Winner-take-all linear memory capacity scales as d² ~ n log n due to extreme values; listwise retrieval via Tail-Average Margin yields d² ~ n with exact asymptotic theory.
arXiv preprint arXiv:2412.06538 , year=
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Muon achieves higher storage capacity than SGD and matches Newton's method in one-step recovery rates for associative memory under power-law distributions, while saturating at larger critical batch sizes and showing faster initial multi-step dynamics.
Deep sequence models develop geometric memory in embeddings that encodes novel global relationships, transforming l-fold composition tasks into 1-step navigation via a natural spectral bias connected to Node2Vec.
In a stylized one-layer transformer, pre-training encodes factual knowledge via relation-specific feature directions and attention patterns; fine-tuning extracts it through a relation-covering mechanism that succeeds when enough latent templates are triggered, with a failure regime explaining inauds
TIDE augments standard transformers with per-layer token embedding injection via an ensemble of memory blocks and a depth-conditioned router to mitigate rare-token undertraining and contextual collapse.
citing papers explorer
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Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval
Winner-take-all linear memory capacity scales as d² ~ n log n due to extreme values; listwise retrieval via Tail-Average Margin yields d² ~ n with exact asymptotic theory.
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Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory
Muon achieves higher storage capacity than SGD and matches Newton's method in one-step recovery rates for associative memory under power-law distributions, while saturating at larger critical batch sizes and showing faster initial multi-step dynamics.
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Deep sequence models tend to memorize geometrically; it is unclear why
Deep sequence models develop geometric memory in embeddings that encodes novel global relationships, transforming l-fold composition tasks into 1-step navigation via a natural spectral bias connected to Node2Vec.
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Provable Knowledge Acquisition and Extraction in One-Layer Transformers
In a stylized one-layer transformer, pre-training encodes factual knowledge via relation-specific feature directions and attention patterns; fine-tuning extracts it through a relation-covering mechanism that succeeds when enough latent templates are triggered, with a failure regime explaining inauds
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TIDE: Every Layer Knows the Token Beneath the Context
TIDE augments standard transformers with per-layer token embedding injection via an ensemble of memory blocks and a depth-conditioned router to mitigate rare-token undertraining and contextual collapse.