Better Think Thrice: Learning to Reason Causally with Double Counterfactual Consistency

Despite their strong performance on reasoning benchmarks, large language models (LLMs) have proven brittle when presented with counterfactual questions, suggesting weaknesses in their causal reasoning ability. While recent work has demonstrated that labeled counterfactual tasks can be useful benchmarks of LLMs' causal reasoning, producing such data at the scale required to cover the vast potential space of counterfactuals is limited. In this work, we introduce double counterfactual consistency (DCC), a lightweight inference-time method for measuring and guiding the ability of LLMs to reason causally. Without requiring labeled counterfactual data, DCC verifies a model's ability to execute two important elements of causal reasoning: causal intervention and counterfactual prediction. Using DCC, we evaluate the causal reasoning abilities of various leading LLMs across a range of reasoning tasks and interventions. Moreover, we demonstrate the effectiveness of DCC as a training-free test-time rejection sampling criterion and show that it can directly improve performance on reasoning tasks across multiple model families.

Do LLMs Act Like Rational Agents? Measuring Belief Coherence in Probabilistic Decision Making

Large language models (LLMs) are increasingly deployed as agents in high-stakes domains where optimal actions depend on both uncertainty about the world and consideration of utilities of different outcomes, yet their decision logic remains difficult to interpret. We study whether LLMs are rational utility maximizers with coherent beliefs and stable preferences. We consider behaviors of models for diagnosis challenge problems. The results provide insights about the relationship of LLM inferences to ideal Bayesian utility maximization for elicited probabilities and observed actions. Our approach provides falsifiable conditions under which the reported probabilities \emph{cannot} correspond to the true beliefs of any rational agent. We apply this methodology to multiple medical diagnostic domains with evaluations across several LLMs. We discuss implications of the results and directions forward for uses of LLMs in guiding high-stakes decisions.

interwhen: A Generalizable Framework for Verifiable Reasoning with Test-time Monitors

We present a test-time verification framework, interwhen, that ensures that the output of a reasoning model is valid wrt. a given set of verifiers. Verified reasoning is an important goal in high-stakes scenarios such as deploying agents in the physical world or in domains such as law and finance. However, current techniques either rely on the generate-test paradigm that verifies only after the final answer is produced, or verify partial output through a step-extraction paradigm where the task execution is externally broken down into structured steps. The former is inefficient while the latter artificially restricts a model's problem solving strategies. Instead, we propose to verify a model's reasoning trace as-is, taking full advantage of a model's reasoning capabilities while verifying and steering the model's output only when needed. The key idea is meta-prompting, identifying the verifiable properties that any partial solution should satisfy and then prompting the model to follow a custom format in its trace such that partial outputs can be easily parsed and checked. We consider both self-verification and external verification and find that interwhen provides a useful abstraction to provide feedback and steer reasoning models in each case. Using self-verification, interwhen obtains state-of-the-art results on early stopping reasoning models, without any loss in accuracy. Using external verifiers, interwhen obtains 10 p.p. improvement in accuracy over test-time scaling methods, while ensuring 100% soundness and being 4x more efficient. The code for interwhen is available at https://github.com/microsoft/interwhen

