Deep Learning Without Training (zenodo.org)

Researchers introduced a deterministic, matrix-free framework for deep representation learning that constructs feature representations in a single, fully parallelizable pass — no iterative optimization or gradient descent required. The method builds a weighted Hilbert space using a "Goldilocks (Gamma) measure" in a log-prime basis, producing a log-prime orthogonal channel set whose multiplicative/rational independence yields native orthogonality (no Gram–Schmidt). Under a weighted spectral basis this basis gives a diagonal “surrogate” so per-mode updates are independent; an analytic Koopman–tangent projection and a variational principle then select representations by balancing representation energy against harm to geometric primitives (polynomial moments and spectral curves defined by Koopman invariants). Why this matters: the approach offers a deterministic, interpretable alternative to stochastic gradient methods for tasks with strong spectral or geometric-invariant structure. On Fashion-MNIST it hits 85–88% classification accuracy—comparable to a standard CNN—while authors estimate a 10–1000× reduction in energy consumption. Key technical implications include single-pass, fully parallel computation, continuous compression–accuracy trade-offs, and analytic, mode-wise updates. Caveats: the method leverages specific spectral/Koopman assumptions and was demonstrated on a single benchmark, so its generality across diverse, high-dimensional tasks remains to be validated.