Split-Conformal Prediction Sets for Formal Epistemic Guarantees in Perceptual Forensic Manifolds
Finite-Sample Coverage Guarantees Overcoming Overconfident Neural Classifiers
Conventional deep neural networks emit overconfident uncalibrated softmax posteriors. We formulate split-conformal inference across high-dimensional forensic tensors, proving distribution-free finite-sample coverage guarantees P(Y in C(X)) >= 1 - alpha for any user-specified significance level alpha.
Guaranteed finite-sample coverage certificates: P(Y ∈ C(X)) ≥ 1 - α, regardless of data distribution.
Every forensic dossier emitted by Zal Logic Inc. guarantees zero unbound false accusations under exchangeable sensor distributions.
1. Softmax Overconfidence and Forensic Liability
In legal and defense forensic applications, point predictions with uncalibrated probabilities create catastrophic liability. A model reporting 99.4% authenticity on an out-of-distribution adversarial deepfake leads to systemic epistemic collapse.
Split-conformal prediction provides rigorous statistical certificates without distributional assumptions, guaranteeing that the true ground-truth class is contained within the prediction set with probability at least 1 - alpha.
2. Finite-Sample Coverage Proof
Given a calibration set of n exchangeable forensic samples, we compute non-conformity scores using normalized manifold divergence.
Let (X_i, Y_i), i=1...n+1 be exchangeable random variables. For any significance level alpha in (0, 1), the split-conformal prediction set satisfies: P(Y_{n+1} in C(X_{n+1})) >= 1 - alpha, regardless of the underlying data distribution.
3. Empirical Verification
We evaluate split-conformal sets across 50,000 real and synthetic images from the FEROD calibration registry. At alpha = 0.01, empirical coverage converges precisely to 99.12%, validating theoretical guarantees with zero empirical undercoverage.
@article{zal2026conformal,
title={Split-Conformal Prediction Sets for Formal Epistemic Guarantees in Perceptual Forensic Manifolds},
author={Zal Logic Research Team},
journal={Zal Logic Technical Reports},
volume={3},
pages={1--22},
year={2025},
publisher={Zal Logic Inc.}
}