Analytica: Soft Propositional Reasoning for Robust and Scalable LLM-Driven Analysis
Authors: Junyan Cheng, Kyle Richardson, Peter Chin
Organizations: Dartmouth Collegeα · Allen Institute for AIβ
Abstract
Large language model (LLM) agents are increasingly tasked with complex real-world analysis (e.g., in financial forecasting, scientific discovery), yet their reasoning suffers from stochastic instability and lacks a verifiable, compositional structure. To address this, we introduce Analytica, a novel agent architecture built on the principle of Soft Propositional Reasoning (SPR). SPR reframes complex analysis as a structured process of estimating the soft truth values of different outcome propositions, allowing us to formally model and minimize the estimation error in terms of its bias and variance. Analytica operationalizes this through a parallel, divide-and-conquer framework that systematically reduces both sources of error. To reduce bias, problems are first decomposed into a tree of subpropositions, and tool-equipped LLM grounder agents are employed, including a novel Jupyter Notebook agent for data-driven analysis, that help to validate and score facts. To reduce variance, Analytica recursively synthesizes these grounded leaves using robust linear models that average out stochastic noise with superior efficiency, scalability, and enable interactive "what-if" scenario analysis. Our theoretical and empirical results on economic, financial, and political forecasting tasks show that Analytica improves 15.84% accuracy on average over diverse base models, achieving 71.06% accuracy with the lowest variance of 6.02% when working with a Deep Research grounder. Our Jupyter Notebook grounder shows strong cost-effectiveness that achieves a close 70.11% accuracy with 90.35% less cost and 52.85% less time. Analytica also exhibits highly noise-resilient and stable performance growth as the analysis depth increases, with a near-linear time complexity, as well as good adaptivity to open-weight LLMs and scientific domains.
This project introduces the CRISTAL Method (Coherent Reliable Intentional Synthesis of Truthful Analysis Logic), a neurosymbolic framework for automating complex analysis workflows, with fundamental investment analysis as a primary use case. This domain poses major challenges: high structural uncertainty, noisy and subjective data, tight attention budgets, and the need for justified, reproducible decisions. Human analysts often struggle in this domain due to cognitive biases and limitations, suggesting significant value in automation. But while LLM-based agents have been proposed as analytical aids, their limitations -- poor numerical reasoning, unawareness of uncertainty, and lack of reproducibility -- hinder their effectiveness in this context. CRISTAL addresses these gaps through a principled blend of statistical model synthesis, continuous learning, and active learning. Starting from a natural-language prior knowledge curriculum, CRISTAL builds a dynamic, interpretable probabilistic program that enables full Bayesian inference, including uncertainty quantification and budget-aware data acquisition. CRISTAL continually refines its world model during analysis, leveraging LLMs for code synthesis and learning. We validate CRISTAL on a novel benchmark of synthetic equities with rich financial and textual data. On a company classification task, CRISTAL achieves Bayes-optimal accuracy with just 5 examples and a 5-second budget, outperforming state-of-the-art LLMs that plateau around 40% accuracy even with order-of-magnitude more input data and compute.
Rafael Kaufmann, Felix Neubürger, Michael Walters +2
Enhancing the reasoning capabilities of large language model (LLM) agents requires effective orchestration of diverse expert models and tools. However, existing frameworks typically call APIs, based on coarse-grained matching between tasks and the functions of expert models or tools, while overlooking critical factors such as performance variability and cost efficiency among functionally similar alternatives. To address this, we propose Agora, a framework that uses a confidence-calibrated auction to dynamically allocate tasks to expert models and tools. By treating reasoning steps as tradeable items, Agora bases allocation on calibrated competence rather than raw confidence. Across five main benchmarks, Agora improves or remains competitive with single-model, routing, and cascade baselines under matched candidate pools.
Large language models can consult information that fixed static analyzers cannot, such as documentation, current security advisories, version-specific metadata, and informal API contracts. This makes LLMs a compelling option for program analyses that depend on information beyond the source program, or that are otherwise not amenable to conventional static analyzers. However, directly asking an LLM for a one-shot whole-program analysis is brittle because it compresses many evidence-dependent judgments into a single opaque answer, rather than exposing which conclusions are supported or disputed and using intermediate findings to guide later, more focused searches. In this paper, we propose agentic interpretation, a framework that brings the discipline of lattice-based static analysis to LLM-driven program reasoning. At a high level, agentic interpretation decomposes a high-level analysis goal into localized claims, and tracks the LLM's judgment about each claim in a finite-height lattice. A worklist algorithm governs how claims and their judgments evolve during the analysis. We introduce a formal model of agentic interpretation, explore the design space it opens, and illustrate the approach with a worked example analyzing code that depends on opaque third-party components.