Anatomy of Associative Recall in Fixed-State Recurrences: A Matched-State Decomposition, an Interference Wall, and a Curriculum That Breaks It

Julian Boesch; Andrew Wee

Home/Archive/arXiv

arXiv · 2609.16183

Anatomy of Associative Recall in Fixed-State Recurrences: A Matched-State Decomposition, an Interference Wall, and a Curriculum That Breaks It

Julian Boesch·Andrew Wee

View original source ↗Read source document ↗Export metadata ↓

Abstract

Fixed-state recurrences--linear attention and state-space models--are reported to lag behind attention on associative recall, but whole-architecture comparisons cannot say which ingredient is responsible. We decompose masked multi-query recall at a fixed state budget along three single-knob axes: a short causal convolution, the transition structure (rank-1 delta rule vs. diagonal), and decay. The convolution dominates (~+0.5 recall in both families under matched training): comparisons that pit convolution-free cells against a convolution-equipped Mamba measure the missing convolution, not the recurrence. The rank-1 transition beats its diagonal ablation by +0.19/+0.32 at 16/32 pairs, but the margin shrinks to +0.03 once both cells carry the convolution, and a state-matched Mamba-2 ties the unarmed rank-1 cell: no class claim survives. Cells that solve 32-pair recall degrade gracefully with load yet fall to chance retrieving 4 pairs from a distractor haystack--flat across lengths and transitions. Interference under sparse supervision, not capacity: a distance curriculum takes the unchanged architecture from 0.021 to 1.000. Training is a lock-in lottery--a seed either locks in or does not--and the curriculum is the lever. Lock-in rises from 1/10 to 7/10 (p=0.02); dense supervision adds nothing; at L=256 a shaped ramp reopens a boundary the uniform curriculum cannot (4/5 vs. 0/9); and at L=512, where the ramp collapses (0/6), gating it on measured accuracy locks in 6/6 (p=0.001). Bidirectional denoiser cells, reading the query before the haystack, show no measurable advantage over causal training (ten seeds), and collision-key retrieval needs two layers. Arming for recall is free on an S_5 state-tracking guardrail--the armed cell is significantly better at every depth (p<=0.0044). These replace "recurrent models are bad at recall" with a measured decomposition and two cheap interventions.

Explore related subjects

cs.LG cs.CL

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Julian Boesch, Andrew Wee. 2026-09-14. Anatomy of Associative Recall in Fixed-State Recurrences: A Matched-State Decomposition, an Interference Wall, and a Curriculum That Breaks It. https://arxiv.org/abs/2609.16183

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Probabilistic Approach for Model Alignment with Human Comparisons

A growing trend involves integrating human knowledge into learning frameworks, leveraging subtle human feedback to refine AI models. While these approaches have shown promising results in practice, the theoretical understanding of when and why such approaches are effective remains limited. This work takes steps toward developing a theoretical framework for analyzing the conditions under which human comparisons can enhance the traditional supervised learning process. Specifically, this paper studies the effective use of noisy-labeled data and human comparison data to address challenges arising from noisy environment and high-dimensional models. We propose a two-stage "Supervised Learning+Learning from Human Feedback" (SL+LHF) framework that connects machine learning with human feedback through a probabilistic bisection approach. The two-stage framework first learns low-dimensional representations from noisy-labeled data via an SL procedure and then uses human comparisons to improve the model alignment. To examine the efficacy of the alignment phase, we introduce a concept, termed the "label-noise-to-comparison-accuracy" (LNCA) ratio. This paper identifies from a theoretical perspective the conditions under which the "SL+LHF" framework outperforms the pure SL approach; we then leverage this LNCA ratio to highlight the advantage of incorporating human evaluators in reducing sample complexity. We validate the framework on a real high-dimensional crowdfunding-prediction task: under a fixed query budget, trading labels for comparisons improves accuracy precisely when labels are scarce, and the findings hold when the evaluator is replaced by real large language models. A study conducted via Amazon Mechanical Turk (MTurk) further validates the model primitives.

cs.LG↗

arXiv2026

An Initial Introduction to Cooperative Multi-Agent Reinforcement Learning

Multi-agent reinforcement learning (MARL) has exploded in popularity in recent years. While numerous approaches have been developed, they can be broadly categorized into three main types: centralized training and execution (CTE), centralized training for decentralized execution (CTDE), and decentralized training and execution (DTE). CTE methods assume centralization during training and execution (e.g., with fast, free, and perfect communication) and have the most information during execution. CTDE methods are the most common, as they leverage centralized information during training while enabling decentralized execution -- using only information available to that agent during execution. Decentralized training and execution methods make the fewest assumptions and are often simple to implement. This text is an introduction to cooperative MARL -- MARL in which all agents share a single, joint reward. It is meant to explain the setting, basic concepts, and common methods for the CTE, CTDE, and DTE settings. It does not cover all work in cooperative MARL as the area is quite extensive. I have included work that I believe is important for understanding the main concepts in the area and apologize to those that I have omitted. Topics include simple applications of single-agent methods to CTE as well as some more scalable methods that exploit the multi-agent structure, independent Q-learning and policy gradient methods and their extensions, as well as value function factorization methods including the well-known VDN, QMIX, and QPLEX approaches, and centralized critic methods including MADDPG, COMA, and MAPPO. I also discuss common misconceptions, the relationship between different approaches, and some open questions.

cs.LG↗

arXiv2026

Transductive Off-policy Proximal Policy Optimization

Proximal Policy Optimization (PPO) is a popular model-free reinforcement learning algorithm, esteemed for its simplicity and efficacy. However, due to its inherent on-policy nature, its proficiency in harnessing data from disparate policies is constrained. This paper introduces a novel off-policy extension to the original PPO method, christened Transductive Off-policy PPO (ToPPO). Herein, we provide theoretical justification for incorporating off-policy data in PPO training and prudent guidelines for its safe application. Our contribution includes a novel formulation of the policy improvement lower bound for prospective policies derived from off-policy data, accompanied by a computationally efficient mechanism to optimize this bound, underpinned by assurances of monotonic improvement. Comprehensive experimental results across six representative tasks underscore ToPPO's promising performance.

cs.LG↗