Neurosymbolic Routing for Reliable Reasoning on Resource-Constrained Edge Devices

Large language models (LLMs) with chain-of-thought reasoning achieve state-of-the-art performance across complex problem-solving tasks, but their verbose reasoning traces and large context requirements make them impractical for edge deployment. These challenges include high token generation costs, large KV-cache footprints, and inefficiencies when distilling reasoning capabilities into smaller models for mobile devices. Existing approaches often rely on distilling reasoning traces from larger models into smaller models, which are verbose and stylistically redundant, undesirable for on-device inference. In this work, we propose a lightweight approach to enable reasoning in small LLMs using LoRA adapters combined with supervised fine-tuning. We further introduce budget forcing via reinforcement learning on these adapters, significantly reducing response length with minimal accuracy loss. To address memory-bound decoding, we exploit parallel test-time scaling, improving accuracy at minor latency increase. Finally, we present a dynamic adapter-switching mechanism that activates reasoning only when needed and a KV-cache sharing strategy during prompt encoding, reducing time-to-first-token for on-device inference. Experiments on Qwen2.5-7B demonstrate that our method achieves efficient, accurate reasoning under strict resource constraints, making LLM reasoning practical for mobile scenarios. Videos demonstrating our solution running on mobile devices are available on our project page.

Inference-time computation has greatly enhanced the performance of large language models (LLMs) on challenging reasoning tasks, but this strategy can incur high inference costs. One solution is to route intermediate chain-of-thought (CoT) states to language models of different sizes; however, existing approaches rely on handcrafted routing strategies that limit performance, or on training large process reward models that may be infeasible in many applications. We formulate stepwise model routing as a constrained decision-making problem, which we solve by training a small control policy using reinforcement learning in conjunction with threshold calibration to tune the performance-efficiency tradeoff. We validate our method on three math benchmarks (GSM8K, MATH500, and OmniMath) on both open and closed models. Our method consistently improves the accuracy-cost tradeoff compared to handcrafted approaches, while achieving a comparable tradeoff to methods that require training large process reward models.

Large Language Models (LLMs) excel at multi-step reasoning, yet increasing the structural complexity of inference does not consistently improve system-level returns. Methods such as Tree of Thoughts (ToT), Graph of Thoughts (GoT), and Adaptive Graph of Thoughts (AGoT) can boost accuracy on some benchmarks, but often introduce substantial overhead in token consumption and latency, and their gains can be unstable across task distributions-sometimes underperforming simpler Chain-of-Thought (CoT) or direct input-output prompting (IO). We attribute this inefficiency to stage-wise and node-wise heterogeneity inside GoT-style reasoning pipelines: high-quality planning and final synthesis are globally coupled and typically benefit from strong models, whereas many intermediate subtasks are localized and can be solved accurately by lighter models with far fewer tokens. Motivated by these observations, we propose RouteGoT, a budget-controllable, node-adaptive routing framework for graph-structured reasoning. RouteGoT performs in-graph routing by prioritizing strong models for planning and synthesis, while dynamically allocating lightweight models and cost-effective strategies to leaf subtasks based on predicted difficulty. It further integrates explicit budget constraints into a global inference scheduler to control graph expansion under a user-specified token budget, enabling predictable performance-cost trade-offs. Experiments across reasoning, retrieval, and multi-hop QA benchmarks show that RouteGoT matching or improving accuracy while substantially reducing token usage; specifically, it achieves an average 8.1 percentage points accuracy improvement and 79.1% output token reduction compared to AGoT. Furthermore, RouteGoT outperforms existing routing baselines by maintaining a superior cost-accuracy trade-off, demonstrating improved robustness under varying budget targets and tasks.