Optimal history encoding for elastic-plastic hereditary laws: Sharp input and constitutive approximation
arXiv:2607.09974
2026
Memory
2 ideas extracted · analyzed Aug 30, 2026
What the math gives to ML
The paper identifies cumulative variation, rather than elapsed time or token count, as the correct coordinate for compressing causal histories governed by a nonexpansive hereditary operator. Its sharp equal-variation sampling theorem suggests replacing uniform context or KV-cache subsampling with an adaptive encoder that allocates history points when the representation has accumulated equal amounts of variation, yielding a worst-case error proportional to total variation divided by 2N. The material-law-aware result also suggests compressing a transformed state trajectory rather than the raw input when the downstream decoder is known, while convex projection supplies a stable recurrent update for constrained memory states.
Ideas from this paper
△ Mechanism confirmed, baseline not beaten
2026
Compress a causal sequence by retaining history positions at equal increments of cumulative representation variation instead of at uniform time intervals. Use the resulting N representatives in a decoder that reconstructs piecewise-constant keys and values; the paper's minimax result predicts a worst-case reconstruction error of total variation divided by 2N, independent of where rapid changes occur.
Useful8/10
Difficulty5/10
Novelty6/10
Unverified
2026
Turn a recurrent or state-space memory into a constrained hereditary state: the latent state remains in a learned convex domain, and only input motion that reaches the boundary changes the plastic component. This creates a nonexpansive, rate-independent memory that should suppress unstable state growth and make the representation depend on meaningful cumulative changes rather than arbitrary update frequency.
Useful6/10
Difficulty4/10
Novelty5/10