# Adversarial robustness: the order-(k-1) evasion boundary

Composition-based DNA classifiers, including this one and other homology-free engineered-sequence
detectors, reduce to a k-mer frequency statistic. A detector that reads k-mer counts is an
order-(k-1) sufficient statistic, which has a direct security consequence: an adversary who
reproduces the order-(k-1) composition of the target class produces sequence the detector cannot
separate from genuine, because the two have the same expected k-mer spectrum.

## Test

Fit an order-m Markov model to real human coding sequence, generate synthetic sequence from it,
and measure whether a k-mer detector separates real human from the order-m synthetic. Sweeping
both the detector word length k and the adversary order m gives the boundary:

| detector | m=0 | m=1 | m=2 | m=3 | m=4 | m=5 | m=6 | m=7 |
|---|---|---|---|---|---|---|---|---|
| k=4 | 1.00 | 0.97 | 0.87 | 0.51 | 0.50 | 0.50 | 0.50 | 0.50 |
| k=6 | 1.00 | 0.98 | 0.92 | 0.79 | 0.66 | 0.52 | 0.58 | 0.52 |
| **k=8 (this model)** | 1.00 | 0.97 | 0.93 | 0.88 | 0.82 | 0.80 | 0.72 | 0.55 |

(AUROC, real human vs order-m-matched synthetic.)

## Result

Each detector reaches chance when the adversary matches its order: k=4 breaks at m=3, k=6 at m=5,
and k=8 at m=7. This model uses 8-mers, so evading it by composition matching requires reproducing
the order-7 statistics of the target class, which fixes every 8-mer frequency. Lower-order forgeries,
including anything that matches only hexamer or shorter composition, are caught. Longer words push
the bar higher at the cost of more parameters and data.

## The neural model is not evaded

Scoring the same order-m-matched synthetic human with Carbon-8B (zero-shot per-base likelihood)
separates it from real human at every order, including the order where this model reaches chance:

| adversary order m | this model (k=8) | Carbon-8B |
|---|---|---|
| 5 | 0.80 | 1.00 |
| 6 | 0.72 | 1.00 |
| 7 | 0.55 | 1.00 |
| 8 | 0.54 | 1.00 |

At order 7 the k=8 detector is at chance while Carbon-8B holds at 1.00, because the model reads
long-range structure (codon-pair grammar, gene organization, motif context) that no fixed-order
composition encodes. Where composition runs out at high adversary order, the model still separates.

## Implication for biosecurity screening

Homology-free, composition-based screening has an inherent evasion boundary. It catches naive
recoding and composition that drifts from the target, but by construction it cannot flag a
construct matched to the order-(k-1) statistics of a natural class. Raising k raises the bar the
adversary must clear; this model's 8-mers force an order-7 match. Detecting an order-(k-1)-matched
adversary requires signal that is not in global composition at all: per-position, context-dependent
modeling of the kind a neural sequence model provides. This boundary is a property of the method,
and it applies equally to other composition-based detectors.