What problem does it solve? When designing or explaining a machine learning model, equations and architectures often feel arbitrary — softmax here, sigmoid there, a loss term bolted on. This Skill provides a disciplined method for deriving each component so it is forced by a constraint rather than asserted, and for stress-testing the result afterward. ## Core Features & Use Cases - Derivation moves: Read free variables out of an equation, cancel intractable terms via ratios or symmetries, derive functional forms (exponential, sigmoid, softmax) from constraints, and name the leftover gaps that become the next hard problem. - Architecture construction: Build global objectives from local per-part quantities, solve the single-item case exactly, frame new models as N named modifications to understood ones, and justify every restriction by what it buys computationally. - Interrogation and validation: Trace one concrete input end-to-end, choose the scaling axis where the mechanism must diverge from a baseline, probe internal units, run capacity and interference analysis, perturb input statistics, and extract falsifiable predictions. - Use Case: You are reading a paper on Hopfield networks or designing a new objective and the equations feel arbitrary. Apply this Skill to derive the energy function from local connection happiness, derive the Hebbian rule from the N=1 case, and identify the capacity limit and failure mode before writing any code. ## Quick Start Use the mechanism-derivation skill to derive the loss function and update rule for my model so each piece is forced rather than asserted, then stress-test the design.
