arXiv:2507. 11688v4 Announce Type: replace Abstract: Contemporary large models often exhibit behaviors suggesting the presence of low-level primitives that compose into modules with richer functionality, but these fundamental building blocks remain poorly understood.
arXiv:2607. 06634v1 Announce Type: new Abstract: Compact networks built from Clifford algebra Cl(3,0) primitives are exactly SO(3)-equivariant and learn synthetic 3D vector laws from few samples.
arXiv:2602. 24264v2 Announce Type: replace-cross Abstract: Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems.
arXiv:2606. 11391v1 Announce Type: new Abstract: Tensor Product Representations provide the structural fidelity required for symbolic reasoning in models but suffer from exponential dimensionality growth when encoding deep recursive structures.
arXiv:2606. 01372v1 Announce Type: cross Abstract: Can neural networks learn abstract algebraic rules, or do they merely memorize training patterns?
arXiv:2602. 17510v2 Announce Type: replace-cross Abstract: We introduce LoRA-CRAFT (\textbf{C}ross-layer \textbf{R}ank \textbf{A}daptation via \textbf{F}rozen \textbf{T}ucker), abbreviated CRAFT throughout, an extremely parameter-efficient fine-tuning (PEFT) method that applies Tucker tensor decomposition to pre-trained attention weight matrices stacked across transformer layers and trains only small square adaptation matrices on the resulting frozen Tucker factors.
arXiv:2607. 07066v1 Announce Type: cross Abstract: Transformers have demonstrated a remarkable ability to learn algorithmic reasoning, yet mechanistic analyses have mostly focused on globally invertible operations such as cyclic addition and group composition.
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:2601. 22402v2 Announce Type: replace-cross Abstract: Rotary Positional Embeddings (RoPE) have become the standard for Large Language Models (LLMs) due to their ability to encode relative positions through geometric rotation.
arXiv:2609.01129v1 Announce Type: new Abstract: We identify a recurrent algebraic regularity in Transformer attention: a sparse subset of effective OV operators $T=OV^\top$ nearly closes under compos...
arXiv:2609.37659v1 Announce Type: cross Abstract: There has been significant work on understanding the In-Context Learning capabilities of Large Language Models, especially on the induction circuit....
The paper investigates how transformer language models perform few‑shot learning for a simple addition task, showing that the ability is concentrated in a handful of attention heads. Using dimensionality reduction, the authors identify low‑dimensional subspaces—three heads with six‑dimensional spaces in Llama‑3‑8B‑Instruct—where specific dimensions encode the units digit via trigonometric patterns and magnitude via low‑frequency components. They also derive a mathematical identity linking aggregator and extractor subspaces, enabling tracking of information flow from examples to the final prediction.
arXiv:2609.40127v1 Announce Type: cross Abstract: Modern transformers pair impressive capabilities with substantial memory and compute demands. Low-rank weight factorization reduces both while keepin...