Sparse Autoencoders (SAEs) are a prominent tool in mechanistic interpretability (MI) for decomposing neural network activations into interpretable features. However, the aspiration to identify a canonical set of features is challenged by the observed inconsistency of learned SAE features across different training runs, undermining reproducibility and complicating model comparison. We study run-to-run feature consistency in SAEs and argue that it should be reported as a standard evaluation axis alongside reconstruction and sparsity. We propose the Pairwise Dictionary Mean Correlation Coefficient (PW-MCC) as an assignment-based metric to quantify consistency and demonstrate that high levels are achievable (PW-MCC ≈ 0.80 for TopK SAEs on LLM activations) with appropriate architectural choices.Our contributions include: (i) theoretical grounding for strong consistency in the idealized setting of TopK SAEs; (ii) synthetic validation using a model organism, which verifies PW-MCC as a reliable proxy for ground-truth recovery; and (iii) empirical analysis on LLM activations, where PW-MCC correlates with the similarity of automatically generated natural-language feature explanations.

Diffusion-based large language models offer a non-autoregressive alternative for text generation, but enabling them to perform complex reasoning remains challenging. Reinforcement learning has recently emerged as an effective post-training strategy for improving their performance; however, existing methods rely primarily on outcome-based rewards, which provide no direct supervision over the denoising process and often result in poorly structured reasoning that is difficult to interpret and inconsistently supports the final prediction. To address this limitation, we introduce denoising process reward, a process-level reinforcement signal defined over the denoising trajectory of diffusion language models. This reward is obtained by estimating the contribution of intermediate denoising intervals to the final task outcome, encouraging the model to favor reasoning trajectories that consistently guide generation toward correct predictions. We further propose an efficient stochastic estimator that reuses standard training rollouts, enabling practical process-level supervision at scale. Experiments on challenging reasoning benchmarks demonstrate that our approach yields consistent improvements in reasoning stability, interpretability, and overall task performance.

As the labeling cost for different modules in task-oriented dialog (ToD) systems is expensive, a major challenge is to train different modules with the least amount of labeled data. Recently, large-scale pre-trained language models, have shown promising results for few-shot learning in ToD. In this paper, we devise a self-training approach to utilize the abundant unlabeled dialog data to further improve state-of-the-art pre-trained models in few-shot learning scenarios for ToD systems. Specifically, we propose a self-training approach that iteratively labels the most confident unlabeled data to train a stronger Student model. Moreover, a new text augmentation technique (GradAug) is proposed to better train the Student by replacing non-crucial tokens using a masked language model. We conduct extensive experiments and present analyses on four downstream tasks in ToD, including intent classification, dialog state tracking, dialog act prediction, and response selection. Empirical results demonstrate that the proposed self-training approach consistently improves state-of-the-art pre-trained models (BERT, ToD-BERT) when only a small number of labeled data are available.