arXiv AI

How to Build Marcus's Algebraic Mind: Algebro-Deterministic Substrate over Galois Fields

arXiv:2605. 21379v3 Announce Type: replace-cross Abstract: In The Algebraic Mind (2001), Marcus held that any adequate cognitive architecture needs operations over variables, recursively structured representations, and an individual/kind distinction, and that multilayer perceptrons support none of them; he left a register-and-treelet implementation as a conjecture.

arXiv AI
Jun 24

Repeated Shared Access Enables Grokking, but Edit Propagation Depends on an Addressable Memory

arXiv:2606. 20737v2 Announce Type: replace Abstract: We study factual edit propagation in a controlled synthetic knowledge-graph QA setting using a 2x2 grid that crosses loop recurrence with shared-memory access: a dense transformer (Dense), a looped transformer (Loop), a dense backbone with shared memory (Dense+Mem), and a looped backbone with shared memory (loop-memory coupling, LMC).

By Yanan Niu
arXiv AI
Aug 11

ZenBrain: A Neuroscience-Inspired 7-Layer Memory Architecture for Autonomous AI Systems

arXiv:2604. 23878v3 Announce Type: replace Abstract: ZenBrain is a seven-layer, neuroscience-derived memory architecture for LLM agents that unifies fifteen mechanisms - from Two-Factor synaptic consolidation to a Simulation-Selection sleep loop - under a single MemoryCoordinator: nine foundational algorithms plus six Predictive Memory Architecture components.

By Alexander Bering
arXiv Machine Learning
Jul 16

Algebraic Representability as the Limiting Regime of Grokking: An Exactly Solvable Model with Holomorphic Activations

arXiv:2607. 13749v1 Announce Type: new Abstract: Neural networks trained on modular arithmetic exhibit grokking, a delayed transition from memorisation to generalisation known to depend on model capacity: too little and the network memorises slowly or not at all, too much and it generalises almost immediately.

By Chon-Fai Kam, Xavier Cadet, Miloud Bessafi, Frederic Cadet