Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ ZENODOarrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
versions View all 2 versions
addClaim

Gradient-Flow-Based Compute--Performance Trade-offs for Intelligent Systems

Observation Quotients, Preimage Geometry, and Fractal Residual Spines
Authors: Takahashi, K;

Gradient-Flow-Based Compute--Performance Trade-offs for Intelligent Systems

Abstract

This paper develops a mathematically explicit framework for compute–performance trade-offs in intelligent systems whose coarse-grained dynamics can be modeled as Evolution Variational Inequality (EVI) gradient flows on quadratic Wasserstein spaces. Under a “gradient-flow universal intelligence process (UIP)” hypothesis, the work isolates structural mechanisms that constrain how far a given architecture can push performance under finite compute, rather than proposing another empirical scaling law. The first module studies observation quotients: Borel observation maps from a UIP state space into a lower-dimensional observation space. Under a metric analogue of Riemannian submersions, the paper proves an Image–EVI theorem showing that Wasserstein EVI flows are stable under such quotients. This provides conditions under which coarse observables (embeddings, task metrics, or compressed statistics) still evolve as EVI gradient flows with the same contraction parameter. The second module introduces a notion of preimage Minkowski dimension for localized sets of epsilon-optimal parameters in a metric parameter space, together with a resolution-dependent prototype complexity. Under an explicit geometric regularity assumption and a separate coverage-based implementability condition, any empirical scaling law of the form error ≲ N^{−α} must satisfy a structural ceiling α ≤ κ / d_pre, where κ is a local Hölder exponent and d_pre is the preimage dimension. This links approximation exponents to the geometry of near-optimal preimages, independently of a specific training algorithm. The third module models deep residual or iterative architectures as fractal residual spines: nonexpansive limit maps decomposed into 1-Lipschitz residual updates with summable tails. The paper proves linear-in-depth truncation bounds and combines them with standard JKO time-discretization error estimates to obtain joint bounds of the form error ≲ C_disc h^γ + n ∑_{k>L} a_k. These bounds can be read as design rules for time step, iteration count, and effective residual depth in compute-limited AI systems. Keywords: Wasserstein gradient flows, EVI, compute–performance trade-offs, observation quotients, scaling laws, preimage Minkowski dimension, prototype complexity, residual networks, JKO scheme, optimal transport, intelligent systems.

Keywords

LLM, intelligent systems, Artificial intelligence, Information Theory, JKO scheme, Geometry, EVI, preimage Minkowski dimension, observation quotients, Large Language Models, optimal transport, AI, residual networks, gradient flows, Machine learning, scaling laws

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green
Related to Research communities