LIMEN Topological Learning via Intrinsic Thresholding in Neural Autoencoders

We introduce LIMEN (Learning through Intrinsic Minimal Emergent Nodes), a method that addresses a fundamental gap in representation learning: existing approaches evaluate latent space quality through task performance, labels, or imposed statistical priors, but no method measures the intrinsic geometric diversity of a learned representation without any external reference. LIMEN 􏰂lls this gap by introducing a single learnable silence threshold, implemented as a DeadZoneTanh activation, that a neural autoencoder optimizes by back- propagation to self-organize its latent space. This threshold behaves as a phase transition order parameter: below a critical value the latent space is topologically rich; above it the network collapses into silence. Latent space quality is measured by the algebraic rank of a low-dimensional binary matrix over GF(2), computable in microseconds on standard CPU hardware without external prior or imposed distribution. We validate LIMEN on ten physically heterogeneous real-world corpora spanning particle physics, astrophysics, nuclear engineering, arithmetic structure, photometry, spectroscopic surveys, combinatorial mathematics, quantum cryptography, deterministic chaos, and real DNS turbulence. LIMEN produces distinct, reproducible topological signatures across all domains without labels or supervision. Rank scores are interpreted relative to a stochastic baseline of approximately 0.90, established by pure white noise corpora, and range from 0.9975 (KIC 8462852, Tabby's Star) to 0.8460 (binary combinatorial matrices), with each corpus exhibiting a characteristic natural threshold to which the learnable parameter con- verges spontaneously, constituting a scalar 􏰂ngerprint of the underlying physical process. The stability of this ordering across random initialization seeds con􏰂rms that LIMEN signatures re􏰃ect genuine properties of the data rather than artifacts of the training procedure. Hybrid corpus experiments reveal an unexpected asymmetric topological transfer: mi- nority corpora of high topological complexity act as catalysts, enriching the latent geometry of dominant corpora beyond their isolated performance. These results position LIMEN as an intrinsic latent space diversity metric and a computationally minimal foundation for scaling toward world models and higher-dimensional architectures.