Recent work showed that language models represent character counts on curved 1D manifolds, with attention heads performing geometric transformations to enable computation. We test whether this generalizes across four ordinal tasks (bracket depth, indentation, table position, numeric magnitude) in Gemma-2-2B, Gemma-2-9B, and Qwen3-4B.
arXiv:2607. 04167v1 Announce Type: new Abstract: Recent work showed that language models represent character counts on curved 1D manifolds, with attention heads performing geometric transformations to enable computation.
The paper investigates how large language models (LLMs) organize reasoning operations—such as problem formulation, goal decomposition, and deduction—within their hidden representation spaces. It shows that these operations are separable in held‑out representations, with peak separability in middle layers, and that token‑wise alignment of operations becomes more distributed across spans as layers deepen. Attention‑masking experiments reveal that representations aligned to operations at chunk onsets depend on prior reasoning context, indicating a geometric correspondence between linguistic reasoning expressions and internal model structure.
arXiv:2608.20999v1 Announce Type: new Abstract: Multimodal LLMs apply the language model interface to visual inputs, where ordinal regression tasks such as age estimation, image quality assessment, a...
arXiv:2509. 10534v3 Announce Type: replace-cross Abstract: The attention mechanism in a Transformer architecture matches key to query based on both content -- the what -- and position in a sequence -- the where.
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:2511. 21594v3 Announce Type: replace Abstract: Large language models (LLMs) achieve state-of-the-art results across many natural language tasks, but their internal mechanisms remain difficult to interpret.
arXiv:2510. 18315v2 Announce Type: replace-cross Abstract: We investigate how embedding dimension affects the emergence of an internal "world model" in a transformer trained with reinforcement learning to perform bubble-sort-style adjacent swaps.
arXiv:2606. 01269v1 Announce Type: new Abstract: Transitive inference is the challenge of inferring that A < C from knowing only adjacent relations (A < B, B < C).
The paper audits frozen decoder‑only large language models (LLMs) on geometric reasoning tasks using parametric CAD constraints. It probes hidden states for linear decodability, forced‑choice generation, activation‑level influence, and behavioral steerability, finding that pretraining improves decoding of local geometric relations but not sketch‑level DOF status. The study shows that decodable information is not always actionable: generation often fails to express it, and steering interventions do not reliably control outputs, revealing divergences among decodability, generation, activation influence, and steerability.
The paper proposes an encoder Transformer that explicitly separates semantic, absolute positional (AP), and relative positional (RP) information, restricting the masked‑language‑modeling objective to the semantic stream. This disentanglement reveals that the AP subspace collapses into a low‑frequency two‑dimensional manifold reflecting document structure, that attention heads specialize into structure‑ and semantic‑oriented groups with RP supporting only the latter, and that standard positional encodings fail to robustly encode macroscopic structure. The approach preserves positional encoding and improves performance on 49 out of 65 linguistic phenomena in the Flash‑Holmes probing benchmark.
The paper investigates how large language models encode and use relational information among tokens across transformer layers. By analyzing activations from prompts that require inferring relationships among three cyclic tokens (months, hours, weekdays, musical notes), the authors find a consistent layerwise progression: intermediate layers capture pairwise relationships, while later layers encode the full three‑token relationship to predict the next token. They also identify geometrically structured token relationships that do not influence prediction, and show that constraining models to use only causally relevant joint representations improves next‑token accuracy.
arXiv:2602. 15029v3 Announce Type: replace Abstract: The internal representations learned by language models consistently exhibit striking geometric structure: calendar months organize into a circle, historical years form a smooth one-dimensional manifold, and cities' latitudes and longitudes can be decoded using a linear probe.