Any convex L-Lipschitz functional on a compact convex subset of a separable Hilbert space can be uniformly approximated to arbitrary accuracy by an explicit convex L-Lipschitz reconstruction from finitely many linear measurements, exactly implementable by a ReLU-MLP.
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Transformers are limited to a linearly growing number of accessible output sequences with prompt length, with exponential decay in accessible proportion beyond a critical point, even under unbounded context.
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Structure-Preserving Reconstruction of Convex Lipschitz Functionals on Hilbert Spaces from Finite Samples
Any convex L-Lipschitz functional on a compact convex subset of a separable Hilbert space can be uniformly approximated to arbitrary accuracy by an explicit convex L-Lipschitz reconstruction from finitely many linear measurements, exactly implementable by a ReLU-MLP.
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How Many Different Outputs Can a Transformer Generate?
Transformers are limited to a linearly growing number of accessible output sequences with prompt length, with exponential decay in accessible proportion beyond a critical point, even under unbounded context.