Conditional Constrained Routing and Metric Bridging for SymbolicAI Workflows Under CPU-Only Budgets

Abstract

Modular language-agent systems increasingly combine large language models, tool calls, and symbolic operators, but objective design and evaluation practice remain misaligned: trajectory-quality surrogates, benchmark-native outcomes, and deployment constraints are often optimized in isolation. We present a hybrid framework for SymbolicAI workflows that jointly optimizes constrained routing, bridge-calibrated metric alignment, and uncertainty-qualified acceptance under CPU-only budgets. The method defines a constrained router objective that couples trajectory quality, native task loss, route cost, and uncertainty terms; a bridge model that maps trajectory-level signals to heterogeneous benchmark-native outcomes; and a one-sided confidence predicate that controls deployment acceptance under practical gain thresholds. Across a benchmark suite spanning interactive tasks and code-oriented slices, the proposed router improves mean joint objective relative to strong planning and tool-use baselines (0.739 versus 0.701 for fixed-route SymbolicAI and 0.688 for OR- Toolformer-style routing), and the full bridge model improves both gain and calibration relative to distance-only controls (mean Γ = 0.060; AUROC = 0.742; ECE = 0.118). Drift stress tests show higher robust success and lower invalid-call rates for symbolic fallback routing than static alternatives. Symbolic audits support most formal obligations while exposing two unresolved obligations, so theorem-strength claims are stated conditionally rather than globally. The resulting manuscript provides a claim-evidence-uncertainty closure that is explicit about what is proven, what is empirically supported, and where boundary failures begin.