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arXiv preprint arXiv:2102.11174 , year =

12 Pith papers cite this work. Polarity classification is still indexing.

12 Pith papers citing it
abstract

We show the formal equivalence of linearised self-attention mechanisms and fast weight controllers from the early '90s, where a ``slow" neural net learns by gradient descent to program the ``fast weights" of another net through sequences of elementary programming instructions which are additive outer products of self-invented activation patterns (today called keys and values). Such Fast Weight Programmers (FWPs) learn to manipulate the contents of a finite memory and dynamically interact with it. We infer a memory capacity limitation of recent linearised softmax attention variants, and replace the purely additive outer products by a delta rule-like programming instruction, such that the FWP can more easily learn to correct the current mapping from keys to values. The FWP also learns to compute dynamically changing learning rates. We also propose a new kernel function to linearise attention which balances simplicity and effectiveness. We conduct experiments on synthetic retrieval problems as well as standard machine translation and language modelling tasks which demonstrate the benefits of our methods.

citation-role summary

background 2 method 1

citation-polarity summary

years

2026 11 2025 1

representative citing papers

WriteSAE: Sparse Autoencoders for Recurrent State

cs.LG · 2026-05-12 · unverdicted · novelty 8.0 · 2 refs

WriteSAE introduces sparse autoencoders with rank-1 matrix atoms for recurrent state updates, allowing replacement tests that outperform deletion on 92.4% of positions and a formula predicting logit changes with R²=0.98.

Learning, Fast and Slow: Towards LLMs That Adapt Continually

cs.LG · 2026-05-12 · unverdicted · novelty 7.0 · 2 refs

Fast-Slow Training uses context optimization as fast weights alongside parameter updates as slow weights to achieve up to 3x better sample efficiency, higher performance, and less catastrophic forgetting than standard RL in continual LLM learning.

Test-Time Training with Next-Token Prediction

cs.CL · 2026-06-19 · unverdicted · novelty 6.0

TTT-NTP adapts pretrained LLMs at test time by training fast weights to match next-position hidden states from the forward pass, yielding consistent gains on long-context benchmarks across Llama, Mistral, and Qwen models.

Memory by Design: Probabilistic Sequence Layers

stat.ML · 2026-05-29 · unverdicted · novelty 6.0

The design-model framework unifies sub-quadratic sequence models as Bayesian filters and introduces a covariance-tracking Bayesian Layer that improves retrieval robustness beyond training regimes on MQAR and RULER benchmarks.

A Single-Layer Model Can Do Language Modeling

cs.CL · 2026-05-11 · unverdicted · novelty 6.0

A 130M-parameter 1-layer GPN achieves FineWeb-Edu perplexity 18.06, within 13% of a 12-layer Transformer++ (16.05) and 18% of a 10-layer GDN (15.34).

citing papers explorer

Showing 12 of 12 citing papers.

  • WriteSAE: Sparse Autoencoders for Recurrent State cs.LG · 2026-05-12 · unverdicted · none · ref 28 · 2 links

    WriteSAE introduces sparse autoencoders with rank-1 matrix atoms for recurrent state updates, allowing replacement tests that outperform deletion on 92.4% of positions and a formula predicting logit changes with R²=0.98.

  • Tensor Cache: Eviction-conditioned Associative Memory for Transformers cs.LG · 2026-05-21 · unverdicted · none · ref 27

    Tensor Cache augments sliding-window attention with an eviction-fed outer-product associative memory and a training correction to improve long-context performance under bounded memory.

  • Learning, Fast and Slow: Towards LLMs That Adapt Continually cs.LG · 2026-05-12 · unverdicted · none · ref 48 · 2 links

    Fast-Slow Training uses context optimization as fast weights alongside parameter updates as slow weights to achieve up to 3x better sample efficiency, higher performance, and less catastrophic forgetting than standard RL in continual LLM learning.

  • Preconditioned DeltaNet: Curvature-aware Sequence Modeling for Linear Recurrences cs.LG · 2026-04-22 · unverdicted · none · ref 46

    Preconditioned delta-rule models with a diagonal curvature approximation improve upon standard DeltaNet, GDN, and KDA by better approximating the test-time regression objective.

  • Sparse Delta Memory: Scaling the State of Linear RNNs through Sparsity cs.LG · 2026-07-08 · conditional · none · ref 108 · internal anchor

    SDM sparsifies the Gated DeltaNet update rule to enable 1000x larger recurrent memory states at iso-FLOP, improving long-context recall and short-context reasoning over GDN and matching full attention at 8B scale.

  • A Hippocampus for Linear Attention: An Exact Memory for What the Recurrent State Forgets cs.AI · 2026-07-02 · unverdicted · none · ref 18

    HOLA pairs a compressive delta-rule recurrent state with a residual-selected exact KV cache and decoupled RMSNorm-gamma read, yielding lower perplexity than both standard linear attention and full-attention baselines on Wikitext and LAMBADA plus stronger needle-in-haystack recall.

  • Test-Time Training with Next-Token Prediction cs.CL · 2026-06-19 · unverdicted · none · ref 20

    TTT-NTP adapts pretrained LLMs at test time by training fast weights to match next-position hidden states from the forward pass, yielding consistent gains on long-context benchmarks across Llama, Mistral, and Qwen models.

  • Memory by Design: Probabilistic Sequence Layers stat.ML · 2026-05-29 · unverdicted · none · ref 28

    The design-model framework unifies sub-quadratic sequence models as Bayesian filters and introduces a covariance-tracking Bayesian Layer that improves retrieval robustness beyond training regimes on MQAR and RULER benchmarks.

  • Multi-Mixer Models: Flexible Sequence Modeling with Shared Representations cs.LG · 2026-05-27 · unverdicted · none · ref 6

    Oryx hybridizes attention and linear recurrent mixers along the sequence axis with high parameter sharing, outperforming single-mixer baselines on language modeling and retrieval at up to 1.4B scale under mixed training.

  • A Single-Layer Model Can Do Language Modeling cs.CL · 2026-05-11 · unverdicted · none · ref 9

    A 130M-parameter 1-layer GPN achieves FineWeb-Edu perplexity 18.06, within 13% of a 12-layer Transformer++ (16.05) and 18% of a 10-layer GDN (15.34).

  • StateX: Enhancing RNN Recall via Post-training State Expansion cs.CL · 2025-09-26 · unverdicted · none · ref 16

    StateX post-trains RNNs to expand recurrent state size, improving recall and in-context learning with negligible parameter growth.

  • Reversible Foundations: Training a 120B Sparse MoE through State-Preserving Scaling cs.LG · 2026-06-05 · unverdicted · none · ref 58

    A 120B sparse MoE model with 460 experts was trained on one 8-GPU node to loss 1.78 using reversible recurrence and state-preserving scaling from a 1.78B dense seed, with 5.93B active parameters.