Given a task in the form of a basic description and its training examples, prompt optimization is the problem of synthesizing the given information into a text prompt for a large language model. Humans solve this problem by also considering the different facets that define a task (e.g., counter-examples, explanations, analogies) and including them in the prompt. However, it is unclear whether existing algorithmic approaches, based on iteratively editing a given prompt or automatically selecting a few in-context examples, can cover the multiple facets required to solve a complex task. In this work, we view prompt optimization as that of learning multiple facets of a task from a set of training examples. We exploit structure in the prompt optimization problem and break down a prompt into loosely coupled semantic sections. The proposed algorithm, UniPrompt, (1) clusters the input space and uses clustered batches so that each batch likely corresponds to a different facet of the task, and (2) utilizes a feedback mechanism to propose adding, editing or deleting a section, which in turn is aggregated over a batch to capture generalizable facets. Empirical evaluation on multiple datasets and a real-world task shows that prompts generated using UniPrompt obtain higher accuracy than human-tuned prompts and those from state-of-the-art methods. In particular, our algorithm can generate long, complex prompts that existing methods are unable to generate.

Despite demonstrating emergent reasoning abilities, Large Language Models (LLMS) often lose track of complex, multi-step reasoning. Existing studies show that providing guidance via decomposing the original question into multiple subproblems elicits more robustness in LLM reasoning – a decomposer generates the subproblems, and a solver solves each of these subproblems. However, these techniques fail to accommodate coordination between the decomposer and the solver modules (either in a single model or different specialized ones) – the decomposer does not keep track of the ability of the solver to follow the decomposed reasoning. In this paper, we propose LM2 to address these challenges. LM2 modularizes the decomposition, solution, and verification into three different language models. The decomposer module identifies the key concepts necessary to solve the problem and generates step-by-step subquestions according to the reasoning requirement. The solver model generates the solution to the subproblems that are then checked by the verifier module; depending upon the feedback from the verifier, the reasoning context is constructed using the subproblems and the solutions. These models are trained to coordinate using policy learning. Exhaustive experimentation suggests the superiority of LM2 over existing methods on in- and out-domain reasoning problems, outperforming the best baselines by 8.1% on MATH, 7.71% on JEEBench, and 9.7% on MedQA problems (code available at https://github.com/ LCS2-IIITD/Language_Model_Multiplex).

Large Language Models (LLMs) prompted to generate chain-of-thought (CoT) exhibit impressive reasoning capabilities. Recent attempts at prompt decomposition toward solving complex, multi-step reasoning problems depend on the ability of the LLM to simultaneously decompose and solve the problem. A significant disadvantage is that foundational LLMs are typically not available for fine-tuning, making adaptation computationally prohibitive. We believe (and demonstrate) that problem decomposition and solution generation are distinct capabilites, better addressed in separate modules, than by one monolithic LLM. We introduce DaSLaM, which uses a decomposition generator to decompose complex problems into subproblems that require fewer reasoning steps. These subproblems are answered by a solver. We use a relatively small (13B parameters) LM as the decomposition generator, which we train using policy gradient optimization to interact with a solver LM (regarded as black-box) and guide it through subproblems, thereby rendering our method solver-agnostic. Evaluation on multiple different reasoning datasets reveal that with our method, a 175 billion parameter LM (text-davinci-003) can produce competitive or even better performance, compared to its orders-of-magnitude larger successor, GPT-4. Additionally, we show that DaSLaM is not limited by the solver’s capabilities as a function of scale; e.g., solver LMs with diverse sizes give significant performance improvement with our solver-agnostic decomposition technique. Exhaustive ablation studies evince the superiority of our modular finetuning technique over exorbitantly large decomposer LLMs, based on prompting alone.