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arXiv2026

A Deeper Analysis of Block-Sparse Featurizers

The recently introduced block-sparse featurizer (BSF; Fel et al., 2026) is similar to a sparse autoencoder (SAE), but its atomic unit is a small subspace (a block of directions) rather than a single direction. It is designed for features that live on low-dimensional manifolds, which are especially frequent in vision. This work studies the BSF's strengths and weaknesses, finding how it still somewhat suffers from classic SAE failure modes, like feature splitting and composition. We propose several architectural changes to the BSF, including a Tournament Top-K selection rule that significantly reduces feature splitting, and we also extend the block paradigm to the crosscoder.

cs.LG↗

arXiv2026

Social Caption: Evaluating Social Understanding in Multimodal Models

Social understanding abilities are crucial for multimodal large language models (MLLMs) to interpret human social interactions. We introduce SOCIAL CAPTION, a framework grounded in interaction theory to evaluate social understanding abilities of MLLMs along three dimensions: Social Inference (SI), the ability to make accurate inferences about interactions; Holistic Social Analysis (HSA), the ability to generate comprehensive descriptions of interactions; Directed Social Analysis (DSA), the ability to generate relevant information from interactions. We analyze factors influencing model performance in social understanding, such as scale, architectural design, and spoken context. Experiments with MLLM judges demonstrate a path towards scaling automated evaluation of multimodal social understanding.

cs.CL↗

arXiv2026

Real-Time Neuromorphic Spectrum Intelligence Simulator

We present the Real-Time Neuromorphic Spectrum Intelligence Simulator (RT-NuSIS), a modular framework to study spiking neural network (SNN) and memristor-inspired agents for dynamic spectrum access under constrained energy budgets and adversarial conditions. RT-NuSIS couples leaky integrate-and-fire neuronal dynamics, memristive synaptic models, physics-informed energy-harvesting models (triboelectric and RF), and adversary models including jamming and Byzantine behavior. We formalize the simulator mathematically, prove boundedness, present a mean-field adversary threshold, analyze per-step complexity, and provide a reproducible benchmark harness for energy-per-inference, latency, and robustness metrics. The codebase is modular, deterministic by seed, and designed for large-scale event-driven simulations.

eess.SP↗

arXiv2026

Simulation-free and finite-time diffusion model

The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions. Conventional approaches typically trade off simulation-free training against finite-time generation. We propose a framework for designing the reference process that achieves both simultaneously. The key idea is to prescribe tractable time-dependent conditional distributions and then construct the reference process realizing them as its marginals. This framework reveals that score matching is not fundamental to diffusion-model training but instead emerges naturally through reversal of the reference process. We further show that conditional flow matching arises as the small-noise limit of the proposed framework.

cs.LG↗

arXiv2026

Learning to Optimize by Differentiable Programming

Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn how to design them. Modern frameworks such as PyTorch, TensorFlow, and JAX enable this paradigm through efficient automatic differentiation. Embedding first-order methods within these systems allows end-to-end training that improves convergence and solution quality. Guided by Fenchel-Rockafellar duality, the tutorial demonstrates how duality-informed iterative schemes such as the alternating direction method of multipliers, and the primal-dual hybrid gradient can be learned and adapted through representative case studies.

cs.MS↗

arXiv2021

Quantum Machine Learning for Finance

Quantum computers are expected to surpass the computational capabilities of classical computers during this decade, and achieve disruptive impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from Quantum Computing not only in the medium and long terms, but even in the short term. This review paper presents the state of the art of quantum algorithms for financial applications, with particular focus to those use cases that can be solved via Machine Learning.

quant-ph↗

arXiv2026

Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification

We propose a conjugate and calibrated Gaussian process (GP) model for multi-class classification by exploiting the geometry of the probability simplex. Our approach uses Aitchison geometry to map simplex-valued class probabilities to an unconstrained Euclidean representation, turning classification into a GP regression problem with fewer latent dimensions than standard multi-class GP classifiers. This yields conjugate inference and reliable predictive probabilities without relying on distributional approximations in the model construction. The method is compatible with standard sparse GP regression techniques, enabling scalable inference on larger datasets. Empirical results show well-calibrated and competitive performance across synthetic and real-world datasets.

