arXiv:2608. 06839v1 Announce Type: new Abstract: Artificial Neural networks (ANNs) are often treated as black-box models, making explainability a central challenge in deep learning.
arXiv:2607. 05168v1 Announce Type: new Abstract: Why do intelligent systems need to perform explicit symbolic reasoning?
arXiv:2510. 14538v3 Announce Type: replace Abstract: Neuro-symbolic (NeSy) AI aims to develop deep neural networks whose predictions comply with prior knowledge encoding, e.
The paper proposes Sphere Neural Networks (SphNNs), which replace the conventional zero‑radius vector representation with spheres of non‑zero radius to better capture biological cognition and enable symbolic reasoning. By relaxing the zero‑radius constraint, the authors argue that concepts can be represented as spatial regions, allowing reasoning through model construction and inspection. SphNNs employ a transition map that achieves Aristotelian syllogistic reasoning without training data, aiming to address the black‑box nature and symbolic reasoning limitations of current neural networks.
The paper introduces adVersarial Parameter Decomposition (VPD), a method that splits a language model’s parameters into simple subcomponents, each responsible for a small part of the model’s algorithm. VPD optimizes these decompositions so that the model’s input‑output behavior remains intact even when many subcomponents are removed, including adversarially chosen ones. This approach enables a new form of circuit analysis by tracing how sequences of parameter subcomponents interact to produce outputs for specific inputs.
arXiv:2608. 04285v1 Announce Type: new Abstract: Neurosymbolic AI systems that integrate machine learning and symbolic reasoning are rapidly gaining attention.
arXiv:2606. 26454v1 Announce Type: new Abstract: Sphere neural networks have achieved symbolic level syllogistic reasoning without training data, raising the question of where the limit of the scaling law for logical reasoning lies, i.
Softly Symbolified Kolmogorov–Arnold Networks (S2KAN) integrate symbolic primitives into the training of Kolmogorov–Arnold Networks, allowing each activation to be expressed as a sparse combination of symbolic and dense terms. The sparsification is differentiable and guided by a minimum description length–inspired objective, enabling end‑to‑end optimization. Across real‑world prediction tasks, dynamical‑system forecasting, and synthetic symbolic benchmarks, S2KAN achieves higher symbolic fidelity, often with smaller models while maintaining competitive predictive accuracy.
arXiv:2602. 04843v2 Announce Type: replace Abstract: Frontier large language models increasingly solve complex tasks involving abstract concepts through extended test-time thinking.
The paper introduces SAE‑IDF, a data‑driven approach that uses sparse autoencoders to encode symbols into interpretable sparse codes, re‑weights dimensions by rarity, and matches units across heterogeneous symbolic systems. On 12 tasks spanning six symbolic system types, SAE‑IDF outperforms dense LLM baselines (Gemma‑2‑9B and Llama‑3.1‑8B) by up to 45 points, consistently across layers and configurations. Each sparse dimension carries a human‑readable meaning, allowing matches to decompose into named concepts, thereby enabling a scalable, universal symbolic backbone.
The paper introduces a flexible symbolic framework that efficiently computes logical explanations for deep neural networks by parameterizing explanations with internal neuron activations and leveraging general-purpose logical engines like SMT solvers. Unlike previous methods that rely on specialized verifiers or are limited to individual input features, this approach is not restricted in shape and can scale to deep architectures. Experiments on image recognition and medical benchmarks demonstrate improved computational efficiency and the ability to explain networks that were previously intractable for logic-based methods.
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.