Breaking Free from MMI: A New Frontier in Rationalization by Probing Input Utilization

Extracting a small subset of crucial rationales from the full input is a key problem in explainability research. The most widely used fundamental criterion for rationale extraction is the maximum mutual information (MMI) criterion. In this paper, we first demonstrate that MMI suffers from diminishing marginal returns. Once part of the rationale has been identified, finding the remaining portions contributes only marginally to increasing the mutual information, making it difficult to use MMI to locate the rest. In contrast to MMI that aims to reproduce the prediction, we seek to identify the parts of the input that the network can actually utilize. This is achieved by comparing how different rationale candidates match the capability space of the weight matrix. The weight matrix of a neural network is typically low-rank, meaning that the linear combinations of its column vectors can only cover part of the directions in a high-dimensional space (high-dimension: the dimensions of an input vector). If an input is fully utilized by the network, {it generally matches these directions (e.g., a portion of a hypersphere), resulting in a representation with a high norm. Conversely, if an input primarily falls outside (orthogonal to) these directions}, its representation norm will approach zero, behaving like noise that the network cannot effectively utilize. Building on this, we propose using the norms of rationale candidates as an alternative objective to MMI. Through experiments on four text classification datasets and one graph classification dataset using three network architectures (GRUs, BERT, and GCN), we show that our method outperforms MMI and its improved variants in identifying better rationales. We also compare our method with a representative LLM (llama-3.1-8b-instruct) and find that our simple method gets comparable results to it and can sometimes even outperform it.