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.

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.

A Fourier Space Perspective on Diffusion Models

Diffusion models are state-of-the-art generative models on data modalities such as images, audio, proteins and materials. These modalities share the property of exponentially decaying variance and magnitude in the Fourier domain. Under the standard Denoising Diffusion Probabilistic Models (DDPM) forward process of additive white noise, this property results in high-frequency components being corrupted faster and earlier in terms of their Signal-to-Noise Ratio (SNR) than low-frequency ones. The reverse process then generates low-frequency information before high-frequency details. In this work, we study the inductive bias of the forward process of diffusion models in Fourier space. We theoretically analyse and empirically demonstrate that the faster noising of high-frequency components in DDPM results in violations of the normality assumption in the reverse process. Our experiments show that this leads to degraded generation quality of high-frequency components. We then study an alternate forward process in Fourier space which corrupts all frequencies at the same rate, removing the typical frequency hierarchy during generation, and demonstrate marked performance improvements on datasets where high frequencies are primary, while performing on par with DDPM on standard imaging benchmarks.