Mechanistic Interpretability of Structure-Aware Numerical Reasoning in LLaMA 3.1 8B

Recent work has shown that large language models (LLMs) exhibit strong numerical sequence modeling capabilities and show promise in time-series prediction. While LLMs display in-context learning capabilities, the mechanisms with which they accomplish time-series prediction remain unclear. Specifically, whether they truly understand the underlying structure, which at a minimum requires reasoning over first differences in the sequence of numbers. To study this, we investigate Llama 3.1-8B from a mechanistic interpretability point of view. Mechanistic interpretability is an emerging field concerned with the reverse engineering of the algorithms learned by neural networks such as LLMs. To assess Llamas' numerical sequence modeling capabilities and to facilitate our mechanistic interpretability analysis, we create a sequence modeling task that cannot be solved without picking up structural cues. Specifically, we sample n random numbers and repeat them with an offset. We find that Llama displays strong performance on our tasks suggesting that it can pick up on the underlying structure. To understand the mechanisms that allow it to do so, we perform probing experiments and activation patching based counterfactual analysis. Probing reveals that the model computes and stores first differences in its internal representations without explicit supervision, indicating that it tracks structural information about the sequence. Activation patching reveals that Llama retrieves the relevant first-difference with a mechanism similar to an induction circuit and subsequently adds it to the current value. Notably, our work represents one of the first studies to identify this form of concept induction in LLMs.

A Graph Signal Processing Perspective on Numerical Sequence Representations in LLM In-Context Learning

Pretrained large language models (LLMs) have demonstrated in-context learning (ICL) capabilities for numerical inference over sequences serialized as text. Prior work has identified and characterized this form of numerical inference primarily through output-level evaluations such as prediction error. However, how numerical information is organized within LLM representations remains much less understood. To study this internal organization, we adopt a graph signal processing perspective in which attention induces a weighted graph over tokens, while token hidden states define signals on its nodes. Quantitative graph-spectral diagnostics and qualitative token-graph visualizations reveal that representations become more clearly differentiated by input dynamical complexity as context length increases. Simpler inputs produce attention-induced token graphs with stronger global connectivity and smoother, spectrally concentrated hidden-state signals, whereas more complex inputs produce more localized graphs and hidden-state signals with broader spectral support and greater high-frequency energy. Together, these findings point to systematic, context-dependent internal signatures associated with numerical ICL that are conserved across model families.

Credit Cards, Confusion, Computation, and Consequences: What Can We Uncover About Language Model Reasoning?

We introduce CreditCardQA, the first financial literacy benchmark for numerical reasoning derived from real credit card agreements. The dataset contains 1,800 questions, including first-person variants that reflect how consumers naturally ask about fees, interest, and payments. We evaluate a range of large language and reasoning models under Chain-of-Thought (CoT) and Program-of-Thought (PoT) prompting. Overall, PoT yields consistent performance gains, particularly for models with weaker baseline reasoning, and narrows gaps between open- and closed-source systems. Through error analysis, we show that failures arise less from arithmetic and more from misapplied financial rules, missed conditions, and misunderstandings of contractual terms. We further analyze question difficulty and find that comparisons, conditional logic, and monetary constraints are especially challenging. We also find that errors often arise in edge cases such as late-payment penalties or small-balance scenarios that are more likely to affect lower-income or financially vulnerable individuals.

DS@GT ARC at CheckThat! 2026: LLM-Based Trace Ranking and Grouped Reward Modeling for Multilingual Numerical Claim Verification

Automated verification of numerical claims is a challenging problem, as it requires both language understanding and quantitative reasoning. This paper describes our system for CLEF 2026 CheckThat! Task 2, which focuses on ranking reasoning traces generated by large language models (LLMs) and predicting a final verdict for numerical claims in English and Arabic. We explore two approaches. The first approach fine-tunes an LLM-based verifier using LoRA to score each reasoning trace independently as a binary classification problem, and selects the final verdict using Best-of-N selection. We further experiment with adaptive sub-claim decomposition to break complex claims into simpler parts before verification. The second approach uses a lightweight TF-IDF reward model with handcrafted numeric and temporal overlap features to score traces, and aggregates scores by verdict group to determine the final prediction. For Arabic, we compare a general multilingual model against AraBERT, a language-specific model pretrained on Arabic text. Our results show that the LLM-based approach outperforms the lightweight reward model on most metrics, particularly Recall@5, while the reward-based approach shows stronger performance on the Conflicting class. Sub-claim decomposition did not improve performance, suggesting that claim splitting introduces noise rather than aiding reasoning. For Arabic, AraBERT outperforms the multilingual baseline across most metrics.

Localizing Anchoring Pathways in Language Models

Irrelevant numbers in a prompt can shift language model judgments, producing anchoring effects in numerical reasoning. We study where this anchor-sensitive signal is carried inside language models using a controlled multiple-choice setup with shared answer options. We define a logit-difference metric comparing the correct answer option with the answer option corresponding to the anchor, and validate that it tracks behavioral anchoring. Using attribution-based circuit localization on 7B--8B Qwen and Llama base and instruction-tuned models, we find that edge-level methods recover this signal more faithfully than node-level methods. Low- and high-anchor circuits transfer strongly within a model, suggesting shared pathway structure across anchor direction. However, sparse transfer across base and instruction-tuned variants is less reliable, indicating that post-training changes which pathways matter most. Overall, our results provide a mechanistic account of how anchoring-related decision signals are carried inside language models.