Learning (Consolidation)
Learning is the τ-categorical PPAS algorithm (VI.D50) operating intra-organismally on the synaptic weight space of the neural τ³-computer (VI.D52). Hebbian rules, STDP, and reward-modulated plasticity are all implementations of the same verification-guided approximation: the prover proposes weight perturbations; verification is fitness-relative-to-task; consolidation is the transfer of accepted approximations from labile (hippocampal) to stable (cortical) substrate.
τ-Definition
Learning is the τ-categorical PPAS algorithm (VI.D50) operating intra-organismally on the synaptic weight space of the neural τ³-computer (VI.D52). Hebbian rules, STDP, and reward-modulated plasticity are all implementations of the same verification-guided approximation: the prover proposes weight perturbations; verification is fitness-relative-to-task; consolidation is the transfer of accepted approximations from labile (hippocampal) to stable (cortical) substrate.
Categorical invariant. PPAS functor (VI.D50) restricted to the synaptic weight configuration space W ⊂ ℝ^E of the τ³-computer's weighted edge set E, with two complementary timescale-stratified verification stages: synaptic consolidation (minutes–hours, late-LTP, protein synthesis) and systems consolidation (days–years, hippocampus-to-neocortex transfer via sleep replay).
Primary registry anchor:
VI.D52
τ-Derivation Chain
-
I.K0— Universe Postulate -
VI.D15— Life Sector -
VI.D50— PPAS Algorithm on Fitness Landscapes — generic verification-guided search -
VI.D52— Neural Architecture as τ³ Computer — provides the synaptic weight space -
VI.P19— Sleep as Temporal Lemniscate Second Lobe — provides the consolidation phase -
VI.D90— Sleep Repair Function — REM/NREM as substrate for replay-driven systems consolidation -
VI.T53— Sleep Consolidates Levels 1–2 — formal anchor for the consolidation morphism
Empirical Correlate
Biomarker: Synaptic consolidation: late-phase LTP requiring protein synthesis (CREB phosphorylation, BDNF expression, structural spine remodeling) within hours of induction. Systems consolidation: hippocampal sharp-wave ripples (140–200 Hz) coupled to cortical slow oscillations (~0.8 Hz) and thalamic spindles (12–14 Hz) during NREM, replaying waking activity in compressed (~20×) temporal sequences. Reward-modulated plasticity: phasic dopamine bursts encoding reward prediction error from VTA/SNc.
Measurable range: Synaptic weight dynamic range: edges modulated over ~2 orders of magnitude. STDP window: ±20–40 ms with sign reversal at coincidence. Sharp-wave ripple rate: ~0.5–1 Hz during NREM. One-shot hippocampal encoding: episodic memory in a single exposure; cortical consolidation timescale: weeks to years (longer for richer/contextual memories).
Observation method: In vivo: multi-electrode recording (sharp-wave ripples, replay), calcium imaging of cell assemblies, fMRI repetition suppression, MEG of memory reactivation. In vitro: hippocampal slice LTP/LTD induction with pharmacological dissection (NMDA, AMPA, CaMKII, PKA blockers). Behavioral: paired-associate learning, motor sequence acquisition, declarative recall after consolidation interval (with vs. without sleep — Walker et al. body of work).
Calibration anchor: LG-Y02-kinetic-pseudoscalar-channel
Anchor chain:
- VI.L18 chirality channel
- L-glutamate / D-serine NMDA-receptor co-agonism (the core stereospecific Hebbian gate)
- L-handed receptor and channel proteins implementing every plasticity-rule binding site
Manuscript reference: manuscript-sources/book-06/part06/ch41-learning-sleep.tex
Lean Coverage
Status: Planned