AI DEVELOPMENT / DEDICATED BUILD
Neuro-symbolic AI
Combine learned representations with explicit rules, constraints, or reasoning so perception and structured knowledge can complement each other.
What it is
Combine learned representations with explicit rules, constraints, or reasoning so perception and structured knowledge can complement each other.
This page separates the concept, implementation path, interactive experiment, evaluation criteria, failure modes, and sources so the topic can be studied without relying on a summary tile.
Core concepts
- Neural components handle high-dimensional noisy inputs.
- Symbolic components encode explicit rules or constraints.
- A bridge converts learned outputs into symbols, soft constraints, or differentiable logic.
- Constraints can be applied after inference, during training, or inside a joint architecture.
- Evaluation must isolate failures from the neural, symbolic, and interface layers.
Architecture / workflow
- Define the perception problem and symbolic constraints separately.
- Train or obtain a neural representation.
- Map neural outputs to symbolic facts or soft truth values.
- Apply rules/constraints and produce a final decision with traceable provenance.
- Test disagreement cases where neural confidence and symbolic rules conflict.
Technical foundations
- A simple pipeline can threshold neural probabilities into symbolic predicates.
- Differentiable logic replaces hard truth values with continuous relaxations so constraints can influence gradients.
- Constraint loss can be added to ordinary task loss.
- Post-hoc symbolic validation can reject outputs without retraining the neural model.
Evaluation checklist
- Neural-only vs symbolic-only vs combined baselines.
- Constraint-satisfaction rate.
- Accuracy on cases designed to violate known rules.
- Traceability of the final decision.
- Sensitivity to threshold choices and noisy predicates.
Failure modes and limits
- The combined system can inherit both neural and rule-base errors.
- Hard thresholds may discard useful uncertainty.
- Rules can conflict with each other or with changing domain knowledge.
- A symbolic trace can create false confidence if upstream perception was wrong.
Practical build path
- Train or mock a probabilistic classifier.
- Apply a simple validated rule layer.
- Add cases where the classifier is confident but violates a rule.
- Compare post-hoc constraints with constraint-guided training.
Primary / authoritative references
AUTHORED STUDY COMPANION / 3.4
Keep learned scores inside explicit constraints
Prerequisites. Binary choices, objective functions and feasibility.
A predicted score and a feasible decision are different objects. Three candidate choices have scores 0.8,0.6,0.7. At most two may be selected, and choices 0 and 2 cannot coexist. Thresholding all scores at 0.5 selects all three and violates both constraints.
The companion enumerates all eight assignments, removes infeasible ones and maximizes the score sum over the remainder. It chooses (1,1,0) with objective 1.4. This small exact solver demonstrates the interface between uncertain learned preferences and explicit symbolic constraints. The scores are fixtures, not a trained or calibrated model.
Feasibility is only as meaningful as the encoded constraints. A perfectly solved incomplete model can still produce an unacceptable real-world decision. For a larger problem, choose a suitable SAT/SMT, integer-programming or constraint solver and validate its translation. Record unsatisfiable inputs distinctly from an implementation failure or a low-quality feasible optimum.
| Element | Model | Interpretation |
|---|---|---|
| Scores | 0.8, 0.6, 0.7 | Preference objective |
| Constraints | Capacity ≤2; not both 0 and 2 | Feasible set |
| Solver | Enumerate eight assignments | Exact optimum of this model |
Predict, run, compare
At capacity two, the best feasible selection is choices 0 and 1. At capacity zero the all-zero assignment remains feasible, with objective zero.
Download executable notebooks and source Inspect source ↗
Open constraint.ipynb in the package. Run cells in order, compare with the reference, then change the stated input. Restart the kernel to reset.
Computed reference result — local CPU fixture
{
"selected": [
1,
1,
0
],
"objective": 1.4,
"feasible_count": 6,
"unconstrained_pick": [
1,
1,
1
],
"scope": "enumerated three-variable exact constraint solver; scores are fixed fixtures, not calibrated probabilities"
}This is the recorded result of the included code under the package environment. It is not a live service or device measurement.
Extend the experiment
Add a requirement to choose at least one item, then set capacity to zero. Return an explicit infeasible status and test that it cannot be mistaken for a successful empty plan.
Check your reasoning: A high learned score authorizes violating a hard constraint:
- Always — The objective does not override feasibility.
- Only when confidence exceeds 90% — A score is not an authorization mechanism.
- No, unless the actual constraint policy is explicitly changed — Correct. Constraints define the permitted decisions in this model.
This is an explained self-check, not a certification of mastery.
Claim-specific sources
Reviewed 2026-10-02: this worked example and its explicit assumptions. Source links and notebook results do not establish production or hardware validation.