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name: symbolic-problems description: "Formulate and diagnose NeuroMANCER symbolic variables, objectives, constraints, aggregate losses, Node graphs, and constrained parametric Problems." disable-model-invocation: true metadata: disco-role: operating license: NOASSERTION

Symbolic problems

Use this route when the task is about NeuroMANCER 1.5.6 symbolic programming: Variable expressions, comparison constraints, .minimize() objectives, PenaltyLoss/BarrierLoss/AugmentedLagrangeLoss, dictionary-wired Node components, Problem computation graphs, or differentiable constrained parametric optimization.

Route quickly

1. Prefer module-qualified imports so the code does not depend on incidental top-level re-exports: neuromancer.constraint, neuromancer.loss, neuromancer.system, and neuromancer.problem.
2. Define input/output keys first. Use variable("key") for values supplied by a batch and use a Node to produce decision-variable tensors such as x.
3. Build expressions, call .minimize(...), and write inequalities in the mathematical direction intended by the model. Check the residual sign and tensor shapes before selecting a loss.
4. Give every node, objective, and constraint an explicit unique name. Keep symbolic input keys and output keys unique; set check_overwrite=True while diagnosing a new graph.
5. Construct Problem(nodes, loss, grad_inference=False, check_overwrite=False). Supply a batch dictionary containing every required key and a string name; Problem.forward prefixes every returned key with that name.
6. Run the bundled CPU-only check when a minimal executable confirmation is useful: scripts/core_smoke.py.

Detailed contracts and examples are in:

• references/api-reference.md — factories, operators, exact class signatures, output keys, graph and gradient behavior.
• references/workflows.md — formulation, validation, loss selection, and a small end-to-end CPU recipe.
• references/troubleshooting.md — key, naming, tensor, comparator, graph rendering, and autograd failures.

Boundaries and sibling routes

• Route static/sequence/graph data schemas, splitting, collators, and Trainer or Lightning details to ../data-training/SKILL.md.
• Route ODE/PINN/DAE/SDE models, integrators, and physics residual construction to ../dynamics-modeling/SKILL.md.
• Route rollout loops, preview horizons, PSL simulators, and control signals to ../control-simulation/SKILL.md.
• Route SLiM maps, structured layers, and differentiable operator solvers to ../structured-operators/SKILL.md.

This route can still own the symbolic objective or constraint attached to a model from a sibling route; hand off the model/data/rollout portion rather than repeating it here.

Verification stance

The contracts here are distilled from the package implementation, public constraint/loss/problem/component/gradient documentation, the symbolic tutorials, the parametric-programming formulations, and the variable, constraint, loss, problem, and system tests for the versioned 1.5.6 package. The bundled smoke is deterministic, CPU-only, uses no network or training loop, and checks that a tiny Node-to-Problem loss remains differentiable.