Executable Counterfactuals: Improving LLMs' Causal Reasoning Through Code

Counterfactual reasoning, a hallmark of intelligence, consists of three steps: inferring latent variables from observations (abduction), constructing alternatives (interventions), and predicting their outcomes (prediction). This skill is essential for advancing LLMs' causal understanding and expanding their applications in high-stakes domains such as scientific research. However, existing efforts in assessing LLM's counterfactual reasoning capabilities tend to skip the abduction step, effectively reducing to interventional reasoning and leading to overestimation of LLM performance. To address this, we introduce executable counterfactuals, a novel framework that operationalizes causal reasoning through code and math problems. Our framework explicitly requires all three steps of counterfactual reasoning and enables scalable synthetic data creation with varying difficulty, creating a frontier for evaluating and improving LLM's reasoning. Our results reveal substantial drop in accuracy (25-40%) from interventional to counterfactual reasoning for SOTA models like o4-mini and Claude-4-Sonnet. To address this gap, we construct a training set comprising counterfactual code problems having if-else condition and test on out-of-domain code structures (e.g. having while-loop); we also test whether a model trained on code would generalize to counterfactual math word problems. While supervised finetuning on stronger models' reasoning traces improves in-domain performance of Qwen models, it leads to a decrease in accuracy on OOD tasks such as counterfactual math problems. In contrast, reinforcement learning induces the core cognitive behaviors and generalizes to new domains, yielding gains over the base model on both code (improvement of 1.5x-2x) and math problems. Analysis of the reasoning traces reinforces these findings and highlights the promise of RL for improving LLMs' counterfactual reasoning.

Characterizing Deep Research: A Benchmark and Formal Definition

Information tasks such as writing surveys or analytical reports require complex search and reasoning, and have recently been grouped under the umbrella of \textit{deep research} -- a term also adopted by recent models targeting these capabilities. Despite growing interest, the scope of the deep research task remains underdefined and its distinction from other reasoning-intensive problems is poorly understood. In this paper, we propose a formal characterization of the deep research (DR) task and introduce a benchmark to evaluate the performance of DR systems. We argue that the core defining feature of deep research is not the production of lengthy report-style outputs, but rather the high fan-out over concepts required during the search process, i.e., broad and reasoning-intensive exploration. To enable objective evaluation, we define DR using an intermediate output representation that encodes key claims uncovered during search-separating the reasoning challenge from surface-level report generation. Based on this formulation, we propose a diverse, challenging benchmark LiveDRBench with 100 challenging tasks over scientific topics (e.g., datasets, materials discovery, prior art search) and public interest events (e.g., flight incidents, movie awards). Across state-of-the-art DR systems, F1 score ranges between 0.02 and 0.72 for any sub-category. OpenAI's model performs the best with an overall F1 score of 0.55. Analysis of reasoning traces reveals the distribution over the number of referenced sources, branching, and backtracking events executed by current DR systems, motivating future directions for improving their search mechanisms and grounding capabilities. The benchmark is available at https://github.com/microsoft/LiveDRBench.

FrugalRAG: Learning to retrieve and reason for multi-hop QA

We consider the problem of answering complex questions, given access to a large unstructured document corpus. The de facto approach to solving the problem is to leverage language models that (iteratively) retrieve and reason through the retrieved documents, until the model has sufficient information to generate an answer. Attempts at improving this approach focus on retrieval-augmented generation (RAG) metrics such as accuracy and recall and can be categorized into two types: (a) fine-tuning on large question answering (QA) datasets augmented with chain-of-thought traces, and (b) leveraging RL-based fine-tuning techniques that rely on question-document relevance signals. However, efficiency in the number of retrieval searches is an equally important metric, which has received less attention. In this work, we show that: (1) Large-scale fine-tuning is not needed to improve RAG metrics, contrary to popular claims in recent literature. Specifically, a standard ReAct pipeline with improved prompts can outperform state-of-the-art methods on benchmarks such as HotPotQA. (2) Supervised and RL-based fine-tuning can help RAG from the perspective of frugality, i.e., the latency due to number of searches at inference time. For example, we show that we can achieve competitive RAG metrics at nearly half the cost (in terms of number of searches) on popular RAG benchmarks, using the same base model, and at a small training cost (1000 examples).

RE-IMAGINE: Symbolic Benchmark Synthesis for Reasoning Evaluation

Recent Large Language Models (LLMs) have reported high accuracy on reasoning benchmarks. However, it is still unclear whether the observed results arise from true reasoning or from statistical recall of the training set. Inspired by the ladder of causation (Pearl, 2009) and its three levels (associations, interventions and counterfactuals), this paper introduces RE-IMAGINE, a framework to characterize a hierarchy of reasoning ability in LLMs, alongside an automated pipeline to generate problem variations at different levels of the hierarchy. By altering problems in an intermediate symbolic representation, RE-IMAGINE generates arbitrarily many problems that are not solvable using memorization alone. Moreover, the framework is general and can work across reasoning domains, including math, code, and logic. We demonstrate our framework on four widely-used benchmarks to evaluate several families of LLMs, and observe reductions in performance when the models are queried with problem variations. These assessments indicate a degree of reliance on statistical recall for past performance, and open the door to further research targeting skills across the reasoning hierarchy.

