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Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete

arXiv:2606.01532v2 Announce Type: replace 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. 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.e., they are Turing complete. We revisit this belief in the regime most...

arXiv CS 7d ago

Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete

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. 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.e., they are Turing complete. We revisit this belief in the regime most relevant to long-form...

arXiv CS 8d ago

Turing Patterns for Multimedia: Reaction-Diffusion Multi-Modal Fusion for Language-Guided Video Moment Retrieval

Announce Type: new Abstract: Video-language models are pivotal for tasks such as moment retrieval and highlight detection, yet they often struggle to capture the dynamic, non-linear interactions between temporal video sequences and textual semantics. Existing approaches, relying on static cross-attention or prompt-tuning mechanisms, fail to adaptively model the evolving relationships between modalities, leading to suboptimal alignment and limited generalization. Inspired by systems biology,...

arXiv CS 8d ago

Jira Is Turing-Complete

Hacker News 16d ago

Soliton crystal formation in Kerr cavities with an avoided mode crossing: a theoretical study

arXiv:2606.03202v1 Announce Type: new Abstract: We theoretically and numerically investigate the formation of soliton crystals in Kerr microresonators in the presence of an avoided mode crossing (AMX). Our study combines dynamical simulations based on a modified Lugiato-Lefever equation (LLE) with a stability analysis of its stationary solutions. We show that, depending on its strength and spectral position, the AMX can either stabilize otherwise unstable soliton crystals or induce Turing...

arXiv Physics 7d ago

An Algebraic View of the Expressivity of Recurrent Language Models

new Abstract: What formal languages can a recurrent neural language model recognize? Formal results in the literature conflict: some authors report Turing-completeness, while others show equivalence to regular languages. The reason for this discrepancy is that the underlying arithmetic model differs.

arXiv CS 8d ago

An Algebraic View of the Expressivity of Recurrent Language Models

arXiv:2606.01765v2 Announce Type: replace Abstract: What formal languages can a recurrent neural language model recognize? Formal results in the literature conflict: some authors report Turing-completeness, while others show equivalence to regular languages. The reason for this discrepancy is that the underlying arithmetic model differs.

arXiv CS 2d ago

Bank of England reveals which animals could feature on new banknotes

Bank of England reveals which animals could feature on new banknotes Animals are set to replace historical figures on Bank of England notes in the biggest such change since the 1960s The Bank of England is planning on replacing historical figures on banknotes with animals - chosen by the public. Gone will be Sir Winston Churchill on the £5, Jane Austen on the £10, JMW Turner on the £20, and Alan Turing on the £50 note. Instead, they will feature a selection of wildlife, native to the UK,...

Daily Mirror 7d ago

Blockchain Infrastructure for Intelligent Cyber--Physical--Social Systems:Post-Quantum Security, Interoperability, and Trustworthy Data Economies in the Era of Embodied AI

Announce Type: new Abstract: The deployment of embodied artificial intelligence via world-model-based robotics presents a transformative opportunity for blockchain infrastructure, establishing urgent demand for trustworthy data provenance, cross-organizational governance, and incentive-compatible sharing across decentralized ecosystems. Simultaneously, quantum computing advances recognized by the 2025 Nobel Prize in Physics and the Turing Award threaten the cryptographic primitives securing...

arXiv CS 2d ago

A Variational Framework for the Complexity of PDE Solutions

arXiv:2510.21290v3 Announce Type: replace Abstract: Partial Differential Equations (PDEs) are fundamental mathematical models for describing physical phenomena, yet most PDEs of practical interest require numerical approximations. The feasibility of such methods is constrained by existing computational models. Since digital computers are the primary realizations of numerical computations, and Turing machines define their theoretical limits, computability of PDE solutions is of fundamental...

arXiv CS 1d ago