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.
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.
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.
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.
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.
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.
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.
arXiv:2608. 14585v1 Announce Type: new Abstract: Euclidean geometry is a compelling testbed for AI reasoning, as it demands the combination of intuitive diagram understanding, axiomatic deduction, and algebraic computation.
arXiv:2606. 09707v1 Announce Type: new Abstract: As deep learning models scale, managing, inspecting, and modifying large checkpoints has become increasingly challenging.
arXiv:2601. 13731v2 Announce Type: replace-cross Abstract: Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations.
arXiv:2607. 02166v1 Announce Type: cross Abstract: The rapid advancements in using neural networks as implicit data representations have attracted significant interest in developing machine learning methods that analyze and process the weight spaces of other neural networks.
arXiv:2606. 17522v1 Announce Type: cross Abstract: Deep neural networks are widely believed to derive their expressive power from their ability to form \textbf{hierarchical representations}, capturing progressively more abstract and compositional features across layers.
arXiv:2603. 18104v5 Announce Type: replace Abstract: Prevailing AI training assumes reverse-mode automatic differentiation over IEEE-754 arithmetic.