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
arXiv:2604. 07242v3 Announce Type: replace Abstract: Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures.
By Vincent Abbott, Gioele Zardini
arXiv:2608. 01633v1 Announce Type: new Abstract: Large language models (LLMs) enable neural architecture search (NAS) directly over executable neural network programs.
By Zhen Liu, Wanqi Zhou, Shuanghao Bai, Yuhan Liu, Jinjun Wang, Jingwen Fu
arXiv:2608. 16773v1 Announce Type: new Abstract: Prototype-based neural networks are hailed as interpretable-by-design architectures.
By Jules Soria, Alban Grastien, Romain Xu-Darme, Julien Girard-Satabin, Zakaria Chihani, Daniela Cancila
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
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:2603. 21014v2 Announce Type: replace Abstract: Mechanistic interpretability seeks to understand how Large Language Models (LLMs) represent and process information.
By Florent Draye, Vedant Palit, Abir Harrasse, Tung-Yu Wu, Jiarui Liu, Punya Syon Pandey, Roderick Wu, Chih-Hao Hsu, Terry Jingchen Zhang, Zhijing Jin, Bernhard Sch\"olkopf
arXiv:2601. 22594v2 Announce Type: replace-cross Abstract: The high-level concepts that a neural network uses to perform computation need not be aligned to individual neurons (Smolensky, 1986).
By Aryaman Arora, Zhengxuan Wu, Jacob Steinhardt, Sarah Schwettmann
arXiv:2606. 07998v1 Announce Type: cross Abstract: Recent advances in generative AI, especially powerful Large Language Models (LLMs) and Large Reasoning Models (LRMs), raise concerns over the interpretability, safety and sustainability of these large and opaque AI models.
By Ian Seet, Jonas Bozenhard, Simon Osterman
arXiv:2608. 04285v1 Announce Type: new Abstract: Neurosymbolic AI systems that integrate machine learning and symbolic reasoning are rapidly gaining attention.
By Agnese Chiatti, Michael Cochez, Cristina Cornelio, Sebastijan Dumancic, Artur d'Avila Garcez, Luis C. Lamb, Lia Morra, Mathias Niepert, Robert Peharz, Alberto Speranzon, Maarten Stol, Annette Ten Teije, Thiviyan Thanapalasingam, Frank Van Harmelen, Emile Van Krieken, Antonio Vergari, Benjie Wang
Graph eXplainable AI (G-XAI) is increasingly important for making Graph Neural Networks interpretable and accountable. While a growing number of explainers are available, choosing the right method and assessing the trustworthiness of its outputs remains unclear.
arXiv:2605. 08934v2 Announce Type: replace Abstract: Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components.
By Ward Gauderis, Thomas Dooms, Steven T. Homer, Kola Ayonrinde, Geraint A. Wiggins