Independent AI Research
PGAN combines proven mathematical theory, hippocampal neuroscience, and phase oscillator dynamics into a single architecture that learns after deployment.
The Problem
GPT, Claude, Gemini, Llama — they all share the same fundamental limitation. Knowledge is distributed across billions of weight parameters with no address, no structure, no way to update a single fact without retraining the entire model.
The industry workaround is RAG: copy-pasting retrieved text into the prompt. It is expensive, it scales poorly, and it forgets everything when you close the session.
Our Approach
The hippocampus does not use matrix multiplications. It uses phase-coupled oscillators — theta rhythms that gate gamma-frequency information in real time. We implement this mechanism directly.
The result is PGAN: an architecture where knowledge lives as explicit phase patterns. One Hebbian update — a single multiplication — writes a new fact. No backpropagation, no GPU, microseconds on a $3 chip.
Architecture
Each component is derived from mathematical theory and validated experimentally. The CNOT gate equation is identical to hippocampal theta-gamma coupling — not an analogy, the same differential equation.
Dense Associative Memory on the unit circle S¹. Patterns stored as explicit phase vectors — addressable, readable, writable in-place.
Dense Associative Memory on the sphere S². Mathematically equivalent to Transformer attention, but derived from capacity theory.
Injection-locking dynamics that couple S1 and S2. Validated against hippocampal theta-gamma recordings from human patients.
What No Other AI Can Do
Every language model today — GPT, Claude, Gemini, Llama — is frozen after training. Close the session and everything is forgotten. PGAN is fundamentally different. It learns new facts on the device, in microseconds, without cloud, without GPU, without retraining.
You talk to the model. It instantly encodes new associations into its phase memory — a dedicated, addressable memory layer inspired by the hippocampus. No training loop, no optimizer, no gradient computation. A single mathematical operation.
While idle, the model consolidates daily memories into permanent weights — exactly like the hippocampus replays experiences during sleep. The temporary memory resets, ready for the next day. Knowledge becomes permanent without cloud computing.
Your personal knowledge lives in one separable layer. Remove it — and the model is clean, shareable, with zero private data. No differential privacy algorithms, no federated learning infrastructure, no "machine unlearning" research needed. The architecture enforces privacy by design.
Publications
Three papers deposited on Zenodo with DOI. Covering capacity theory, spherical attention, and neuroscience validation.
Labs · Live Demo
The same coupled-oscillator physics that powers PGAN's S1 memory generalises to molecular dynamics. DynamicsFold runs two complementary propagators: a zero-shot v3 head (129 K trainable params + frozen ESM-2) that predicts trajectories directly from sequence, and a per-system v2 model (349 K params per domain) trained on a short MD seed. Both evolve the torus manifold without the κ-rescaling heuristic that plagues first-generation methods.
Upload a PDB structure, pick a mode. Zero-shot — ESM-2 reads the sequence and the v3 head generates a trajectory in ~2 minutes, no training. Per-system — a phase-flow ODE trains on a short MD seed, then rolls out thousands of frames 14× faster than classical MD. The trajectory streams to an NGL Viewer canvas so you can watch the protein breathe.
Result · zero-shot generalisation
On five mdCATH domains the model never saw during training, zero-shot v3 beats per-system v2 on 4/5 in NLL and 4/5 in KL. Sequence generalises the phase-flow dynamics — the head does not need to retrain.
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