More Bang for the Buck: Improving the Inference of Large Language Models at a Fixed Budget using Reset and Discard (ReD)

After a weak verifier accepts a large-language-model response, a second call may resample or reroute. Because correctness is hidden, action selection is an identification problem. We order three gates: recoverable stopping debt, two-sided FIT action support, and held-out value from an outcome-blind selector. In a pinned 152-query MBPP+ experiment, a Qwen2.5-14B Base-only false-positive stop leaves +2.592 percentage points of Qwen2.5-7B recovery (query-cluster 95% interval [+1.618, +3.664]). Separately, after 7B Base-test rejection, fixed escalation to 14B exceeds leave-one-out 7B resampling by +2.882 points [+0.931, +5.201]; this is fixed-action ranking, not conditional selection. An all-episode audit produces a +2.697-point realized-maximum gap, but for two actions this statistic equals (1/2)E|Delta| - (1/2)|E Delta| and contains no observable-history term. It lies inside an exact-fold exchangeable reference (mean +3.158; 95% interval [+2.434, +3.947]). The audit unconditionally acts on 1,520 episodes: 1,240 observable stops and 280 verifier rejections; 198 stops are evaluator-only false positives. Neither tested outcome-blind controller improves on fixed rerouting. A separate LiveCodeBench ladder has all-zero FIT action advantages despite exclusive TEST rescues. A preregistered BigCodeBench support gate then finds only 23/19 and 22/19 signed episodes/queries against minima of 25/20, so L1-L4, DEV, and TEST stay unopened. Stopping debt exists, but current evidence does not identify when to resample rather than reroute.

Standard evaluation of large language models assumes stable model rankings across inference conditions. We challenge this assumption by varying the token generation budget, i.e., the maximum tokens a model may produce, across seven levels (64--4,096), evaluating four models on three reasoning benchmarks (56,476 inferences). We report four findings: (i) 3--19% of items exhibit non-monotone behavior (accuracy decreasing with more budget), even after controlling for truncation, and this phenomenon is model-specific (cross-model overlap: 6--14%). (ii) Model rankings reverse across budgets on all benchmarks ($p {<} 0.01$, McNemar). (iii) Oracle analysis reveals model complementarity up to $+27.8$pp, most pronounced at constrained budgets. (iv) A budget-aware router captures 14.1% of the oracle gap cross-domain; budget features help within-domain ($+1.6$ to $+5.7$pp) but are domain-specific and hurt transfer ($-1.2$pp). These results argue for budget-conditioned evaluation protocols.

Large language models (LLMs) provide strong reasoning capabilities but are expensive to serve at scale, whereas small language models (SLMs) are cheaper but less reliable on difficult problems. We introduce PyroDash, a cost-aware framework for token-level SLM-LLM collaborative inference. During generation, the SLM decides whether to request assistance by emitting a control token. A Collaborate Engine then sends the query and partial reasoning trace to a frozen LLM for completion through a single handoff. The policy is internalized in the SLM, requiring neither a separate router, LLM retraining, nor access to LLM logits. PyroDash trains the SLM in three stages: control-token embedding learning, offloading-oriented supervised fine-tuning, and cost-aware alignment with Group Relative Policy Optimization. Its reward balances answer accuracy against inference cost normalized by LLM-only inference. Across five mathematical reasoning benchmarks, PyroDash supports different accuracy-cost operating points. With $λ=0.05$, it achieves 64.04 percent average accuracy, 6.36 percentage points above the LLM-only baseline, while reducing cost by 20.4 percent. With $λ=0.6$, it achieves 54.55 percent accuracy with a 1.90 percent LLM token ratio and 0.012 LLM calls per example, reducing total cost from USD 49.36 to USD 1.78. These results show that learned token-level handoffs can reduce LLM use while preserving strong reasoning performance.