arXiv:2606. 01372v1 Announce Type: cross Abstract: Can neural networks learn abstract algebraic rules, or do they merely memorize training patterns?
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The paper introduces BRo-JEPA, a world model that learns modular arithmetic operations as rotations in latent space. Using MNIST and EMNIST datasets, BRo-JEPA achieves near-perfect zero‑shot generalization to unseen operations, outperforming standard supervised and JEPA baselines by a large margin. The model demonstrates that latent transformations can encode underlying algebraic structures, enabling strict zero‑shot operation generalization.
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: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. 14108v1 Announce Type: cross Abstract: We introduce Adelic operation-preserved embeddings (AOE), a training-free representation that captures both a number's real value and its modular (p-adic) signatures.
The paper investigates how large language models activate a latent symbolic reasoning circuit—comprising abstraction, induction, and retrieval—when presented with in-context examples. By tracking this circuit across different shot counts and model families, the authors show that its components become detectable and functional long before the model reaches high accuracy. They further demonstrate that per-head causal contributions can increase eightfold from 1- to 10-shot, and that interventions such as cross-shot activation patching or function vector injection can dramatically improve accuracy, even at 0-shot, by leveraging the pre‑existing circuit in the model weights.
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.