cs.LG↗

arXiv2026

TPR-Attention for Combinatorial Generalization

Systematic generalization remains a significant challenge in deep learning. In particular, combinatorial generalization - generalizing to new configurations of known factors of variation - is effortless for humans but difficult for standard neural architectures that rely on statistical correlations rather than explicit structural representations. We introduce a new architectural component that embeds structured inductive bias into deep learning: an attention mechanism operating over tensor-product representations (TPRs). Through controlled experiments on compositional tasks, we show that this TPR-attention mechanism outperforms existing architectural components in combinatorial generalization. These results highlight the value of integrating explicit compositional structure into neural attention and point toward a promising path for models capable of systematic generalization.

cs.LG↗

arXiv2024

A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances Over Random Projections

Unimodality, pivotal in statistical analysis, offers insights into dataset structures and drives sophisticated analytical procedures. While unimodality's confirmation is straightforward for one-dimensional data using methods like Silverman's approach and Hartigans' dip statistic, its generalization to higher dimensions remains challenging. By extrapolating one-dimensional unimodality principles to multi-dimensional spaces through linear random projections and leveraging point-to-point distancing, our method, rooted in $α$-unimodality assumptions, presents a novel multivariate unimodality test named mud-pod. Both theoretical and empirical studies confirm the efficacy of our method in unimodality assessment of multidimensional datasets as well as in estimating the number of clusters.

stat.ME↗

arXiv2026

Kolmogorov--Arnold against bounded translations

Historically originating from Hilbert's 13th problem, the Kolmogorov-Arnold representation theorem (KART) has recently experienced a major revitalisation through its applications to neural networks, specifically Kolmogorov-Arnold Networks (KANs). While the exact representation is well established, its stability under continuous adversarial perturbations of the hidden layer remains a critical open question. In this paper, we investigate the robustness of KART against bounded adversarial translations. We provide an explicit, self-contained, and constructive proof of an approximate representation using fixed, piecewise linear inner functions. Crucially, our construction employs a single outer function that remains invariant for all summands and is independent of the specific adversarial translation, provided its maximum bound is known a priori.

cs.LG↗

arXiv2026

Fully Distributed GNE Algorithms for Multi-Robot Placement without Consensus on Multipliers

Recent machine learning research has increasingly focused on equilibrium analysis in non-cooperative games rather than solely on optimal solutions. Many such problems involve shared constraints and can be formulated as Generalized Nash Equilibrium Problems (GNEPs). For strongly monotone games, existing methods compute consensus-based variational GNEs (v-GNEs) by exchanging Lagrange multipliers. We propose a fully distributed continuous-time algorithm for shared linear equality constraints that converges without multiplier exchange and reaches any GNE, reducing communication overhead and improving privacy. Discrete-time schemes are also provided, and the method is validated on a multi-robot placement task.

cs.LG↗

arXiv2026

Ontology-Guided Neuro-Symbolic Inference: Grounding Language Models with Mathematical Domain Knowledge

Language models exhibit fundamental limitations -- hallucination, brittleness, and lack of formal grounding -- that are particularly problematic in high-stakes specialist fields requiring verifiable reasoning. I investigate whether formal domain ontologies can enhance language model reliability through retrieval-augmented generation. Using mathematics as proof of concept, I implement a neuro-symbolic pipeline leveraging the OpenMath ontology with hybrid retrieval and cross-encoder reranking to inject relevant definitions into model prompts. Evaluation on the MATH benchmark with three open-source models reveals that ontology-guided context improves performance when retrieval quality is high, but irrelevant context actively degrades it -- highlighting both the promise and challenges of neuro-symbolic approaches.

