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.
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.
arXiv:2608.29530v1 Announce Type: cross Abstract: Modern systems in artificial intelligence (AI) somehow excel in domains for which they seem poorly suited. Intelligence has traditionally been modele...
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.
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.
The paper introduces the Native Predicate Neuron, a differentiable logic‑reasoning module that can be inserted into standard neural architectures. It learns to alternate between logical operations using a single trainable parameter and employs a dual‑nature gradient mechanism that performs hard logical operations during training while remaining differentiable for backpropagation. Experiments on Fully‑Connected, Convolutional, Recurrent, and Transformer models show that adding Predicate Neurons speeds convergence, improves accuracy, and reduces loss, especially on tasks involving monotonic reasoning or discontinuities.
arXiv:2608. 16773v1 Announce Type: new Abstract: Prototype-based neural networks are hailed as interpretable-by-design architectures.
Neuro‑Symbolic Geometric Abstraction (NeuSOGA) is a framework that converts raw observations into explicit symbolic mathematical representations. It achieves this by sequentially generating topological and geometric abstractions, using tools such as Euclidean Distance Transforms, Segment Anything, and Implicit Area Splines. The resulting analytical implicit models are interpretable, editable, and support arbitrary‑order smoothness, additive composition, and closed‑form evaluation across diverse sensing modalities.
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.
arXiv:2605.18202v2 Announce Type: replace-cross Abstract: Neuro-Symbolic Concept-based Models (NeSy-CBMs) are a family of architectures that integrate neural networks with symbolic reasoning for enha...
NeuroRule is a knowledge distillation framework that transforms high‑capacity neural networks into explainable rule‑sets. It adapts the EVOTER rule‑set evolution infrastructure to evolve propositional logic expressions that capture the neural network’s performance. The approach includes a conciseness objective to enhance explainability and demonstrates viability even without access to the original training data.
arXiv:2606. 04381v1 Announce Type: cross Abstract: Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space.
arXiv:2604. 27007v2 Announce Type: replace Abstract: We provide a causal analysis of Binary Spiking Neural Networks (BSNNs) to explain their behavior.