Predictive Horizons and Representational Geometry: How Temporal Depth, Behavioral Regime, and Substrate-Independent Structure Co-Organize Internal Representations Across Biological and Artificial Systems

Version 2 — revised in response to an external structural review and an automated critique pass. See "Response to Review" appendix in the PDF for the change log.

A structural pattern worth investigating has emerged across several recent preprints spanning computational neuroscience (q-bio.NC) and language modeling (cs.CL): the *temporal depth* of a predictive objective—how far ahead a system predicts, and at what granularity—appears to co-determine the geometric organization of the internal representations that system develops. This is a heuristic reading, not a formal derivation; the papers cited do not share a single mathematical framework, but they do converge on a family of related empirical findings that invite a unified interpretive lens. We synthesize six to eight specific findings: (1) successor representations trained on natural language with variable temporal horizons spontaneously produce syntactic and semantic geometric organization whose character depends systematically on horizon length [corpus:arxiv:2605.24585]; (2) exploratory behavioral regimes, which implicitly extend effective predictive horizon, yield more spatially organized and transition-preserving latent geometries in maze-navigating agents [corpus:arxiv:2605.27929]; (3) digital twins of mouse V1 that predict neural responses more accurately exhibit flatter eigenspectra—higher-dimensional, less dominated by a few modes—suggesting that representational geometry is diagnostic of model quality beyond accuracy alone [corpus:arxiv:2605.23122]; (4) event segmentation and metastable neural dynamics are argued to constitute the same phenomenon at different levels of description, with a spatio-temporally nested hierarchy of timescales [corpus:arxiv:2605.31473] — a connection we treat as analogical rather than mechanistic (see §3 and Weakly-Connected Addendum); (5) sparse autoencoder decomposition of LLM layers reveals that semantic features alone recover ~94% of peak brain-encoding performance, and that these features map onto cortical topography with spatial specificity [corpus:arxiv:2605.23035]; (6) efficient coding under resource constraints theoretically drives neural systems toward criticality, providing a normative account of why temporal and spatial correlation structure takes the form it does, though the derivation is for Gaussian population coding models and has not been formally extended to transformer architectures [corpus:arxiv:2605.22598]; (7) maximum-entropy network connectivity, constrained by task requirements rather than by a specific learning algorithm, predicts the emergence of functionally specialized neuron populations whose diversity scales with context number, with the derivation specific to 2-layer feed-forward networks [corpus:arxiv:2605.25607]. The falsification path for the central claim—that predictive horizon is a primary organizer of representational geometry—is concrete: train matched architectures on the same corpus with identical capacity but systematically varied horizon lengths, then measure eigenspectrum flatness, syntactic decodability, and cortical alignment as a function of horizon. If geometry varies non-monotonically with horizon independently of accuracy, the hypothesis is supported; if geometry tracks accuracy alone, it is refuted. ---

Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename.

Cited arXiv preprints: 2605.22598, 2605.23032, 2605.23035, 2605.23122, 2605.24585, 2605.25214, 2605.25607, 2605.26551, 2605.27929, 2605.28693, 2605.28710, 2605.28740, 2605.28773, 2605.30295, 2605.30315, 2605.30882, 2605.31473, 2606.01311, 2606.02544, 2606.02559