Latent Geometry and Perceptual Actualization: A Multiplicative Framework for History-Dependent Cognition

Present perception and adaptive action are not determined by immediate sensory inputs alone. While predictive processing and Bayesian frameworks interpret this history- dependence through explicit error minimization, recent neuroscience reveals a deeper, structural motif operating across multiple biological timescales. We synthesize independent lines of evidence—from long-term memory structures such as silent hippocampal engrams shaping consolidation (Choucry et al., 2026) and reversible engram state-switching (O’Leary et al., 2024), to real-time, trial-by-trial dynamics including internal-state-gated prefrontal attractor geometry (Osako et al., 2026), context-dependent communication subspaces (Binish et al., 2026), NMDA-mediated perceptual history biases (Toso et al., 2026), and wave-based analog computation organizing spiking activity within synaptic substrates (Miller et al., 2026). Rather than treating these as disparate phenomena, we propose a unified framework: latent topology. We argue that these mechanisms reflect a scale-invariant principle wherein non-active, latent configurations of prior relational structures exert a *multiplicative*—rather than additive—constraint on present neural dynamics. From the biophysical gating of NMDA receptors to the macro- scale reshaping of attractor manifolds by somatostatin-expressing (SOM) interneurons (Bos et al., 2025), this multiplicative constraint dynamically restricts the agent’s state- space reachability. Consequently, latent topology functions as an embodied substrate that structures the agent’s immediate affordance landscape, transforming Historical Memory Assembly into a geometry of present adaptive action. This concept is distinct from sedimented content, stored traces, weighted priors, and active representational geometry. Its microcircuit-level implementation is supported by evidence on multiplicative gain modulation by distinct interneuron classes (Bos et al., 2025). We outline four classes of testable predictions—including a sub-linear relationship between perceptual reorganization and incremental energetic cost, and predictions that distinguish the latent- topology framework from canonical predictive-processing accounts. The recurring structural motif reviewed here suggests that articulating latent topology as a primary theoretical concept is empirically tractable and theoretically productive. **Keywords:** latent topology; adaptive behavior; affordance landscape; multiplicative constraint; silent engrams; attractor dynamics; embodied cognition; convergent evidence; reversible state switching of engrams between accessible and inaccessible configurations (O’Leary et al., 2024); internal-state-gated reorganization of attractor geometry in prefrontal cortex (Osako et al., 2026); communication subspaces that selectively relay context-dependent information between human prefrontal and motor cortex (Binish et al., 2026); NMDA-mediated across-trial history bias in perceptual decisions (Toso et al., 2026); and wave- based analog computation organizing spiking activity within synaptic substrates (Miller et al., 2026) — a common structural pattern emerges. Non-active, latent configurations of prior relational structure exert influence on the actualization of present perceptual dynamics in a manner consistent with multiplicative — rather than additive — integration with present input.