A nonlinear neural cognitive architecture via geometric regulation, hybrid dimensional control, projected interface coupling, and structural memory - R04

CNIT Theory — Version 4 (R04) Coupled Neural and Interactive Topology: a geometric and hybrid-control framework for nonlinear cognitive architectures This deposit presents Version 4 (R04) of CNIT (Coupled Neural and Interactive Topology), a geometric framework for nonlinear cognitive architectures in which the neuron is established as the primitive object of the theory. Each neuron occupies a position in a cluster of variable local dimension, carries a multi-component state including a discrete affectation history and a three-valued operational mode (inactive, active, wandering), and produces a vector output whose dimension tracks its cluster under Master Field supervision. ADVANCES R04 vs R03 Version 3 established the full geometric and supervisory machinery but left the individual neuron as an undifferentiated element and provided no mechanism for structural adaptation during learning. Version 4 closes this gap through seven new architectural mechanisms. 1. Wandering state and "scout protocol": A neuron in wandering mode is not committed to a fixed output but probes a sub-manifold of its specialisation ball, drawing samples uniformly from it. It is exempt from the cognitive energy realignment that governs all active neurons. A wandering neuron becomes a pilot only after satisfying a confirmation criterion on a fixed number of consecutive steps, preventing commitment to the first favourable probe. A new qualitative convergence observable tracks the distributed wandering population across all clusters and is accessible to the Master Field. 2. Conditional neurogenesis with bounded hierarchy: On pilot confirmation, a daughter neuron is generated, geometrically specialised inside the pilot's specialisation ball. The daughter may produce one granddaughter, hyper-specialised inside the daughter's ball. The hierarchy is bounded at depth two. A sterile daughter — whose weight norm remains below the pruning threshold for a fixed number of cycles — is suppressed and its centre is recorded in a dead zone, preventing re-exploration of sterile regions. 3. Gaussian front with "neuronal escort" protocol: When a pilot neuron validates a hit, it generates a Gaussian front of probe neurons around the hit, together with four escort neurons placed symmetrically along the specialisation axis. A confidence index measures collective escort confirmation as the fraction of escorts whose own probe succeeds. Daughter generation is conditional on this index exceeding a minimum threshold, preventing commitment to isolated lucky probes. All probe and escort neurons carry exactly zero weight in the backward chain until a finding is confirmed. 4. Polynomial weighting of the backward chain: The weight update decomposes into independent additive terms with adaptive exponents driven by the sign of the cognitive energy derivative. Coefficients may be negative (pejorative feedback). This replaces the single-term gradient of Version 3. 5. Reduced backward weight for wandering neurons: Wandering neurons in Support mode contribute to the backward chain with a reduced coefficient, consolidating output amplitude without disrupting the established solution. 6. Vigilant accompaniment: After full classification, the network enters a post-convergence phase in which wandering neurons in Support mode reinforce output amplitude with decreasing intensity. A keep-best mechanism saves a complete weight snapshot at each new MSE minimum, preventing end-of-training degradation. 7. Stuck-pattern recovery: Patterns saturating in the wrong direction for more than a fixed number of cycles trigger a targeted sign perturbation of the output weights, with increasing amplitude on repeated detection, to escape basin trapping without full reinitialization. THEORETICAL RESULTS: All seven theorems of Version 3 are retained. Four new formal results are established: structural capacity conservation under neurogenesis (the set of realisable functions can only grow at each neurogenesis event) ; finite-time extinction of sterile daughters with dead-zone update blocking re-exploration; boundedness of the confidence index in the interval from 0 to 1, with the value 0 implying that the hit lies on a local maximum of the error surface (saddle detection) ; and convergence of the backpropagation rule to a stationary point of the loss on each fixed-architecture sub-interval, via the Robbins-Monro stochastic approximation framework. COMPUTATIONAL VALIDATION: The six exploratory tests of Version R04 are retained. Version 4 adds direct benchmark validation on XOR, 3-bit parity, and 4-bit parity. A critical correction is documented: early versions propagated a local pseudo-target to hidden neurons, collapsing internal representations and preventing solution of non-linearly separable problems. Replacing this with standard backpropagation produced an immediate improvement — 4-bit parity is now fully solved (16 out of 16 patterns) in 50 000 cycles with near-zero MSE, a factor-20 speed gain over the pseudo-target version. COMPARATIVE PERFORMANCES: Experimental Setup Dataset: Spiral1000 – two interleaved spirals (500 points per class), 2D input, binary classification. Hyper-parameter grid (fast sweep): hidden ∈ 8, 16 learning rate ∈ 0. 010, 0. 030 settle steps = 1 (MLPs) or 5, 15 (CNIT) Seeds: 2 (deterministic RNG). Training: 800 steps, MSE loss, sigmoid output. Metrics: mean ± std of validation/test MSE and accuracy. Model hidden lr settle meanᵥalₐcc meanₜestₐcc meanₜimeₘs meanᵥalₘse meanₜestₘse CNIT 8 0. 010 15 0. 5600 0. 5525 40. 0 0. 24613 0. 24494 MLP1 16 0. 030 1 0. 5675 0. 5150 5. 0 0. 24605 0. 24837 MLP2 8 0. 030 1 0. 5825 0. 5375 0. 0 0. 24922 0. 24971 The CNIT neural network exhibits strong performance despite being in early development CNIT demonstrates the strongest generalisation on this geometrically structured task, outperforming both MLP baselines on the test set despite using fewer parameters than MLP2 (hidden=16). The iterative recurrent dynamics of CNIT appear to provide a useful inductive bias for spiral-like manifolds. MLP2 achieves the highest validation accuracy but shows a modest drop on the held-out test set. CNIT requires more compute time due to the settle loop, resulting in an ≈8× slowdown compared with MLP1 On the spiral1000 benchmark, CNIT delivers the best test-set generalisation among the three tested architectures. The results highlight a clear trade-off between computational cost and inductive bias, with CNIT offering superior performance on this task at the expense of longer inference time. All data and code will be provided for full reproducibility once main development achieved S. G Avril 2026