The paper investigates how neural networks, particularly Transformers and recurrent models, learn to track group elements by predicting their running product. It finds that Transformers tend to recover quotient classes and that their accuracy can be predicted by the reciprocal of class size, while recurrent networks can capture both normal and non‑normal right‑coset partitions. The study links partial accuracy, learning stages, and internal state representations to the subgroup cosets the models learn to track.
arXiv:2606. 07254v1 Announce Type: new Abstract: State tracking exposes a sharp limitation of sequence models: the relevant signal is often not a summary of observed tokens, but an ordered latent state that evolves through non-commutative transformations.
arXiv:2607. 18759v1 Announce Type: new Abstract: Transformers with relative positional encodings often extrapolate to sequences longer than those seen during training, whereas transformers with learned absolute encodings typically do not.
arXiv:2603. 01959v2 Announce Type: replace Abstract: State-Space Models (SSMs) have recently been shown to achieve strong empirical performance on a variety of long-range sequence modeling tasks while remaining efficient and highly-parallelizable.
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:2609.38149v1 Announce Type: new Abstract: Transformer language models (LMs) are feed-forward: deep-layer representations are never fed back to shallower layers, and the only pathway for informa...
arXiv:2602. 22600v2 Announce Type: replace-cross Abstract: Training selects for behavior, not circuitry: many weight configurations can implement the same function.
arXiv:2607. 14427v1 Announce Type: new Abstract: A depth-recurrent transformer applies a weight-tied core a variable number of times, and prior work has shown that training with a randomized recursion count yields one checkpoint usable across a range of inference depths.
arXiv:2607. 05872v1 Announce Type: new Abstract: Memory-efficient optimizers such as GaLore train large language models by projecting gradients onto a rank-r subspace recomputed every T steps, assuming this subspace is a slowly drifting object that can be tracked.
arXiv:2511. 05963v4 Announce Type: replace Abstract: Transformers replace recurrence with a memory that grows with sequence length and self-attention that enables ad-hoc lookups over past tokens.
Subspace-Decomposed JEPAs (SD-JEPA) split the latent space of Joint-Embedding Predictive Architectures into two orthogonal subspaces: a low-dimensional progression subspace trained with a cosine-margin triplet loss and a high-dimensional content subspace regularised by SIGReg. The authors prove that the anti-collapse forces act on disjoint coordinates, allowing additive composition rather than competition. SD-JEPA outperforms the LeWM baseline on most control benchmarks and the strongest non-LeWM JEPA baseline on Push‑T, with a subspace-ablation confirming the split as essential. The 1‑D angular progression coordinate serves as a scene-aware compass, advancing with task progress, regressing on backtracking, and relocalising under perturbations to separate surprise from meaning.
arXiv:2609.37974v1 Announce Type: cross Abstract: Masked diffusion models (MDMs) generate text by unmasking several tokens per step, but they are trained and sampled under different conditions. The m...
arXiv:2607. 05316v1 Announce Type: cross Abstract: Large language models generate one token at a time, yet their responses show remarkably consistent length structure: step-by-step solutions converge in predictable token counts, retrievals stop after a few sentences, retractions extend responses by measurable amounts.