A Minimal Memory-Field AI Simulator with Self-Archiving Stability — Interactive Archive Edition
A Minimal Memory-Field AI Simulator with Self-Archiving Stability
A minimal computational prototype inspired by Inward Physics that models AI memory as a dynamic scalar field. It demonstrates a predictable failure mode (runaway amplification), then applies a simple saturation mechanism that stabilizes the system and enables basic self-archiving behavior. [oai_citation:1‡A_Minimal_Memory_Field_AI_Simulator_with_Self_Archiving_Stability.pdf](sediment://file_0000000069bc71fdb9e034d3662cc8ff)
This is a reaction–diffusion-style memory model for long-running AI systems: diffusion smooths memory, relaxation pulls toward baseline, and an attention source term amplifies local structure. Stability is achieved via saturation, preventing unbounded growth.
AI stability, long-running AI, memory field dynamics, scalar field modeling, reaction–diffusion systems, attention-driven amplification, saturation nonlinearity, numerical instability control, exploding gradient analogs, coherence metrics, self-archiving systems, checkpoint alternatives, drift mitigation, dynamical systems simulation, computational modeling.
These terms are intentionally technical to attract researchers, builders, and systems engineers.
Memory is represented as a scalar field μ(x,t) ∈ ℝ⁺ evolving on a one-dimensional domain under diffusion, relaxation toward baseline μ₀, and an attention-driven source term S(x,t). [oai_citation:2‡A_Minimal_Memory_Field_AI_Simulator_with_Self_Archiving_Stability.pdf](sediment://file_0000000069bc71fdb9e034d3662cc8ff)
∂μ/∂t = D∇²μ − λ(μ − μ₀) + S(x,t)
The observed failure mode is unbounded amplification: μ grows without bound and the simulation overflows. The stabilization mechanism introduces saturation: [oai_citation:3‡A_Minimal_Memory_Field_AI_Simulator_with_Self_Archiving_Stability.pdf](sediment://file_0000000069bc71fdb9e034d3662cc8ff)
S(x,t) → S(x,t) · (1 − μ/μ_max)
This is a lightweight in-browser visual that mirrors the report’s core idea: attention amplifies local memory, diffusion smooths, relaxation returns to baseline, and saturation prevents runaway growth. Toggle saturation to see the difference.
Status: IDLE · Variance: 0.000 · Archives: 0
Archive log:
The report includes a compact reference implementation using explicit stepping, a discrete Laplacian, saturation, and clipping to maintain non-negativity and bounded evolution. [oai_citation:5‡A_Minimal_Memory_Field_AI_Simulator_with_Self_Archiving_Stability.pdf](sediment://file_0000000069bc71fdb9e034d3662cc8ff)
import numpy as np
import matplotlib.pyplot as plt
# Parameters
D = 0.05
lam = 0.15
mu0 = 0.10
mu_max = 2.0
# Grid
N = 400
x = np.linspace(-10, 10, N)
dx = x[1] - x[0]
# Initial condition
mu = mu0 + 1.2 * np.exp(-x**2 / (2 * 0.9**2))
def laplacian(u):
return (np.roll(u,1) - 2*u + np.roll(u,-1)) / dx**2
dt = 0.45 * dx * dx / (2 * D)
for t in range(400):
A = 0.25 * np.exp(-x**2 / (2 * 0.8**2))
S = A * (1 - mu / mu_max)
dmu = D * laplacian(mu) - lam * (mu - mu0) + S
mu += dt * dmu
mu = np.clip(mu, 0, mu_max)
plt.plot(x, mu)
plt.title("Memory Field μ(x) at Final Time")
plt.xlabel("x")
plt.ylabel("μ(x)")
plt.show()
Does this claim AI consciousness?
Why do you use saturation?
What is “self-archiving” here?
How is this related to AI drift?
μ(x,t): memory density field (scalar).
D: diffusion coefficient (spreads memory).
λ: relaxation strength (returns to baseline μ₀).
S(x,t): attention-driven amplification (source term).
μmax: saturation cap limiting runaway growth.
Coherence threshold: variance level triggering archiving.
No part of this work may be reproduced, distributed, or transmitted without prior written permission, except for brief quotations used in scholarly review or citation. [oai_citation:10‡A_Minimal_Memory_Field_AI_Simulator_with_Self_Archiving_Stability.pdf](sediment://file_0000000069bc71fdb9e034d3662cc8ff)
Scope: Exploratory prototype. Minimal model. No learning parameters. No claims of consciousness. [oai_citation:11‡A_Minimal_Memory_Field_AI_Simulator_with_Self_Archiving_Stability.pdf](sediment://file_0000000069bc71fdb9e034d3662cc8ff)
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