BrainIAc: A Multi-Scale Adaptive Dynamical Systems Framework for Computational Neuroscience (v2.2)

Multiscale Spiking Neural Learning System with Biological Control Substrate Overview This project presents a unified computational framework for learning in spiking neural networks (SNNs) coupled with a hierarchical biological control substrate. The system integrates: event-driven neural dynamics (BrainSystem) local and global synaptic learning rules optimizer-based parameter updates a molecular-to-organismal control layer (CellSystem + Organism) formally specified architectural constraints enforced via CI-gated invariants The framework is designed to study how learning emerges from structured operator interactions across multiple biological and temporal scales, rather than from a single monolithic optimization process. Core Design Principle The system is defined by a strict separation: Neural dynamics generate activity; learning rules observe activity and modify parameters; biological layers modulate the learning and dynamical regimes through bounded control signals. This separation enforces a layered architecture where: execution is causal and kernel-native learning is state-dependent but non-intrusive to execution biological modulation acts as a higher-order constraint system System Architecture The framework is composed of four coupled subsystems: 1. Neural Dynamics Layer (BrainSystem) Defines the fast-timescale evolution of neuronal states: spiking neuron models (LIF, Izhikevich, Hodgkin–Huxley) synaptic integration and propagation deterministic timestep execution no learning logic embedded in kernel This layer defines a contractive dynamical system over neural state space. 2. Learning Operator Layer Defines synaptic parameter evolution via structured operators: Hebbian learning (correlation-driven updates) Oja rule (stabilized Hebbian normalization) STDP (temporal spike-timing dependence) EProp (eligibility trace-based online credit assignment) BPTT (trajectory-based global optimization) All learning rules are implemented through a unified interface: initialization trace update gradient computation parameter update state validation reset and teardown Learning rules differ in locality, temporal scope, and state requirements, but share a common operator contract. 3. Optimizer Layer A decoupled optimization stage converts learning signals into parameter updates: Adam optimizer (primary implementation) first- and second-moment tracking independent of neuron model and learning rule class This layer ensures stable convergence across heterogeneous neuron families. 4. Biological Control Substrate A multiscale modulation system bridges molecular dynamics and neural computation. 4.1 Molecular Layer (Protein System) explicit Protein** representation decay, expression, and repair dynamics frozen structural representation (no external mutation interface) Defines the lowest-level dynamical substrate. 4.2 Cellular Control System (CellSystem) homeostatic regulation of protein abundance bounded attractor dynamics (expression / repair balance) scalar projection interface into higher systems guarantees stable equilibrium under perturbation Outputs: scalar biological signals used for modulation 4.3 Organismal Integration Layer (Organism) Defines the coupling boundary between biology and neural computation: ModulationMap (Protein → Brain parameter mapping) multiplicative-only coupling into BrainSystem parameters strict execution ordering: CellSystem update modulation projection BrainSystem execution This layer enforces directional coupling from biology → neural dynamics, without feedback into molecular state. Multiscale Temporal Structure The system is explicitly organized into separated timescales: Scale Component Fast Neural dynamics (BrainSystem) Medium Synaptic learning rules Slow Cellular homeostasis (CellSystem) Slower Organismal modulation Slowest Adaptive parameter drift (LVL5 k/beta system) This hierarchy ensures stability through separation of dynamical regimes. Learning Rule Classification Learning mechanisms are grouped into two classes: Online Learning (kernel-native) Hebbian Oja STDP EProp Properties: causal local or semi-local compatible with real-time execution Offline Learning (trajectory-based) BPTT Properties: non-local in time requires stored system trajectories executed outside kernel dynamics Formal System Interpretation The full system is a compositional operator stack over state and parameters: Input→BrainSystem→State Trajectory→Learning Operator→Optimizer→Updated Parameters with an additional biological modulation channel: CellSystem→Organism→Brain Parameters This creates a two-channel system: fast neural dynamics channel slow biological modulation channel CI-Gated Correctness System The framework includes a formal verification layer enforcing: single-entry-point learning rule initialization strict separation between structural and semantic validation projection-level contract enforcement rule-state consistency validation deterministic reproducibility constraints CI gates enforce correctness across: EProp equivalence multilayer compositional invariants heterogeneous neuron family behavior BPTT kernel correctness cross-learning-rule dispatch consistency multiscale biological coupling constraints Empirical Scope Validated properties include: stability of eligibility traces across neuron families bounded threshold and refractory dynamics reproducible learning across LIF and Izhikevich models structured failure modes in Hodgkin–Huxley systems scalability of local learning rules separation between numerical stability and learnability limits Scientific Contribution The framework demonstrates: Learning can be formulated as a compositional operator system Biological modulation introduces hierarchical control over neural plasticity Stability arises from timescale separation and contractive dynamics Learning rule limitations are primarily structural, not numerical Multiscale coupling produces emergent regime constraints on learnability Intended Use The archive is intended for: reproducible research in spiking neural systems study of local learning rules under structured dynamics analysis of multiscale biological-neural coupling benchmarking learning rule scalability across neuron models Limitations The framework does not claim: biological fidelity of full neural tissue universality of learning rules across all regimes equivalence between computational and cognitive learning Reproducibility The archive provides a structured specification of the framework, including its learning theory, multiscale biological control architecture, neural dynamics, and CI-gated correctness constraints. It serves as a formal documentation snapshot aligned with the corresponding codebase state. Future Development Roadmap With Phase 1 completed, the core dynamical substrate has been architecturally defined, experimentally characterized, and validated through formal CI gates. Current work is focused on exposing the framework through a stable external interface while preserving the causal and reproducibility guarantees established during Phase 1. Planned developments include: Python Experiment Interface A dedicated Python control layer is planned to provide: Parameter sweeps Batch experiment orchestration Data collection and visualization Reproducible protocol execution Jupyter-based exploratory analysis The interface is being designed under a strict architectural contract: The C kernel remains the sole owner of state evolution. Python acts only as an experiment orchestration layer. All state mutations occur through versioned kernel APIs. Snapshots are exported as immutable records. Reproducibility and deterministic execution remain kernel-level guarantees. BrainIAc Kernel API A formal API specification has been drafted defining: Ontic core (deterministic state evolution) Snapshot system Policy layer External orchestration interface The objective is to expose the framework as a reusable scientific simulation kernel while preserving causal closure and experimental reproducibility. Future Scientific Directions Potential future research directions include: LVL 6 adaptive topology dynamics Non-ergodic memory kernels State-dependent delays Multi-organism interaction systems Higher-order molecular feedback pathways Task-level embodied learning experiments Comparative learning-rule studies (E-Prop, BPTT, Hebbian, Oja, STDP) License CC BY-NC-ND 4.0Attribution required. No derivatives. No commercial use. Contact Théo ValloisGitHub: EmpireStrikesBack/NeuroModelEmail: [e-mail] Final Note This system should be interpreted as: a hierarchical, contract-enforced, multiscale operator framework for studying learning dynamics in spiking neural systems with biologically constrained modulation.