Book and Solutions Manual

Planned

The companion book and solutions manual are planned learning resources. This page keeps the chapter map visible so readers can see how the long-form material connects to the package, notebooks, derivations, and examples.

The main book develops the mathematics, derivations, hand calculations, and implementation path. The solutions manual keeps solved exercises separate so the book remains readable while still supporting step-by-step study.

Chapter Map

Chapters	Focus	Package connection
0-5	preliminaries, fixed points, contractions, solvers, adjoints, original DEQ	fixed_point, SolverConfig, full_jacobian, vjp, jvp, implicit_adjoint_solve
6-8	MDEQ, Jacobian regularization, message passing and attention	SILVAStack, graph local/global operators, stability diagnostics
9-10	SILVA stimulus/local/global/damping and path sums	SILVALayer, SILVAGraphLayer, SILVAGraphPresetNetwork
11-13	vision channels, molecular ZINC-style equilibria, graph benchmarks	vision classifiers, molecular regressor, graph networks, dataset adapters
14-15	diagnostics, failure modes, and research-grade project structure	solve_with_energy, residual curves, ablation maps, experiment docs
16-24	extension cases: PDEs, homotopy, solver engineering, certificates, diffusion, scientific self-consistency, theory, distributions, algorithmic/quantum reasoning	custom DEQLayer or custom SILVA branches

Shared Derivation Spine

Most chapters return to the same derivation pattern:

\[ z^\star=f_\theta(z^\star,x), \qquad r(z)=f_\theta(z,x)-z, \]

\[ z_{k+1} = (1-\alpha)z_k+\alpha f_\theta(z_k,x), \]

\[ (I-J_f) \frac{dz^\star}{d\theta} = \frac{\partial f_\theta}{\partial\theta}, \qquad (I-J_f^\top)\lambda = \frac{\partial\mathcal L}{\partial z^\star}. \]

The package-native study path is:

• Derivation Workbook
• Solver Derivation Lab
• Implementation Derivations
• Notebooks
• Run Everything

The website pages make the derivation spine package-facing while the long-form book and solved manual are developed.

Where to Go Next

Question	Page
Where can I study the fixed-point mathematics now?	Mathematical Foundations
Which derivations connect equations to implementation?	Derivation Workbook
Which executable learning materials are available?	Notebooks