An Information Bottleneck Framework for Interpretability Through Concise Rationales
Table 2: Average mask length (sparsity) attained by Sparse IB and the Sparse Norm-C baseline for a given prior π for different tasks, averaged over 100 runs.
['Dataset', '[ITALIC] π', 'Sparse Norm-C Mean', 'Sparse Norm-C Var', 'Sparse IB Mean', 'Sparse IB Var']
We measure the sparsity achieved by the explainer during inference by computing the average number of one entries in the input mask m over sentences (the hamming weight) for 100 runs. Our Sparse IB-approach consistently achieves the sparsity level π used in the prior while the norm-minimization approach (Sparse Norm-C) converges to a lower average sparsity for the mask. In summary, our analysis indicates that unlike norm-minimization methods, our KL-divergence objective is able to consistently extract rationales with the specified sparsity rates, and achieves a better trade-off with accuracy. We hypothesize that optimizing the KL-divergence of the posterior p(m|x) may be able to model input salience better than an implicit regularization (through ||m||0). The sparse prior term can learn p(m|x) adaptive to different examples, while ||m|| encourages uniform sparsity across examples. In contrast to Alemi et al. approximately matches the marginal of the prior.