lin-0105

8.1 Why a deep specialization is needed

Chapter 3 described candidate models \(D:J\to \mathcal C\). Chapter 4 lifted their factorization problems through \(T\). A practical neural system adds three pieces of structure:

  1. arrows carry parameters, often with sharing and gauge symmetries;

  2. diagrams contain serial and parallel wiring at large scale; and

  3. repair is computed through reverse information flow.

Ordinary backpropagation handles the third item brilliantly, but by itself it does not declare which paths, cones, or cocones should agree. Deep LINCS adds the sketch and then asks automatic differentiation to respect it.

Design principle

Architecture specifies the factorization problem; differentiation transports it; optimization proposes a repair. None of these three operations should silently redefine the other two.

This gives Deep LINCS a precise place in the symbolic–neural debate developed in Section 0.13. The sketch is not a symbolic reasoner attached to a network. It declares the typed compositional promises that the network realizes. The resulting obstruction is the semantic interface between the declaration and the learned computation; reverse-mode differentiation then transports repair information through that same neural realization.