How Do Transformers Learn to Associate Tokens: Gradient Leading Terms Bring Mechanistic Interpretability

Semantic associations such as the link between "bird" and "flew" are foundational for language modeling as they enable models to go beyond memorization and instead generalize and generate coherent text. Understanding how these associations are learned and represented in language models is essential for connecting deep learning with linguistic theory and developing a mechanistic foundation for large language models. In this work, we analyze how these associations emerge from natural language data in attention-based language models through the lens of training dynamics. By leveraging a leading-term approximation of the gradients, we develop closed-form expressions for the weights at early stages of training that explain how semantic associations first take shape. Through our analysis, we reveal that each set of weights of the transformer has closed-form expressions as simple compositions of three basis functions (bigram, token-interchangeability, and context mappings), reflecting the statistics of the text corpus and uncovering how each component of the transformer captures semantic associations based on these compositions. Experiments on real-world LLMs demonstrate that our theoretical weight characterizations closely match the learned weights, and qualitative analyses further show how our theorem shines light on interpreting the learned associations in transformers.

Unlocking the Pre-Trained Model as a Dual-Alignment Calibrator for Post-Trained LLMs

Post-training improves large language models (LLMs) but often worsens confidence calibration, leading to systematic overconfidence. Recent unsupervised post-hoc methods for post-trained LMs (PoLMs) mitigate this by aligning PoLM confidence to that of well-calibrated pre-trained counterparts. However, framing calibration as static output-distribution matching overlooks the inference-time dynamics introduced by post-training. In particular, we show that calibration errors arise from two regimes: (i) confidence drift, where final confidence inflates despite largely consistent intermediate decision processes, and (ii) process drift, where intermediate inference pathways diverge. Guided by this diagnosis, we propose Dual-Align, an unsupervised post-hoc framework for dual alignment in confidence calibration. Dual-Align performs confidence alignment to correct confidence drift via final-distribution matching, and introduces process alignment to address process drift by locating the layer where trajectories diverge and realigning the stability of subsequent inference. This dual strategy learns a single temperature parameter that corrects both drift types without sacrificing post-training performance gains. Experiments show consistent improvements over baselines, reducing calibration errors and approaching a supervised oracle.

ModeX: Evaluator-Free Best-of-N Selection for Open-Ended Generation

Selecting a single high-quality output from multiple stochastic generations remains a fundamental challenge for large language models (LLMs), particularly in open-ended tasks where no canonical answer exists. While Best-of-N and self-consistency methods show that aggregating multiple generations can improve performance, existing approaches typically rely on external evaluators, reward models, or exact string-match voting, limiting their applicability and efficiency. We propose Mode Extraction (ModeX), an evaluator-free Best-of-N selection framework that generalizes majority voting to open-ended text generation by identifying the modal output representing the dominant semantic consensus among generated texts. ModeX constructs a similarity graph over candidate generations and recursively applies spectral clustering to select a representative centroid, without requiring additional inference or auxiliary models. We further instantiate this selection principle as ModeX-Lite, an improved version of ModeX with early pruning for efficiency. Across open-ended tasks -- including text summarization, code generation, and mathematical reasoning -- our approaches consistently outperform standard single- and multi-path baselines, providing a computationally efficient solution for robust open-ended text generation. Code is released in https://github.com/deeplearning-wisc/ModeX.

Maximizing Information Gain in Privacy-Aware Active Learning of Email Anomalies

Redacted emails satisfy most privacy requirements but they make it more difficult to detect anomalous emails that may be indicative of data exfiltration. In this paper we develop an enhanced method of Active Learning using an information gain maximizing heuristic, and we evaluate its effectiveness in a real world setting where only redacted versions of email could be labeled by human analysts due to privacy concerns. In the first case study we examined how Active Learning should be carried out. We found that model performance was best when a single highly skilled (in terms of the labelling task) analyst provided the labels. In the second case study we used confidence ratings to estimate the labeling uncertainty of analysts and then prioritized instances for labeling based on the expected information gain (the difference between model uncertainty and analyst uncertainty) that would be provided by labelling each instance. We found that the information maximization gain heuristic improved model performance over existing sampling methods for Active Learning. Based on the results obtained, we recommend that analysts should be screened, and possibly trained, prior to implementation of Active Learning in cybersecurity applications. We also recommend that the information gain maximizing sample method (based on expert confidence) should be used in early stages of Active Learning, providing that well-calibrated confidence can be obtained. We also note that the expertise of analysts should be assessed prior to Active Learning, as we found that analysts with lower labelling skill had poorly calibrated (over-) confidence in their labels.

Implementing Active Learning in Cybersecurity: Detecting Anomalies in Redacted Emails

Research on email anomaly detection has typically relied on specially prepared datasets that may not adequately reflect the type of data that occurs in industry settings. In our research, at a major financial services company, privacy concerns prevented inspection of the bodies of emails and attachment details (although subject headings and attachment filenames were available). This made labeling possible anomalies in the resulting redacted emails more difficult. Another source of difficulty is the high volume of emails combined with the scarcity of resources making machine learning (ML) a necessity, but also creating a need for more efficient human training of ML models. Active learning (AL) has been proposed as a way to make human training of ML models more efficient. However, the implementation of Active Learning methods is a human-centered AI challenge due to potential human analyst uncertainty, and the labeling task can be further complicated in domains such as the cybersecurity domain (or healthcare, aviation, etc.) where mistakes in labeling can have highly adverse consequences. In this paper we present research results concerning the application of Active Learning to anomaly detection in redacted emails, comparing the utility of different methods for implementing active learning in this context. We evaluate different AL strategies and their impact on resulting model performance. We also examine how ratings of confidence that experts have in their labels can inform AL. The results obtained are discussed in terms of their implications for AL methodology and for the role of experts in model-assisted email anomaly screening.