Search papers, labs, and topics across Lattice.
This paper introduces Coupled Scaling, a novel framework that elucidates how task structure and architectural optimization influence the scaling behavior of neural networks trained on the same data. By analyzing the relationship between task-conditioned geometry and representational accessibility, the authors derive a set of scaling laws that account for the residual loss in terms of architectural support and task relevance. The key finding reveals that the scaling behavior can be significantly affected by the interplay between architecture and optimization strategies, leading to new insights on how to effectively allocate resources in neural network training.
Scaling behavior of neural networks can vary dramatically based on task structure and architectural choices, challenging conventional scaling theories.
Existing theories derive neural scaling from data geometry or a specified data-model spectrum, but systems trained on the same data can scale differently when architecture or optimization changes the representations they can efficiently reach. We introduce Coupled Scaling, a task-conditioned framework in which finite-budget scaling depends on the relation between task structure and the geometry accessible to an architecture-optimization system. In a solvable mode-truncation model, loss separates into target energy outside architectural support and an unresolved supported tail. For an arbitrary priority order, the residual lies between the best-N supported tail and the tail beyond the largest completed high-value prefix. If the cumulative-tail and coverage log-rates are $\gamma_{A,T}$ and $\rho_{A,O,T}$, the residual exponent lies in $[\rho_{A,O,T}\gamma_{A,T},\gamma_{A,T}]$. Under bounded off-prefix gain, the completed prefix is rate-determining and $\alpha_{A,O,T}=\rho_{A,O,T}\gamma_{A,T}$; for $a_{A,T,j}\asymp j^{-b_{A,T}}$, this gives $\alpha_{A,O,T}=\rho_{A,O,T}(b_{A,T}-1)$. A fixed-kernel specialization derives the training-time exponent from the near-zero tail of a task-weighted spectral measure defined independently of the loss fit. The framework separates architectural support from finite-budget acquisition and motivates two tests: static task-relevant geometry should track loss at a common budget, while multiscale geometry should track coupling-specific exponent ordering, including reversal across contrasting tasks. An audit of released emergence trajectories identifies the controls needed for a direct factorial test that measures geometry separately from the scaling fit.
