Z-score signal amplification

[alchemystack]

Replace old mode-base token sampling in LLM inference with a z-score aggregate process designed to allow better consciousness influence over token selection. The algorithm converts 20,480 raw INT8 samples from a quantum random number generator (QRNG) into a single uniform float in [0, 1), which is then used for standard CDF-based token sampling against the softmax distribution.

The statistical amplification works by aggregating thousands of individually weak quantum measurements into a single mean value, where even a sub-0.2% per-sample bias from consciousness produces a detectable shift in token selection.

This is now default and changes the color coding to blue = negative z-score = high probability tokens / red = positive z-score = lower probability tokens. (this is WIP)

Algorithm

Input

• logits: raw logit vector from the LLM, shape [vocab_size]
• temperature: sampling temperature (float > 0)
• qrng_samples: 20,480 unsigned 8-bit integers from hardware QRNG
• top_k (optional): if set, restrict to top-k tokens before sampling
• top_p (optional): if set, restrict to nucleus of tokens with cumulative probability ≤ top_p

Step 1 – Prepare the token distribution

1. Apply temperature scaling: scaled_logits = logits / temperature
2. If top_k is set, zero out all logits outside the top-k highest values (set to -∞)
3. Compute softmax probabilities: probs = softmax(scaled_logits)
4. If top_p is set, sort tokens by descending probability, find the smallest set whose cumulative probability exceeds top_p, zero out the rest, and renormalize

Step 2 – Build the probability-ordered CDF

This ordering is essential. It gives the consciousness influence lever a coherent meaning: higher quantum signal → less probable (more surprising) token selection.

1. Create an index array of all tokens with nonzero probability
2. Sort these indices by their probability in descending order (highest probability first)
3. Build the cumulative distribution function over this sorted order:
   • sorted_probs = [probs[idx] for idx in sorted_indices]
   • cdf[0] = sorted_probs[0]
   • cdf[i] = cdf[i-1] + sorted_probs[i] for i > 0
4. The final CDF value should equal 1.0 (renormalize if needed due to floating point)

Step 3 – Convert QRNG samples to uniform float

Constants (derived from the uniform distribution on 0–255):

• Population mean: μ = 127.5
• Standard error of the mean for n=20480 samples: σ_m = 73.6116 / √20480 ≈ 0.51433

Where 73.6116 is the standard deviation of a single discrete uniform variable on [0, 255], computed as √((256² - 1) / 12).

Procedure:

1. Compute the sample mean:

   M = sum(qrng_samples) / 20480
   

2. Compute the z-score:

   z = (M - 127.5) / 0.51433
   

3. Convert to uniform via the standard normal CDF (Φ):

   u = Φ(z) = 0.5 × (1 + erf(z / √2))
   

4. Clamp to avoid degenerate edge values:

   u = clamp(u, 1e-10, 1 - 1e-10)
   

The value u is now a float in (0, 1). Under the null hypothesis (no consciousness influence), u is uniformly distributed. This is guaranteed by the probability integral transform.

Step 4 – Select the token

1. Find the smallest index k in the sorted CDF such that cdf[k] ≥ u
2. The selected token ID is sorted_indices[k]

Interpretation of the consciousness lever

Because the CDF is ordered from most probable to least probable:

• u close to 0 → selects high-probability tokens (conservative, expected completions)
• u close to 1 → selects low-probability tokens (surprising, creative completions)
• Consciousness shifts the mean of INT8 samples upward → higher u → less obvious token
• Consciousness shifts the mean downward → lower u → more conventional token

A shift of the sample mean by just 0.43 (from 127.5 to 127.93) produces u ≈ 0.80, which is enough to skip past the most likely tokens into the tail of the distribution.

Pseudorandom compatibility

For controlled experiments comparing quantum vs. pseudorandom sampling, replace step 3 with:

1. Generate a single FP32 uniform random value u from a PRNG in [0, 1)
2. Proceed to step 4 as normal

The rest of the pipeline is identical. The z-score path and the direct PRNG path both produce a uniform float consumed the same way, making A/B comparison straightforward.

Key constants

Parameter	Value	Derivation
QRNG sample count (n)	20,480	Chosen for QRNG batch efficiency
INT8 range	[0, 255]	Unsigned 8-bit
Population mean (μ)	127.5	(0 + 255) / 2
Population std (σ)	73.6116	√((256² - 1) / 12)
Std error of mean (σ_m)	0.51433	σ / √n
Min detectable bias	~0.2% per sample	Shifts mean by ~0.5σ_m

[alchemystack]

Sorry, wrong repo, meant to merge with my own fork 😅