The threat extends beyond accidental errors. When AI writes the software, the attack surface shifts: an adversary who can poison training data or compromise the model’s API can inject subtle vulnerabilities into every system that AI touches. These are not hypothetical risks. Supply chain attacks are already among the most damaging in cybersecurity, and AI-generated code creates a new supply chain at a scale that did not previously exist. Traditional code review cannot reliably detect deliberately subtle vulnerabilities, and a determined adversary can study the test suite and plant bugs specifically designed to evade it. A formal specification is the defense: it defines what “correct” means independently of the AI that produced the code. When something breaks, you know exactly which assumption failed, and so does the auditor.
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Another way to approach the linear combination is to look at it geometrically. This is where the idea of barycentric coordinates can help. A barycentric coordinate system describes the location of a point as the weighted sum of the regular coordinates of the vertices forming a simplex. In other words, it describes a linear combination with respect to a set of points, where in -dimensional space.