arXiv:2510. 15814v2 Announce Type: replace-cross Abstract: Universality results for equivariant neural networks remain rare.
arXiv:2406. 08966v3 Announce Type: replace Abstract: The separation power of a machine learning model refers to its ability to distinguish between different inputs and is often used as a proxy for its expressivity.
arXiv:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries.
arXiv:2410. 06665v4 Announce Type: replace-cross Abstract: This paper explores the characterization of equivariant linear layers for representations of permutations and related groups.
arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...
arXiv:2602. 01083v2 Announce Type: replace Abstract: Weight-space learning studies neural architectures that operate directly on the parameters of other neural networks.
arXiv:2607. 05546v1 Announce Type: cross Abstract: We develop a unified function space theory of deep fully connected neural networks.
The paper introduces the directional linear separability measure (D‑LSM) to quantify how much linear separability is preserved or improved by injective affine maps in neural networks. It characterizes the geometry supporting D‑LSM, proves its invariance under injective affine embeddings, and derives conditions for gated activations (ReLU, GELU, SiLU) to preserve and recover samples. Experiments validate the theoretical bounds, demonstrate affine‑tube constructions that achieve guaranteed recovery, and apply the method to Vision Transformer representations to obtain early post‑activation separability certificates.
arXiv:2606. 16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models.
arXiv:2607. 03798v1 Announce Type: cross Abstract: Symmetry is everywhere in nature and society.
The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error. However, the uniqueness of such neural network representations is not guaranteed, raising questions about practical identifiability.
arXiv:2607. 18930v1 Announce Type: cross Abstract: The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error.