Grammars of Formal Uncertainty: When to Trust LLMs in Automated Reasoning Tasks

Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated formal artifacts. Our systematic evaluation of five frontier LLMs reveals Satisfiability Modulo Theories (SMT) based autoformalization's domain-specific impact on accuracy (from +34.8% on logical tasks to -44.5% on factual ones), with known UQ techniques like the entropy of token probabilities failing to identify these errors. We introduce a probabilistic context-free grammar (PCFG) framework to model LLM outputs, yielding a refined uncertainty taxonomy. We find uncertainty signals are task-dependent (e.g., grammar entropy for logic, AUROC>0.93). Finally, a lightweight fusion of these signals enables selective verification, drastically reducing errors (14-100%) with minimal abstention, transforming LLM-driven formalization into a reliable engineering discipline.

Robust Root Cause Diagnosis using In-Distribution Interventions

Diagnosing the root cause of an anomaly in a complex interconnected system is a pressing problem in today's cloud services and industrial operations. We propose In-Distribution Interventions (IDI), a novel algorithm that predicts root cause as nodes that meet two criteria: 1) **Anomaly:** root cause nodes should take on anomalous values; 2) **Fix:** had the root cause nodes assumed usual values, the target node would not have been anomalous. Prior methods of assessing the fix condition rely on counterfactuals inferred from a Structural Causal Model (SCM) trained on historical data. But since anomalies are rare and fall outside the training distribution, the fitted SCMs yield unreliable counterfactual estimates. IDI overcomes this by relying on interventional estimates obtained by solely probing the fitted SCM at in-distribution inputs. We present a theoretical analysis comparing and bounding the errors in assessing the fix condition using interventional and counterfactual estimates. We then conduct experiments by systematically varying the SCM's complexity to demonstrate the cases where IDI's interventional approach outperforms the counterfactual approach and vice versa. Experiments on both synthetic and PetShop RCD benchmark datasets demonstrate that \our\ consistently identifies true root causes more accurately and robustly than nine existing state-of-the-art RCD baselines. Code is released at https://github.com/nlokeshiisc/IDI_release.

DeduCE: Deductive Consistency as a Framework to Evaluate LLM Reasoning

Despite great performance on Olympiad-level reasoning problems, frontier large language models can still struggle on high school math when presented with novel problems outside standard benchmarks. Going beyond final accuracy, we propose a deductive consistency metric to analyze chain-of-thought output from language models (LMs).Formally, deductive reasoning involves two subtasks: understanding a set of input premises and inferring the conclusions that follow from them. The proposed metric studies LMs' performance on these subtasks, with the goal of explaining LMs' reasoning errors on novel problems: how well do LMs understand input premises with increasing context lengths, and how well can they infer conclusions over multiple reasoning hops? Since existing benchmarks may be memorized, we develop a pipeline to evaluate LMs' deductive consistency on novel, perturbed versions of benchmark problems. On novel grade school math problems (GSM-8k), we find that LMs are fairly robust to increasing number of input premises, but suffer significant accuracy decay as the number of reasoning hops is increased. Interestingly, these errors are masked in the original benchmark as all models achieve near 100% accuracy. As we increase the number of solution steps using a synthetic dataset, prediction over multiple hops still remains the major source of error compared to understanding input premises. Other factors, such as shifts in language style or natural propagation of early errors do not explain the trends. Our analysis provides a new view to characterize LM reasoning -- as computations over a window of input premises and reasoning hops -- that can provide unified evaluation across problem domains.