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TAN DYNAMICS
AI & Continuity Labs
Contact Founder
DeepTech Foundation: Bio-Inspired Neuromorphic AI & Stateful Continuity

Bridging Theoretical Physics,
Neuromorphic Dynamics
& Cognitive Continuity

Pioneering the Temporal Attention Neuron (TAN) to conquer non-Markovian temporal credit assignment, coupled with a verifiable Triadic Cognitive Continuity Architecture that decouples enduring intelligence from transient context limits.

Run Live TAN Simulation Explore Stage 2 Plan
70–82%
Navigation Error Reduction vs LIF
O(1)
State Lookup + Event Replay
RG Flow
Dynamic Plasticity & Abstraction
100%
Immutable Provenance Audit
Interactive Laboratory

Real-Time TAN Dynamical Simulation

Experience how Surprise-Gated Memory Retrieval operates dynamically. Observe the interplay between input signals, temporal attention weights, and non-Markovian membrane integration in real-time.

Simulation Controls
Membrane Decay (\(\lambda\)) 0.85
History Window (\(W\)) 12
Surprise Threshold (\(\tau\)) 0.25
Spike Threshold (\(\theta\)) 0.70
Active Dynamics:
\(S_t = \max(0, x_t - \bar{x}_W - \tau)\)
\(V_t = \lambda V_{t-1} + \tanh(S_t) C_t\)
\(Y_t = \Theta(V_t - \theta)\)
Input \(x_t\) Membrane \(V_t\) Surprise \(S_t\) Spike Output
Spikes: 0
Dynamic Memory Buffer: Active Non-Markovian State Frequency: 60Hz Real-Time
Neuromorphic Innovation

The Temporal Attention Neuron (TAN)

Conventional Leaky Integrate-and-Fire (LIF) and recurrent models struggle with long-horizon credit assignment without massive parameter overhead. The Temporal Attention Neuron fundamentally rethinks single-unit memory through biological surprise gating.

Surprise-Gated Memory Retrieval

A localized sliding window calculates contextual variance. Information is selectively injected into non-Markovian membrane potential only when the event carries true informational surprise.

QKV-Parametrized Temporal Attention

Computes intra-window queries and keys at linear computational complexity, allowing a single neuron to perform contextual retrieval across multi-step horizons.

Provable Noise Habituation

Exhibits biological habituation: steady-state background noise is suppressed automatically, preventing spike runaway while preserving ultra-sensitive responsiveness to genuine state transitions.

TAN Mathematical Specification Formal Definition
1. History Context Buffer
\[ H_t = [x_{t-W+1}, \dots, x_t] \]
2. Surprise Functional
\[ S_t = \max\left(0, x_t - \frac{1}{W}\sum_{k=0}^{W-1} x_{t-k} - \tau\right) \]
3. Non-Markovian Gated Membrane Update
\[ V_t = \lambda V_{t-1} + \tanh(S_t) \cdot C_t \]
Validated across multi-seed statistical benchmarks (Stage 2 Research Plan) against Adaptive LIF, GRU, and S4 models.
System Architecture

The Triadic Cognitive Continuity Engine

Closing an AI session must never mean erasing intelligence. We decouple transient reasoning from perpetual state, providing a verifiable bedrock for autonomous intelligence.

The Brain (WHY)

High-Order Reasoning & Synthesis

Maintains the long-horizon trajectory, intent, philosophical coherence, and strategic decision-making. Governs goal hierarchies and resolves cognitive ambiguities.

The Hands (HOW)

Embodied Deterministic Execution

Interacts directly with environments, code execution engines, operating systems, and native semantic buses. Observes ground truth without hallucination.

Common State (BEING)

Immutable Event & Provenance Layer

PostgreSQL ACID persistence with database-level immutable append-only triggers, optimistic concurrency control (`version`), and Renormalization Group (RG) coarse-graining.

The Constitutional Separation Principle
Observation ≠ Interpretation ≠ Decision
Every memory, goal, and state transition carries an unbroken provenance chain (source ID, device ID, correlation ID, cryptographic timestamp).
Scientific Grounding

Research Publications & Technical Plans

Our systems are engineered on rigorous theoretical foundations, empirical peer validation, and open reproducibility.

Stage 2 Research Plan June 2026

The Temporal Attention Neuron (TAN): Mechanism, Validation, and Dynamics

Comprehensive 8-week multi-seed validation, baseline comparative study against Adaptive LIF, GRU, and S4/Mamba, alongside dynamical phase-space Lyapunov exponent analysis.

Authored by TAN Research Group Request Full Text
Architecture Whitepaper 2026

Cognitive Continuity: Formal State Engineering for Perpetual Agentic Systems

Extending existing conversational AI entities through immutable event logs, optimistic concurrency, and Renormalization Group coarse-graining (\(\text{Experience} \to \text{Memory} \to \text{Principle}\)).

Continuity Phase 1 Spec Request Spec
Leadership

Founding Team

Rooted in theoretical physics, computational neuroscience, and cutting-edge agentic software engineering.

LZ

Li Zexu (Peter Li)

Founder & Principal Investigator
Theoretical Physics & Computational Neuroscience | University of Leeds

Architect of the Temporal Attention Neuron (TAN) framework and the Cognitive Continuity Infrastructure. Dedicated to formulating mathematical foundations that unite physical non-Markovian dynamics with enduring artificial intelligence.

peter@tan-dynamics.com
Get in Touch

Collaborate With TAN Dynamics

Whether you are evaluating our Stage 2 research, seeking enterprise integration of the Cognitive Continuity layer, or inquiring about research partnerships.

Contact Founder: peter@tan-dynamics.com General: contact@tan-dynamics.com