Transformer theory moves from expressivity to sample complexity bounds
Researchers bridge a critical gap in Transformer theory by moving beyond expressivity analysis to quantify sample complexity for learning attention-based models. This work connects loss landscape insights with C-RASP constructions to establish preliminary bounds on how many training examples Transformers need to acquire specific algorithmic behaviors. The finding matters because most prior theoretical work characterized what tasks Transformers can represent in principle, but ignored whether those solutions are actually learnable from realistic data volumes. Understanding learnability directly informs model scaling laws and helps predict when architectural changes or training regimes will fail to converge on desired behaviors.
Modelwire context
ExplainerThe paper's core move is shifting from 'what can Transformers express' to 'how many examples do they need to learn it'. Prior work proved Transformers could represent arbitrary algorithms; this quantifies the training data cost of actually acquiring those behaviors, which is a different (and harder) question.
This directly extends the theoretical framework from 'Invariant Learning Dynamics of Transformers in Inductive Reasoning Tasks' (July 13). That work showed Transformer learning follows predictable low-dimensional manifolds for synthetic tasks. C-RASP sample complexity bounds now put numbers on how many examples are required to reach those manifolds, connecting geometric learning theory to practical data requirements. Together, these papers move from 'learning is structured' to 'learning is structured AND quantifiable', which matters for predicting when scaling laws will plateau or when architectural changes won't converge regardless of compute.
If researchers validate these sample complexity bounds on real in-context learning tasks (n-gram prediction, algorithmic reasoning) within the next six months, the theory has teeth. If the bounds remain loose or only tight for toy problems, the work is elegant but may not predict actual training dynamics at scale.
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MentionsTransformers · C-RASP · LLMs
Modelwire Editorial
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Modelwire summarizes, we don’t republish. arXiv cs.CL originally reported this story as “From Expressivity to Sample Complexity: Narrow Teachers for Transformers via C-RASP”. The full content lives on arxiv.org. If you’re a publisher and want a different summarization policy for your work, see our takedown page.