PoTRE (Poly-Topological Reasoning Ensembles), a heterogeneous framework that decouples inference into four agents that achieves improved reasoning performance using similar or fewer inference tokens compared to heavily scaled homogeneous baselines is introduced.
Abstract
While Large Language Models (LLMs) excel at many tasks, they frequently struggle with complex reasoning that requires long-horizon planning and iterative error correction. Furthermore, standard single-stream prompting proves brittle when models encounter novel abstractions or rigorous domain constraints. We introduce PoTRE (Poly-Topological Reasoning Ensembles), a heterogeneous framework that decouples inference into four agents: (1) Adversarial Refinement Agent, (2) Hierarchical strategic Planning Agent, (3) Spectrum Search Agent, and (4) Direct Chain Agent. A final Task-Adaptive Aggregation Layer dynamically reconciles these perspectives -- via final candidate selection, semantic synthesis, or neuro-symbolic verification -- to produce a robust global solution. We evaluate PoTRE on three frontier benchmarks: ARC-AGI-2, Humanity's Last Exam (HLE), and PRBench Finance. PoTRE achieves state-of-the-art accuracy of 49.92% on HLE, surpassing the previous best official score. We demonstrate that this architectural heterogeneity achieves improved reasoning performance using similar or fewer inference tokens compared to heavily scaled homogeneous baselines.
Recent progress on ARC-AGI-1 from disclosed architectures has come broadly from two regimes: heavy test-time compute over frontier models (evolutionary search, exhaustive sampling, extended chain-of-thought), or benchmark-specific training in which small models are fine-tuned on ARC data, often with task-specialized architectures. We study a third regime: an open-weight model in non-thinking mode (DeepSeek V3.2) under a strict budget, with no ARC-specific fine-tuning. We study what is recoverable through architecture alone, building agentic harnesses that decompose pattern-discovery and program-synthesis stages explicitly. First, we introduce an Explorer-Definer Pipeline that separates pattern discovery from executable transformation synthesis, implemented as a two-stage agent pipeline. Next, we present the Reflective Orchestrator, which augments the pipeline with autonomous exploration of new transformations when previous hypotheses fail on training pairs. On the ARC-AGI-1 public 400-task evaluation set, the pipeline reaches 57.50% pass@2 at \$0.25 per task, and the orchestrator reaches 67.25% pass@2 at \$0.62 per task. Together these architectures lift a 15.50% one-shot baseline by ~52 points without benchmark-specific training or heavy test-time compute. Furthermore, the orchestrator-driven lift tests a falsifiable diagnostic the pipeline produces; unbiased pass@k analysis suggests the pipeline is generation-bound, not selection-bound (selection via training-pair accuracy captures ~95% of the candidate ceiling) and predicts that significant improvement requires broader generation, not better ranking. The orchestrator implements this prediction via adaptive re-exploration and confirms it (unbiased pass@1 lift +9.81 pp, matching selection-mediated pass@2 lift). An additional pipeline ablation identifies its think tool as a significant component, with removal reducing pass@2 by 5.75 pp.
Test-time reasoning methods such as iterative refinement, decomposition, and repeated sampling are often evaluated in isolation, making their gains difficult to compare across models, benchmarks, and evaluation pipelines. We introduce a unified view of these methods as recursion operators over an agent's reasoning trace: GROW, which deepens a single reasoning path; PRUNE, which decomposes and recomposes the problem; and BRANCH, which samples alternative reasoning paths and selects among them. We evaluate all three operators against a single-pass chain-of-thought baseline under a shared harness with identical prompts, token budgets, and grading code. Across five benchmarks and three frontier models, comprising 14 model-benchmark settings, 49,327 graded items, and 151,876 model calls, BRANCH improves accuracy in all 14 settings by an average of 5.98 percentage points and is the best-performing operator in 12. In contrast, GROW yields a mean gain of 2.18 points and degrades performance in two settings, while PRUNE improves accuracy by 0.94 points on average. Analysis shows that BRANCH's advantage arises not only from exploring multiple reasoning paths, but also from recovering from truncation: its gains strongly correlate with the baseline rate of empty, budget-exhausted outputs (r = 0.72). These results weaken the hypothesis that different problems require routing among test-time reasoning operators; at this level of abstraction, repeated branching is consistently dominant. Finally, we show that unpaired evaluation and treating scoring-pipeline failures as model errors can materially change, and even reverse, comparative conclusions, motivating paired scoring as a standard protocol for test-time-compute evaluation.
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Recent meta-reasoning frameworks improve LLM reasoning by wrapping chain-of-thought generation in an iterative control loop, allowing more effective backtracking, termination of reasoning loops, and injection of promising reasoning patterns, among other strategy adjustments. Despite promising results, methods often rely on backward-looking reward functions, utilize coarse search actions, or require additional reasoning controller training requiring many-shot supervision. We introduce Cognitive Demand Steering (CDS), a training-free meta-reasoning framework equipped with residual demand assessment: at each step, an LLM-based progress evaluator characterizes the residual reasoning required to arrive at a solution rather than merely evaluating the previous step. This allows a meta-controller to select reasoning interventions comprising both general-purpose exemplars and actions (e.g., general guidance for quantitative reasoning) that directly tackle this forward-looking demand signal. This shift eliminates the need for any trained component while enabling zero-shot transfer across models and tasks with no adaptation. Rather than relying on coarse characterizations, we employ cognitive scales to both design interventions as well as profile initial problem complexity and residual demand signal over 16 dimensions motivated by cognitive science (e.g., attention and scan, learning and abstraction, spatio-physical reasoning), giving the controller a fine-grained vocabulary for diagnosing. Averaged across three frontier LLMs and six reasoning benchmarks, CDS improves accuracy by $21.9\%$ over direct calls and $9\%$ over standard CoT reasoning, with the largest gains on difficult mathematics and coding tasks.
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Reasoning modes of language models outperform their non-reasoning counterparts on multi-step agentic tasks, but pay a 3-6x premium in output tokens on every episode -- much of it spent re-deriving procedures that are shared across episodes of the same domain. We show this recurring cost can be amortized: a coding agent analyses a small corpus of existing trajectories from a training split and compiles a compact natural-language skill that is injected into the non-reasoning model's system prompt. Across four agentic benchmarks (ALFWorld, tau$^2$-bench telecom and retail, and SpreadsheetBench-Verified), skills recover 55%-100%+ of the reasoning gap for GPT-5.4-mini on held-out tasks -- exceeding the reasoning mode outright on two of four -- while emitting 2.7-6x fewer output tokens and zero reasoning tokens. Notably, reasoning traces are not a prerequisite: skills distilled from non-reasoning trajectories alone remain competitive with skills distilled from paired reasoning/non-reasoning corpora, with domain-dependent differences between the two sources. We interpret these results through a search lens: test-time reasoning is deep search inside a single episode, re-paid at every deployment, while corpus distillation is wide search across episodes, paid once. The two recover overlapping procedural knowledge, and width over cheap trajectories is often the better buy -- with the residual gap on some domains (telecom, SpreadsheetBench) delineating where genuinely per-instance deep search remains necessary.
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