicting transcriptional responses to genetic perturbations is fundamental to functional genomics and therapeutic discovery. Recent deep learning models have shown promise in single-cell perturbation response prediction, but they typically generate each response in isolation, without explicitly leveraging related perturbations. We introduce PT-RAG (Perturbation-aware Two-stage Retrieval-Augmented Generation), a plug-in retrieval-and-conditioning module for generative cellular perturbation response. PT-RAG augments an existing perturbation-response backbone with learned access to related perturbation contexts. The key challenge is that relevance is not fixed in this setting: functionally related genes may elicit different effects across cell types. PT-RAG addresses this with a two-stage retrieval mechanism: GenePT-based semantic retrieval first identifies K candidate perturbations, after which a differentiable Gumbel-Softmax selector adaptively selects retrieved contexts conditioned on the control cell state, the query perturbation, and each candidate perturbation. We evaluate PT-RAG on two backbones, a STATE-style generator used as a frozen random reservoir and a fully trained scGPT, across cross-cell-type and cross-perturbation generalization tasks. PT-RAG consistently improves distributional similarity and often overall predictive quality; for example, on scGPT cross-cell-type results, the 2-Wasserstein distance drops by 5.9% relative to scGPT alone. The code to reproduce our experiments is available at https://github.com/difra100/PT-RAG_NIPS.

cs.LG↗
arXiv2026

TopoLIA: Topology-Inspired Latent Interaction Attention for Drug Discovery

The growing sophistication of drug discovery calls for new advances in artificial intelligence (AI). Transformers have underpinned recent breakthroughs in AI, yet their conventional source-target attention mechanism can become a bottleneck for modeling complex interactions. Here, we introduce TopoLIA, a topology-inspired latent interaction attention mechanism that learns not only how much information should be exchanged between interaction partners, but also how that information should be transformed. Source-target-dependent attention is mediated through a compact latent interaction space, providing a structured representation of complex interactions. We further incorporate topological spectral representations to capture multiscale data geometry and extract algebraic relationships. TopoLIA thus incorporates topological principles into both data representation and neural network architecture. We demonstrate TopoLIA on protein-ligand binding, where persistent spectra encode multiscale topological and geometric patterns in 3D protein-ligand complexes, while latent interaction attention (LIA) enables structured, source-target-dependent information exchange. We pretrain TopoLIA by reconstructing masked multiscale spectral tokens from unlabeled molecular structures, yielding transferable structural representations without task-specific annotations. Across multiple scoring and docking benchmarks, TopoLIA achieves state-of-the-art performance and consistently outperforms its standard-attention counterpart. Rank analyses show that compact latent dimensions yield the best performance, supporting compact interaction spaces as an effective inductive bias for biomolecular learning. More broadly, LIA provides a general framework for structured, source-target-dependent information exchange that is applicable to diverse scientific and AI problems involving complex heterogeneous interactions.

q-bio.BM↗
arXiv2026

Remember to Forget: Gated Adaptive Positional Encoding

Rotary Positional Encoding (RoPE) is widely used in modern large language models. However, when sequences are extended beyond the range seen during training, rotary phases can enter out-of-distribution regimes, leading to spurious long-range alignments, diffuse attention, and degraded retrieval. Existing remedies only partially address these failures, as they often trade local positional resolution for long-context stability. We propose GAPE (Gated Adaptive Positional Encoding), a drop-in augmentation for positional encodings that introduces a content-aware bias directly into the attention logits while preserving the rotary geometry. GAPE decouples distance-based suppression from token importance through a query-dependent gate that contracts irrelevant context and a key-dependent gate that preserves salient distant tokens. We show that weakly protected distant context is exponentially attenuated as a function of the query gate, while selected keys can remain accessible through landmark protection. We further show that GAPE can be implemented within standard scaled dot-product attention. Empirically, GAPE improves long-context robustness across controlled retrieval and language-modeling experiments, extrapolating up to 8x the training length. We further retrofit GAPE into a pretrained 7B model, maintaining performance on standard benchmarks and improving performance at the longest evaluated context. These results support adaptive context suppression as a complement to positional representation for long-context generalization.

cs.LG↗
arXiv2026

Node-level Graph Neural Architecture Search Framework

In recent years, Graph Neural Networks (GNNs) and architecture search frameworks have gained extensive application in non-Euclidean data processing, attributable to their superior capacity in managing unstructured data. Nevertheless, traditional approaches typically apply uniform convolution operations to all nodes, regardless of their varying structural and feature characteristics, which can undermine model performance and result in over-smoothing issues as the number of layers increases. To overcome this limitation, in this work, we propose a \textbf{N}ode-Level \textbf{G}raph \textbf{N}eural \textbf{A}rchitecture \textbf{S}earch (N-GNAS) algorithm. It can automatically choose an appropriate network architecture for each subset of nodes when updating node features. N-GNAS also introduces a contrastive learning loss to separate sample features from different categories and vice versa. In experiments conducted on eight datasets for node and graph classification, our methodology outperforms current leading GNAS techniques and traditional human-designed GNNs. For example, it achieves an accuracy rate of 78.26\% on the CiteSeer dataset.

cs.LG↗
arXiv2026

Oscillatory Neural Dynamics over Sheaves

Effective long-range propagation remains a central challenge in graph neural networks, as increasing a model's propagation depth does not guarantee that distant nodes effectively influence each other. Sheaf neural networks enrich graph propagation through matrix-valued transport between stalks; still, this expressivity alone does not automatically imply effective long-range communication. We introduce ONDA, a long-range graph learning framework based on operator-valued information waves. Stalk-valued representations evolve through second-order dynamics governed by learned sheaf transport operators, combining wave-like propagation with expressive local geometry. We characterize long-range influence through a stalk-wise sensitivity analysis and show that the cross-influence never vanishes. Across long-range propagation, severe graph bottlenecks, graph transfer, and heterophilic benchmarks, ONDA consistently improves over scalar wave propagation, diffusive sheaf baselines, and state-of-the-art models, demonstrating the benefit of coupling wave dynamics with matrix-valued transport.

cs.LG↗
arXiv2026

Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction

Existing molecular and materials learning approaches often rely on a limited set of structural representations, which may capture only selected aspects of complex three-dimensional structure. Here, we introduce mathematical invariant-enabled topological neural networks (MITNNs), a framework that represents complex structures through multiple complementary mathematical views and integrates them with topological neural architectures. MITNNs combine multiscale invariants from topology, spectral theory, commutative algebra, differential geometry, and discrete curvature, capturing complementary structural information from the same system. Systematic invariant-subset, architecture-subset, and ensemble analyses show that predictive performance depends on how mathematical representations and neural architectures are paired, with selected combinations outperforming individual models and the aggregation of all available components. Across protein-ligand binding, metal-organic framework properties, mutation-induced protein solubility, and molecular toxicity prediction, MITNN consistently outperforms existing methods. These results establish MITNN as a mathematically multimodal framework for scientific machine learning.

q-bio.BM↗