The paper proposes a content‑based addressing scheme for long‑context models that replaces the growing token counter in Rotary Position Embedding (RoPE) with unit‑level addresses derived from the content of each unit. By dividing the token stream into units, the method preserves local RoPE behavior while allowing new units to be addressed via learned content maps, avoiding positional mismatches when extending context length. Experiments on character‑level Tiny Shakespeare show that a model trained on 256‑character contexts achieves lower perplexity at 4096 characters using this scheme, and a second diagnostic demonstrates retrieval of multiple serialized facts.
By Mahesh Godavarti
arXiv:2606. 01532v1 Announce Type: new Abstract: Positional encoding (PE) is widely viewed as necessary for transformers to process ordered sequences: without them, the next-token map appears permutation-invariant in its context tokens.
By Qian Li, Xinyu Mao, Shang-Hua Teng
Positional encoding (PE) is widely viewed as necessary for transformers to process ordered sequences: without them, the next-token map appears permutation-invariant in its context tokens. This intuition underlies all prior universality results, which rely on positional information to prove that transformers with chain-of-thought can perform arbitrary computation, i.
arXiv:2607. 26988v1 Announce Type: cross Abstract: What types of decision problems can a causally masked, finite-precision transformer solve for inputs of arbitrary length?
By Franz Nowak, Ryan Cotterell, Reda Boumasmoud
arXiv:2511. 17388v3 Announce Type: replace-cross Abstract: Position information is essential for language modeling.
By Sajad Movahedi, Timur Carstensen, Arshia Afzal, Frank Hutter, Antonio Orvieto, Volkan Cevher
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.
By Kanishk Awadhiya
arXiv:2604. 25800v2 Announce Type: replace Abstract: Chain-of-Thought (CoT) has been shown to empirically improve Transformers' performance, and theoretically increase their expressivity to Turing completeness.
By Oliver Kraus, Yash Sarrof, Yuekun Yao, Alexander Koller, Michael Hahn
The paper introduces a bounded spectral framework to analyze rotary attention in transformer language models, focusing on phase alignment, hidden‑state continuity, and semantic drift. It identifies ordered hidden‑state sequences as suitable domains for spectral decomposition, derives the Rotary Position Embedding (RoPE) attention score as a sum of magnitude‑weighted cosine terms, and proves a local stability lemma linking bounded phase displacement to pre‑softmax score degradation. By defining complex modal coordinates and a weighted coherence functional, the work distinguishes representational continuity from execution‑boundary admissibility, offering a theoretical program for when spectral structure explains continuity and when external governance is required.
By Abraham Chachamovits
arXiv:2606. 06160v1 Announce Type: new Abstract: RoPE-trained transformers distinguish absolute position in their attention patterns, even though RoPE encodes only relative offsets in the inner product.
By Valeria Ruscio, Umberto Nanni, Fabrizio Silvestri
arXiv:2609.38109v1 Announce Type: cross
Abstract: The attention operation is naively position invariant. However, positional information is fundamental to natural language, and therefore a variety of...
By Cutter Dawes, Nick Alonso, Tom Figliolia, Beren Millidge
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.
By Anand Gopalakrishnan, Robert Csord\'as, J\"urgen Schmidhuber, Michael C. Mozer
arXiv:2607. 10034v1 Announce Type: new Abstract: Large language models (LLMs) store factual knowledge in their parameters.
By Roberto Garcia, Jerry Liu, Ronny Junkins, Sabri Eyuboglu, Atri Rudra, Christopher R\'e