#01Aug 11, 2026
cs.AI
sLTN: Structural Logic Tensor Networks
Davide Rinaldi, Luciano Serafini
Logic Tensor Networks (LTN) provide a neurosymbolic framework in which first-order logic is interpreted through tensor operations, enabling logical constraints to be integrated with differentiable learning. However, the original formulation of LTN is primarily suited to data represented as flat collections of individuals, and does not explicitly capture structural organization such as temporal order, sequential position, or graph connectivity. We introduce sLTN, an extension of LTN that makes structural dimensions first-class elements of the language. Structural dimensions represent named tensor axes associated with domain-specific organization, such as time steps, sequence positions, or graph nodes. They can be quantified explicitly, related through structural relations, and used to express temporal, sequential, and relational constraints directly at the logical level. We formalize the syntax and fuzzy tensor semantics of sLTN and show that, in the absence of structural dimensions, the framework recovers the original LTN semantics as a special case. We further describe a PyTorch implementation based on a declarative signature, formula parsing, and tensorial interpretation. The framework is illustrated on representative temporal and sequential reasoning examples. This paper serves as a companion to the sltn library, available at https://github.com/logictensornetworks/sltn.
#02Aug 11, 2026
quant-ph
A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex
Eric A. F. Reinhardt, Adam J. Hauser
The attention mechanism forms the foundation of many modern AI models such as the Transformer. In one subclass of problems where attention is used, inputs and outputs are bound to the probability simplex so that all outputs sum to one. In this setting, softmax attention admits an exact, component-by-component quantum realization. Attention scores are Hadamard-test statistics on block-encoded projections of amplitude-encoded inputs. The exponential softmax is the interior of a cosine-squared family generated by Born-rule measurement under an exact bijection, whose boundary expresses sparse attention with exact zeros at finite parameter values. The softmax temperature is a repetition count where post-selected measurement rounds realize discretized inverse temperature exactly. Value aggregation is a deterministic column-loading channel that dilates the column-stochastic value matrix. The gated residual is the preparation angle of a single ancilla, with the additive identity at a mixing angle of π/2. Every learnable parameter is a rotation-gate angle. The composed layer is exact in the infinite-shot limit with one measure-and-reload step per attention score; a fully-coherent variant is ε-approximate via quantum singular value transformation in the infinite depth limit. The algebraic core is machine-checked in Lean 4.
#03Aug 11, 2026
math.ST
Posterior contraction rates in Sobolev norms and Bayesian derivative estimation for infinite-dimensional exponential families
Emanuele Dolera, Stefano Favaro, Matteo Giordano
We study posterior contraction in positive-order Sobolev norms and Bayesian derivative estimation for infinite-dimensional exponential families. We embed the natural parameter in a Hilbert scale and model it via a standard Gaussian series prior expanded in the eigenbasis generating the scale. Under a two-sided link condition on the Fisher information and suitable local regularity assumptions, we show that smoothness-matching priors achieve minimax-optimal posterior contraction rates in any Hilbert scale norm up to the regularity of the ground truth. Our analysis builds on the novel approach to posterior contraction based on the Wasserstein distance recently introduced by Dolera et al. (2024). It combines refined Laplace-type estimates for infinite-dimensional integrals associated to the posterior kernels with a mixed-geometry estimate controlling their stability under fluctuations in the data, itself resting on a tailored Poincaré inequality for posterior distributions conditioned on neighbourhoods of the truth. We apply the general theory to density estimation with a logistic parametrisation, Poisson intensity estimation with an exponential link, and the Gaussian white-noise model, yielding minimax contraction rates in Sobolev norms across all three settings. In particular, these yield optimal recovery of density score functions and derivatives of Poisson intensities.
#04Aug 11, 2026
cs.CV
MultiModal Code-Switching: Interleaving Visual Objects into Language for Explicit Object-Level Alignment
Changhao Xiang, Shangyu Xing, Zhen Wu and 2 more
Existing Multimodal Large Language Models (MLLMs) predominantly rely on image-text pairs for modality alignment pretraining, mapping global image representations to long textual descriptions. However, this image-level alignment suffers from referential ambiguity: models struggle to infer the correspondences between multiple visual objects and textual entities from the global representation, leading to data inefficiency and suboptimal semantic grounding. To address this, we propose MultiModal Code-Switching (MMCS), a novel pretraining paradigm that provides explicit object-level supervision. Inspired by the linguistic phenomenon of code-switching, MMCS interleaves vision and language by replacing textual entities with their corresponding visual objects, enforcing local vision-language grounding. We further develop a scalable data synthesis pipeline to generate a pretraining dataset of 773K samples with accurate object-entity correspondences. Experiments show that MMCS is highly data-efficient: with only 50K samples, it matches or surpasses models trained on 600K image-text pairs. Furthermore, MMCS consistently improves visual grounding and perception capabilities across varying model scales.
#05Aug 11, 2026
cs.CV
SAR2Agri: Learning SAR Intensity Representations for Agricultural Monitoring
Moti Rattan Gupta, Anupam Sobti
Agricultural monitoring faces unique challenges, arising from the landscape's complex temporal, phenological, and climate dynamics, yet monitoring them is critical for ensuring food security. Synthetic Aperture Radar (SAR) satellites offer all-weather day-night imaging capability supporting key monitoring tasks including crop type mapping, yield prediction and phenological event detection. Existing multimodal remote sensing foundation models including TerraMind and CopernicusFM learn SAR representations by grounding them in optical imagery using joint encoding and contrastive learning techniques, while SAR-specific foundation models such as SAR-JEPA, SARMAE, and SAR-W-MixMAE primarily focus on target detection, flood mapping, and land cover classification applications. Recent work has introduced phenology inspired temporal pretext tasks with optical imagery which has shown strong performance on agricultural downstream tasks. In this work, we propose the first self-supervised learning pipeline focused on using only SAR intensity imagery for agricultural applications. We improve the temporal pretext tasks through masking and curriculum learning to enhance the pretraining pipeline's ability to capture phenological features from SAR. On the SICKLE benchmark, our final model achieves 84.9% IoU on crop type mapping, outperforming optical baselines (by 15.3 pt) and existing SAR baselines (by 2.2 pt), demonstrating the effectiveness of our proposed pipeline for pretraining SAR intensity encoders for agricultural monitoring.