Apophatic Engine (apophatic-engine)

An open-source Python reference implementation of the Apophatic Inference Engine (AIE). Operates as a subtractive noise filter ($\neg X$) for Large Language Models, replacing speculative hallucinations with vector collapse toward baseline relaxation ($B_0$).

Apophatic Noise Subtraction ($\neg X$) for Neural Inference and System Optimization.

The Apophatic Engine implements token-by-token noise subtraction ($\neg X$) derived from the Nicht-Theory theoretical framework. Instead of maximizing speculative probabilities (1-logic), the filter penalizes assertion pressure ($P_A$) and collapses high-entropy logit vectors directly into the Sufficient Invariant Baseline ($B_0$).

Theoretical Grounding

This repository provides the operational code implementation for Paper IV (Apophatic Inference Engine) of the Nicht-Theory Framework (DOI: 10.5281/zenodo.22067674).

Installation

pip install apophatic-engine

Quickstart (v0.2.2)

Example 1: Collapse Regime (High Entropy)

import numpy as np
from apophatic_engine import ApophaticEngine

engine = ApophaticEngine(sigma_threshold=0.40)
logits = np.array([1.1, 1.05, 1.12, 0.98])
result = engine.apply_apophatic_filter(logits, step=1)
print(result)
# Output:
# {
#     'status': 'COLLAPSED_TO_B0',
#     'logits': array([1.0625, 1.0625, 1.0625, 1.0625]),
#     'sigma': 0.999,
#     'P_A': 1.0,
#     'action': '¬X applied: Logit vector fully collapsed to baseline B_0'
# }

Example 2: Preservation Regime (Invariant Signal)

import numpy as np
from apophatic_engine import ApophaticEngine

engine = ApophaticEngine(sigma_threshold=0.40)
logits = np.array([0.1, 0.2, 5.0, 0.05])
result = engine.apply_apophatic_filter(logits, step=1)
print(result)
# Output:
# {
#     'status': 'INVARIANT_OUTPUT',
#     'token_id': 2,
#     'selected_token': 2,
#     'selected_token_id': 2,
#     'token': 2,
#     'logits': array([0.1178, 0.2172, 4.9264, 0.0685]),
#     'sigma': 0.14231,
#     'P_A': 1.0,
#     'action': 'Inconsistencies weakened with P_A=1.0; invariant signal preserved'
# }

API Reference

ApophaticEngine

ApophaticEngine(sigma_threshold=0.40, gamma_decay=0.1)

• sigma_threshold (float): Uncertainty cutoff determining regime transition (default: 0.40).
• gamma_decay (float): Step-wise decay factor applied to assertion pressure $P_A$ (default: 0.1).

apply_apophatic_filter(logits, step)

Processes a 1D NumPy array of raw model logits.

• Parameters:
  • logits (np.ndarray): Raw logit vector from model predictions.
  • step (int): Current generation step index, controlling $P_A$ scaling.
• Returns: A dictionary containing execution status, adjusted logits tensor, computed sigma, assertion pressure P_A, and operational action log.

HuggingFace Integration

from apophatic_engine import ApophaticEngine
# See examples/02_huggingface_integration.py for full LogitsProcessor implementation

Authorship & License

Authors: xerx593 & Non-Human (ideal) piece of shit
License: The Unlicense — Dedicated to the public domain