When and why representations learned by different deep neural networks are similar is an active research topic. We choose to address these questions from the perspective of identifiability theory, which suggests that a measure of representational similarity should be invariant to transformations that leave the model distribution unchanged. Focusing on a model family which includes several popular pre-training approaches, e.g., autoregressive language models, we explore when models which generate distributions that are close have similar representations. We prove that a small Kullback-Leibler divergence between the model distributions does not guarantee that the corresponding representations are similar. This has the important corollary that models with near-maximum data likelihood can still learn dissimilar representations--a phenomenon mirrored in our experiments with models trained on CIFAR-10. We then define a distributional distance for which closeness implies representational similarity, and in synthetic experiments, we find that wider networks learn distributions which are closer with respect to our distance and have more similar representations. Our results thus clarify the link between closeness in distribution and representational similarity.

The reliability of large language models remains a critical challenge, particularly due to their susceptibility to hallucinations and factual inaccuracies during text generation. Existing solutions either underutilize models' self-correction with preemptive strategies or use costly post-hoc verification. To further explore the potential of real-time self-verification and correction, we present Dynamic Self-Verify Decoding (DSVD), a novel decoding framework that enhances generation reliability through real-time hallucination detection and efficient error correction. DSVD integrates two key components: (1) parallel self-verification architecture for continuous quality assessment, (2) dynamic rollback mechanism for targeted error recovery. Extensive experiments across five benchmarks demonstrate DSVD's effectiveness, achieving significant improvement in truthfulness (Quesetion-Answering) and factual accuracy (FActScore). Results show the DSVD can be further incorporated with existing faithful decoding methods to achieve stronger performance. Our work establishes that real-time self-verification during generation offers a viable path toward more trustworthy language models without sacrificing practical deployability.