[R] P.R.I.M.E C-19: Solving Gradient Explosion on Circular Manifolds (Ring Buffers) using Fractional Kernels

HI!

I’ve been building a recurrent memory architecture that navigates a continuous 1D ring (pointer on a circular manifold), and hit a failure mode I think DNC / Pointer Network folks will recognize.

How to imagine what im talking about:

Problem: the “rubber wall” at the wrap seam If the pointer mixes across the boundary (e.g., N−1 → 0), linear interpolation makes the optimizer see a huge jump instead of a tiny step. The result is either frozen pointers (“statue”) or jitter.

Fixes that stabilized it:

1. Shortest‑arc interpolation – Delta = ((target − current + N/2) % N) − N/2 – This makes the ring behave like a true circle for gradients.
2. Fractional Gaussian read/write – We read/write at fractional positions (e.g., 10.4) with circular Gaussian weights. This restores gradients between bins. – Pointer math is forced to FP32 so micro‑gradients don’t vanish in fp16.
3. Read/write alignment Readout now uses the pre‑update pointer (so reads align with writes).

Status:
– Physics engine is stable (no wrap‑seam explosions).
– Still benchmarking learning efficiency vs. GRU/seq‑MNIST and synthetic recall.
– Pre‑alpha: results are early; nothing production‑ready yet.

Activation update:

We also tested our lightweight C‑19 activation. On a small synthetic suite (XOR / Moons / Circles / Spiral / Sine), C‑19 matches ReLU/SiLU on easy tasks and wins on the hard geometry/regression tasks (spiral + sine). Full numbers are in the repo.

License: PolyForm Noncommercial (free for research/non‑commercial).
Repo: https://github.com/Kenessy/PRIME-C-19

If anyone’s solved the “wrap seam teleport glitch” differently, or has ideas for better ring‑safe pointer dynamics, I’d love to hear it. If you want, I can add a short line with the exact spiral/sine numbers to make it more concrete.