cs.AI↗

arXiv2026

TopGQ: Fast GNN Post-Training Quantization Leveraging Topology Information

Existing GNN quantization methods suffer from considerable quantization overhead, which severely limits their practical usage in real-world scenarios. To this end, we present TopGQ, an accurate post-training GNN quantization framework, alleviating redundant quantization overhead. We propose dual-axis scale absorption, which enables activation quantization along both the outer and inner dimensions by merging one into the adjacency matrix. On top of that, we introduce TopPIN, a proxy for nodes' local structure, and use it to group nodes with similar topology during quantization. Experimental results show that TopGQ reduces quantization time by an order of magnitude while preserving accuracy.

cs.LG↗

arXiv2026

A Compositional Kernel Model for Feature Learning

We study a compositional variant of kernel ridge regression in which the predictor is applied to a coordinate-wise reweighting of the inputs. Formulated as a variational problem, this model provides a tractable setting for studying feature learning in compositional architectures. From the perspective of variable selection, we show how relevant variables are recovered while noise variables are eliminated. We prove that both global minimizers and stationary points discard noise coordinates when the noise variables are Gaussian distributed. A central finding is that $\ell_1$-type kernels, such as the Laplace kernel, succeed in recovering features contributing to nonlinear effects at stationary points, whereas Gaussian kernels recover only linear ones.

cs.LG↗

arXiv2026

I-FLOP: Fast Learning of Order and Parents from Interventional Data

We extend the FLOP (fast learning of order and parents) algorithm recently proposed by Wienöbst et al. (2026) from observational to interventional data. In particular, we use the interventional BIC score of Hauser and Bühlmann (2012), adapting it to be used with the iterative Cholesky-based score updates that are partly responsible for FLOP's speed. We show that, in the sample limit, I-FLOP recovers a DAG in the same interventional Markov equivalence class as the data-generating DAG. We compare I-FLOP to existing causal structure learning algorithms on real and simulated interventional data, where it performs favorably in terms of both performance and run time.

stat.ML↗

arXiv2024

ContrastWSD: Enhancing Metaphor Detection with Word Sense Disambiguation Following the Metaphor Identification Procedure

This paper presents ContrastWSD, a RoBERTa-based metaphor detection model that integrates the Metaphor Identification Procedure (MIP) and Word Sense Disambiguation (WSD) to extract and contrast the contextual meaning with the basic meaning of a word to determine whether it is used metaphorically in a sentence. By utilizing the word senses derived from a WSD model, our model enhances the metaphor detection process and outperforms other methods that rely solely on contextual embeddings or integrate only the basic definitions and other external knowledge. We evaluate our approach on various benchmark datasets and compare it with strong baselines, indicating the effectiveness in advancing metaphor detection.

cs.CL↗

arXiv2026

FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnet

We introduce two federated learning frameworks for the classical SPDnet model operating on symmetric positive definite (SPD) matrices with Stiefel-constrained parameters. Unlike standard Euclidean averaging, which violates orthogonality, our approach preserves geometric structure through two efficient aggregation strategies: ProjAvg, projecting arithmetic means onto the Stiefel manifold, and RLAvg, approximating tangent-space averaging via retractions and liftings. Both methods are computationally efficient, independent of the optimizer, and enable scalable federated learning for signal processing applications whose features are SPD matrices. Simulations on EEG motor imagery benchmarks show that FedSPDnet outperforms federated EEGnet in F1 score and robustness to federation and partial participation, while using fewer parameters per communication round.

stat.ML↗

arXiv2026

Functional Degeneracy in Neural Networks: Measurement and Pruning

A central question in modern machine learning is how much a trained model can be compressed without changing its behavior, to reduce the memory, compute and energy required to deploy it. To study this, we quantify functional degeneracy through the behavioral recovery rank, defined as the number of leading behavioral-Hessian eigendirections required to recover a trained model's performance. Using the behavioral recovery rank as a geometric benchmark for compression, we find that structural and magnitude pruning retain more degrees of freedom, even after the task is saturated. This gap suggests that functional redundancy is distributed across parameter directions and is not exposed by individual weights or neurons.

cs.LG↗