Autoregressive chain-of-thought (CoT) reasoning in large language models (LLMs) is fundamentally forward-directed: each step conditions only on prior tokens. This unidirectional inductive bias renders even capable models susceptible to error snowballing, wherein a single logical or arithmetic mistake in an early step irreversibly corrupts the entire reasoning chain. We introduce Teleological Reasoning Infilling (\TRI{}), a training framework that endows decoder-only transformers with a native \emph{goal-conditioned bridging} capability. The key insight is to reframe erroneous reasoning segments as fill-in-the-middle (FIM) tasks: given a verified prefix premise P, a verified downstream milestone S, and the original query Q, the model must synthesise the logical bridge M that connects P to S rigorously and completely. To achieve this with standard causal architectures, we introduce a Prefix-Suffix-Middle (PSM) sequence rearrangement with three non-overlapping sentinel tokens, enabling M to attend to both P and S without any structural modification to the self-attention mechanism. Training proceeds in two stages: (i) Supervised Fine-Tuning (SFT) on symbolically verified (P,S,M) triples extracted from formal mathematics corpora, and (ii) Direct Preference Optimisation (DPO) with a deterministic symbolic verifier (Lean 4 / Python) as the sole reward oracle, eliminating LLM-judge sycophancy. At inference, TRI operates as a surgical repair module within a dual-system loop: a causal draft model generates an initial trace, the verifier pinpoints failures, and TRI infills only the damaged segment, leaving verified sections intact. Comprehensive experiments on three benchmarks demonstrate that TRI achieves state-of-the-art performance across all tasks, while reducing per-problem token expenditure by 31.2%.
Large language models (LLMs) have become increasingly used for various tasks, often coupled with Chain-of-Thought (CoT) prompting to boost accuracy. Recent work has shown that high label-prediction accuracy does not guarantee correct intermediate reasoning, and the causes of reasoning flaws vary from sample to sample, yet existing remedies either focus on a single domain or assume that one flaw type applies uniformly across samples. A simple mitigation method is to provide the model with the correct answer, but we show that this yields no consistent improvement in reasoning quality. This indicates that the problem cannot be fixed by LLMs' awareness of answers, and must instead be addressed through the structure of reasoning. Motivated by this, we propose CRAFT (Consensus Reasoning-knowledge-graph Aggregation for Flaw-aware Trace synthesis), which aggregates the consensus components shared across multiple candidate reasoning traces to synthesize improved ones. CRAFT consistently improves label-prediction accuracy on both logical and mathematical reasoning benchmarks, outperforming most baselines, while its post-processed traces achieve higher quality under fine-grained benchmark evaluation.
Chain-of-thought (CoT) reasoning is widely used to improve both the performance and interpretability of large language models (LLMs), yet the generated reasoning may not faithfully support the final answer. We study this problem from a causal perspective, where a faithful CoT process should follow the chain Z→X→Y, with Z, X, and Y denoting the instruction, reasoning chain, and final answer, respectively. In this process, the instruction should affect the answer only through the reasoning chain. However, conventional autoregressive LLMs condition answer generation on both the instruction and the CoT, which still allows a direct instruction-to-answer shortcut. To address this issue, we propose CASE, a framework that combines training-time causal alignment and inference-time structural enforcement. During training, CASE builds counterfactual-CoT, biased-instruction, and empty-instruction datasets, and applies selective-loss fine-tuning to strengthen CoT-to-answer dependence while suppressing instruction shortcuts. During inference, CASE masks direct attention from instruction tokens to answer tokens, preventing the model from bypassing the generated CoT. We provide an information-theoretic analysis showing how these components promote faithful chains. Experiments on three models and four benchmarks show that CASE achieves a 37% average per-setting relative improvement in overall CoT faithfulness over the strongest baselines, exhibits stronger cross-dataset faithfulness transfer, and maintains competitive average accuracy. Code is available at https://github.com/oddwang/CASE.
Chain-of-thought (CoT) prompting enables large language models (LLMs) to tackle multi-step reasoning tasks, yet the generated intermediate steps are not guaranteed to be logically sound. We present Reason Popper-ly, a neurosymbolic framework that uses inductive logic programming (ILP) to learn relation composition rules from reasoning traces and deploys them as an online verifier for step-level correction. Given an LLM-generated trace, the method checks each inferred step against the learned rule table, diagnoses the violation type, rewrites incorrect steps with symbolically derived repairs, and regenerates the remaining suffix so that the model can produce its final answer conditioned on a verified trace. We evaluate on CLUTRR, a multi-hop kinship reasoning benchmark, using five language models over reasoning chains of 2 to 10 hops. Across all models, Reason Popper-ly consistently improves terminal accuracy over standard CoT, with gains of up to 48 percentage points for small models and 15 points for frontier models on the longest chains. Compared with a fully exogenous symbolic pipeline, our method performs better on harder instances by preserving the model's successful grounding while correcting only verifiable reasoning failures. In addition, step-level ILP verification yields a fine-grained error taxonomy that provides diagnostic insight beyond final-answer accuracy.