The Weight Gram Matrix Captures Sequential Feature Linearization in Deep Networks

Understanding how deep neural networks learn representations remains a central challenge in machine learning theory. In this work, we propose a feature-centric framework for analyzing neural network training by relating weight updates to feature evolution. We introduce a simple identity, the Feature Learning Equation, which identifies the weight Gram matrix as the key object capturing feature dynamics. This enables us to interpret gradient descent as implicitly inducing a hypothetical evolution of features, whose covariance structure - termed the Virtual Covariance - characterizes how representations evolve during training. Building on this perspective, we introduce Target Linearity, a measure quantifying the linear alignment between features and targets. By analyzing the training and layer-wise dynamics, we show that deep networks learn to sequentially transform representations toward target-linear structure. This linearization perspective provides a unified interpretation of several empirical phenomena, including Neural Collapse and linear interpolation in generative models.

ABC3: Active Bayesian Causal Inference with Cohn Criteria in Randomized Experiments

In causal inference, randomized experiment is a de facto method to overcome various theoretical issues in observational study. However, the experimental design requires expensive costs, so an efficient experimental design is necessary. We propose ABC3, a Bayesian active learning policy for causal inference. We show a policy minimizing an estimation error on conditional average treatment effect is equivalent to minimizing an integrated posterior variance, similar to Cohn criteria \citep{cohn1994active}. We theoretically prove ABC3 also minimizes an imbalance between the treatment and control groups and the type 1 error probability. Imbalance-minimizing characteristic is especially notable as several works have emphasized the importance of achieving balance. Through extensive experiments on real-world data sets, ABC3 achieves the highest efficiency, while empirically showing the theoretical results hold.

Pre-trained Language Models Return Distinguishable Probability Distributions to Unfaithfully Hallucinated Texts

In this work, we show the pre-trained language models return distinguishable generation probability and uncertainty distribution to unfaithfully hallucinated texts, regardless of their size and structure. By examining 24 models on 6 data sets, we find out that 88-98% of cases return statistically significantly distinguishable generation probability and uncertainty distributions. Using this general phenomenon, we showcase a hallucination-reducing training algorithm. Our algorithm outperforms other baselines by achieving higher faithfulness metrics while maintaining sound general text quality measures.