Rectifying Belief Space via Unlearning to Harness LLM s’ Reasoning (2025)

Abstract: Large Language Models (LLMs) exhibit sophisticated reasoning yet still generate incorrect answers. We attribute these errors to **Spurious Beliefs**, defined as propositions the model internally considers as true despite being factually false. To reduce reasoning errors, we propose a belief space rectification framework. Our method first identifies the beliefs invoked during inference via an explanation‐based approach with Forward‐Backward Beam Search (FBBS). We subsequently apply unlearning via gradient ascent to suppress spurious beliefs and enhance true ones, thereby effectively rectifying the model’s belief space. Experiments on three QA datasets and three LLMs show that our method significantly reduces erroneous reasoning and improves generalization.

## introduction large language models (llms) trained on massive corpora have demonstrated remarkable reasoning capabilities, even on complex tasks @xcite @xcite . however, they still generate logically flawed or factually incorrect answers. one fundamental question is: why do they generate erroneous outputs, and how can we mitigate such errors? we hypothesize that many of these mistakes arise from spurious beliefs embedded in the model. "belief" is defined by any proposition the model internally considers true, whereas "knowledge" is required to be factually correct @xcite @xcite . crucially, llms do not merely acquire factual knowlif it references the spurious belief "swallows are fish and ... " during its reasoning, it may generate an incorrect answer. this study aims to suppress such spurious beliefs ( ), thereby allowing the model to draw on the true belief "swallows are birds " and ultimately avoid erroneous reasoning. it is important to emphasize that beliefs are formed regardless of whether they are factually correct. consider a conceptual example in figure 1 : a model might mistakenly combine the true belief "fish have gills " with "swallows fly as if swimming " and, could yield a spurious belief such as "swallows are fish and have gills ." if the model references this spurious belief, it may incorrectly answer "yes" to the question "do swallows have gills?" @xcite . this example illustrates how an llm could form incorrect implicit beliefs that are not stated directly in the training corpus. our ultimate goal is to rectify the belief space into a more trusted space by suppressing spurious beliefs and enhancing true ones (e.g., swallows are birds" ), preventing incorrect inferences. in this paper, we propose a framework to rectify the belief space by identifying the beliefs used for the reasoning, and then suppressing references to the spurious beliefs while enhancing references to the true beliefs. to identify the beliefs referenced by the model, we instruct it to explain the information required to generate the answer y from the given input text x. specifically, we introduce a forward-backward beam search (fbbs) that maximizes both the forward likelihood (i.e., the plausibility of the belief given x) and backward likelihood (i.e., the probability of generating y from x and these beliefs) (section 3.1). subsequently, we apply unlearning based on gradient ascent @xcite to the identified beliefs to suppress references to spurious beliefs while giving priority to the true ones (section 3.3). through these steps, the model's belief space is more accurately reorganized, thereby reducing erroneous reasoning. we demonstrate the effectiveness of our framework on multiple qa tasks (hotpotqa @xcite , sciq @xcite , and openbookqa @xcite ) using three publicly available instruction-tuned llms (olmo @xcite , pythia @xcite , and redpajama @xcite ). compared to both the vanilla model (before our method) and baseline approaches that either suppress the incorrect answers themselves or knowledge in the training data, our method improves accuracy by up to 6.4 points for olmo, 5.2 points for pythia, and 8.0 points for redpajama. moreover, on unseen evaluation data, it achieves gains of up to 9.6 points for olmo, 7.1 points for pythia, and 8.4 points for redpajama, underscoring its strong generalization capability. these results notably surpass the vanilla model's performance, indicating that rectifying the belief space can substantially enhance the model's reasoning. furthermore, suppressing or enhancing beliefs does more than simply target individual beliefs; it effectively reorganizes the entire belief space to reduce errors and improve overall generalizability. ## rectifying the belief space we propose a two-phase procedure to rectify the belief space b. first, we identify which beliefs the model relies on when it generates answers (section 3.1 and 3.2). second, we apply an unlearning step to suppress references to spurious beliefs while enhancing references to true ones (section 3.3). here, we denote the spurious belief set as b @xmath0. ## experiments in this study, we demonstrate that rectifying the belief space can reduce erroneous reasoning while preserving overall model performance. ## conclusion in this study, we proposed a method to rectify the belief space by selectively suppressing references to spurious beliefs that lead to erroneous reasoning and enhancing references to true beliefs in the belief space of an llm. specifically, we identify the beliefs used during inference by prompting the model to explain them, and then we apply unlearning. our results demonstrate that our method effectively suppresses spurious beliefs that induce incorrect answers, raising the accuracy on previously misanswered instances without harming overall model performance. moreover, we observed improved generalization on unseen data, highlighting the benefits of improving the correctness of the belief space itself. these findings show that rectifying the belief space offers a promising approach for both mitigating erroneous reasoning and enhancing the model's generalization performance.