Logit Distance Bounds Representational Similarity
#representational similarity #identifiability #discriminative models #autoregressive language models #conditional distributions #invertible linear transformation #logit distance bounds #Kullback‑Leibler divergence #arXiv preprint #Nielsen et al. 2025
📌 Key Takeaways
- Identifiability of models with identical conditional distributions implies linear equivalence of representations.
- Questioning whether this relationship extends to cases where distributions are only approximately close.
- Focus on a broad family of discriminative models, including autoregressive language models.
- Reference to Nielsen et al. (2025) on measuring closeness in a statistical distance.
- Exploration of logit distance bounds as a tool for assessing representational similarity.
📖 Full Retelling
🏷️ Themes
Model interpretability, Representational similarity, Statistical distance measures, Identifiability in machine learning, Autoregressive language models
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Deep Analysis
Why It Matters
This study connects the closeness of model outputs to the similarity of their hidden representations, offering a theoretical foundation for transfer learning and model comparison. By showing that approximate equality of conditional distributions implies approximate linear alignment of representations, it clarifies when two seemingly different models may be interchangeable in practice.
Context & Background
- Identifiability of neural networks has been studied for decades, showing that equal output distributions lead to linearly related hidden layers.
- Recent work by Nielsen et al. (2025) introduced logit distance bounds to quantify representation similarity.
- The new paper extends these ideas to discriminative models beyond language models, aiming to establish approximate equivalence.
What Happens Next
Future research will test the derived bounds on large-scale language models, evaluating how representation similarity correlates with fine-tuning performance. The results could guide architecture design and model distillation strategies.
Frequently Asked Questions
It establishes that if two discriminative models produce similar conditional distributions, their internal representations are approximately linearly related.
It provides a metric to determine when two models can be considered equivalent for practical purposes, aiding in model selection and transfer learning.
The results are proven for a broad family of discriminative models, including autoregressive language models, but may not hold for all architectures.
Empirical validation on real-world datasets and exploration of the bounds’ impact on model distillation and compression.