Adding the output of SymbolicRegression.jl.

New symbolic regression equation/hall_of_fame.csv

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+oid sha256:583c78df9f4ae9e859f59b9b54901b7fcc256495d6941e813e4aa5f78619aaf4
+size 487

New symbolic regression equation/saaq_1_5_delta_q_adaptation_law.md

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+# SAAQ 1.5 Delta-Q Adaptation Law
+
+## Proposed Update Law
+
+The new symbolic-regression result can be expressed in its raw discovered form as:
+
+```latex
+\[
+\mathrm{saaq\_delta\_q\_target}
+\approx
+\left(\sqrt{\mathrm{avg\_pop\_firing\_rate\_hz}}\cdot 0.05727633160985141\right)
+-
+\left(\frac{\mathrm{saaq\_delta\_q\_prev}}{-2.015263764843582}\right)
+\]
+```
+
+A simplified equivalent approximation is:
+
+```latex
+\[
+\mathrm{saaq\_delta\_q\_target}
+\approx
+0.0573\,\sqrt{\mathrm{avg\_pop\_firing\_rate\_hz}}
++
+0.4962\,\mathrm{saaq\_delta\_q\_prev}
+\]
+```
+
+## Variable Breakdown
+
+- **$\mathrm{saaq\_delta\_q\_target}$**: The new target quantization adjustment for the current update step.
+- **$\mathrm{avg\_pop\_firing\_rate\_hz}$**: The average population firing rate, measured in hertz, representing current global spike activity pressure.
+- **$\mathrm{saaq\_delta\_q\_prev}$**: The previous delta-q value carried over from the last update step.
+- **$\sqrt{\mathrm{avg\_pop\_firing\_rate\_hz}}$**: A sublinear activity term that compresses large increases in firing pressure.
+- **$0.05727633160985141$**: The discovered gain on the square-root firing-drive term.
+- **$2.015263764843582$**: The denominator in the carryover term from the raw symbolic-regression expression.
+- **$0.4962$**: The simplified carryover coefficient, indicating that roughly half of the previous delta-q state remains active in the next update.
+
+## Plain-Language Interpretation
+
+### 1. Square-root activity drive
+The first term says that delta-q should increase as population firing increases, but not in a straight linear way. Because the firing term is under a square root, strong activity still matters, but its effect is compressed. That means the system responds to global spike pressure without letting very high firing rates explode the quantization update.
+
+### 2. Half-memory carryover
+The second term says that the new target delta-q does not start from zero at every step. Roughly half of the previous delta-q value is retained. This gives the adaptation law continuity over time instead of forcing the system to constantly re-estimate quantization pressure from scratch.
+
+### 3. Leaky recurrence
+Taken together, the equation behaves like a leaky recurrent controller:
+
+- current firing activity pushes delta-q upward,
+- previous delta-q state persists,
+- but the carryover is less than 1.0, so the process does not simply accumulate forever.
+
+That makes the law stable and interpretable. It acts more like a controlled adaptive process than a noisy feedthrough rule.
+
+## Why It Matters
+
+### Sublinear compression
+The square-root term is important because it creates **sublinear compression**. If spike activity doubles, delta-q does not double with it. This is desirable for hardware-aware SNN quantization because it prevents aggressive overreaction during bursts of collective activity.
+
+### Fatigue compatibility
+This law is naturally compatible with fatigue-style dynamics. Higher activity still raises the quantization target, but it does so in a way that is bounded and softened. That makes it a plausible companion to biologically inspired fatigue or resistance mechanisms instead of fighting them.
+
+### Temporal inertia
+The carryover term provides **temporal inertia**. Delta-q remembers where it was, which helps smooth fast oscillations and prevents quantization from thrashing between states. In practice, this makes the control signal easier to port into a native SNN runtime such as Spikenaut.
+
+## Relationship to SAAQ 1.0
+
+SAAQ 1.0 and SAAQ 1.5 can be framed as a two-layer control structure:
+
+### SAAQ 1.0: voltage bounding
+SAAQ 1.0 establishes the base stabilizer by bounding latent voltage with the L2-normalized voltage law:
+
+```latex
+\[
+V_{\text{norm}} = \frac{V}{\sqrt{\sum V_i^2 + \epsilon}}
+\]
+```
+
+This prevents raw voltage from collapsing the routing process into a single dominant path.
+
+### SAAQ 1.5: quantization adaptation
+SAAQ 1.5 operates one layer above that. Instead of directly bounding voltage, it adapts the quantization target over time based on:
+
+- current global activity pressure,
+- previous quantization state.
+
+So the relationship is:
+
+- **SAAQ 1.0** controls **voltage magnitude**.
+- **SAAQ 1.5** controls **how quantization pressure evolves over time**.
+
+Put more simply, SAAQ 1.0 keeps the system from blowing up, while SAAQ 1.5 tells the system how fast and how far to adapt once it is stabilized.
+
+## Scope and Caveat
+
+This equation should be treated as a **global baseline adaptation law**, not necessarily the final universal law for every routing regime.
+
+That matters because your telemetry already suggests **piecewise routing behavior** across different prompt families and basin structures. So this formula is best understood as:
+
+- a strong global controller,
+- a clean first portable law,
+- and a good candidate for transfer into Spikenaut.
+
+But it may not be the final word. Later work may show that different routing basins need slightly different local adaptation laws.
+
+That does not weaken the discovery. It clarifies the role of SAAQ 1.5:
+
+> a stable, interpretable global delta-q controller that can serve as the baseline adaptation law before basin-conditioned refinements are introduced.
+
+## Portability to Spikenaut
+
+One of the strongest qualities of this equation is that it is small, interpretable, and runtime-friendly. It uses:
+
+- a square root,
+- a scalar gain,
+- and a linear carryover term.
+
+That makes it far easier to port into a native SNN such as Spikenaut than a deeply nested symbolic expression with many fragile operations. Even if later symbolic-regression passes discover more accurate local laws, this version is likely to remain valuable as the first practical adaptation controller for deployment and ablation testing.