The paper introduces a graphical notation, adapted from Penrose tensor notation, to design and represent interpretable AI architectures. This notation provides a global view of an architecture and maps directly onto PyTorch einsum code, enabling clear depiction of tensor manipulations. The authors apply the notation to several interpretable models—concept bottlenecks, sparse probes, prototype networks, neural additive models, and mixtures of linear models—and use it to diagram the key components of the Steerling-8B language model, revealing its residual structure and allowing a concise 33‑line PyTorch implementation.
By Pietro Barbiero
The paper introduces a new graphical notation, adapted from Penrose tensor notation, to design and represent interpretable AI architectures. Unlike symbolic equations or probabilistic models, this notation provides a global view of an architecture while directly mapping to PyTorch einsum code. The authors demonstrate its use on several interpretable models and on the Steerling-8B language model, revealing structural insights and enabling concise code generation.
arXiv:2607. 28755v1 Announce Type: new Abstract: Over the last decade, neural networks have been applied to an increasingly diverse range of applications, including data with rich geometric, topological, or symmetry-related structure.
By Brendan Kennedy, Tegan Emerson, Gregory Roek, Emilie Purvine, Henry Kvinge
arXiv:2608. 13572v1 Announce Type: cross Abstract: We present The Architect, a system that turns Microsoft Excel into an interactive view of deep learning mathematics.
By Mohammad Imrul Jubair, Tom Yeh
arXiv:2608. 11136v1 Announce Type: new Abstract: 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.
By Davide Rinaldi, Luciano Serafini
The paper discusses tensorizing neural networks by reshaping dense weight matrices into higher-order tensors and approximating them with low-rank tensor network decompositions. This approach offers promising model compression and introduces bond indices that create new latent spaces, potentially enhancing interpretability. Despite encouraging empirical results, tensorized neural networks remain underused, and the authors call for more research to address practical scaling and adoption challenges.
By Safa Hamreras, Sukhbinder Singh, Rom\'an Or\'us
The article surveys Dynamic Heterogeneous Graph Representation Learning (DHGRL), a field that tackles the challenges of modeling evolving, multi‑type networks. It introduces a unified definition covering both discrete‑time and continuous‑time DHGs, and proposes an algorithm‑centric taxonomy that groups methods into embedding‑based, GNN‑based, and Transformer‑based approaches, highlighting their biases toward temporal granularity. The survey also reviews key applications, datasets, benchmarks, and outlines future research directions.
By Huan Liu, Pengfei Jiao, Jie Yin, Hongjiang Chen, Zhidong Zhao
arXiv:2505. 15405v3 Announce Type: replace Abstract: While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems.
By Guillermo Bern\'ardez, Marco Montagna, Louis Van Langendonck, Martin Carrasco, Amirreza Akbari, Louisa Cornelis, Mathilde Papillon, Pere Barlet-Ros, Nina Miolane, Lev Telyatnikov
arXiv:2606. 19279v1 Announce Type: new Abstract: Neurosymbolic semantics is fragmented: classical, fuzzy, probabilistic and neural systems each define truth by their own inductive rules.
By Daniel Romero Schellhorn, Till Mossakowski, Bj\"orn Gehrke
arXiv:2607. 19083v1 Announce Type: new Abstract: Equivariant graph neural networks provide a powerful modeling language for three-dimensional scientific data, but their reuse is often limited by implementations tied to specific tasks, outputs, and training regimes.
By Daniele Angioletti, Marco Nobile, Vittorio Limongelli
The survey titled "When Vision Meets Graphs: A Survey on Graph Reasoning and Learning" reviews how visual depictions of graphs can be used as inputs for graph reasoning and learning. It highlights that while Graph Neural Networks dominate graph machine learning, most pipelines ignore the visual form of graphs, despite scientists routinely interpreting graphs visually. The paper organizes existing work into three threads—vision for graph reasoning, vision for graph learning, and scientific graphs—aiming to clarify current capabilities and chart a path toward foundation models that perceive and reason about graphs like scientists do.
By Xinjian Zhao, Wei Pang, Zhixuan Yu, Xiangru Jian, Xiaozhuang Song, Yaoyao Xu, Zhongkai Xue, Dingshuo Chen, Shu Wu, Philip Torr, Tianshu Yu
Euclid-Omni is a unified neuro‑symbolic framework that integrates a formal geometry system with Large Language Models and Vision‑Language Models to solve both calculation and proving problems in Euclidean geometry up to Olympiad level. Its core component, Euclidea, automatically generates deductive reasoning steps and algebraic computations, while a data‑generation pipeline creates synthetic symbolic problems, diagrams, and natural‑language translations for training. Experiments show that VLMs trained on this synthetic data outperform on calculation tasks, and LLMs paired with Euclidea match state‑of‑the‑art proving systems using far less compute and data.
By Zhaoyu Li, Hangrui Bi, Youyuan Zhang, Wenjie Ma, Zenan Li, Zhaolei Zhang, Xujie Si, Kaiyu Yang