A single-layer transformer memorizes random subject-attribute bijections using logarithmic embedding dimension via linear superpositions in embeddings and ReLU-gated selection in the MLP, with zero-shot transfer to new facts and matching multi-hop constructions.
arXiv preprint arXiv:2404.05405 , year =
6 Pith papers cite this work. Polarity classification is still indexing.
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Multi-source transfer learning incurs an intrinsic adaptation cost that can exceed one, with phase transitions separating regimes where bias-agnostic estimators match oracle performance from those where they cannot.
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.
Synthetic pre-pre-training on structured data improves LLM robustness to noisy pre-training, matching baseline loss with up to 49% fewer natural tokens for a 1B model.
Loss-based pruning of training data to limit facts and flatten their frequency distribution enables a 110M-parameter GPT-2 model to memorize 1.3 times more entity facts than standard training, matching a 1.3B-parameter model on the full dataset.
Grokking emerges near the model size where memorization timescale T_mem(P) intersects generalization timescale T_gen(P) on modular arithmetic.
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The Statistical Cost of Adaptation in Multi-Source Transfer Learning
Multi-source transfer learning incurs an intrinsic adaptation cost that can exceed one, with phase transitions separating regimes where bias-agnostic estimators match oracle performance from those where they cannot.