Exploring Practical Gaps in Using Cross Entropy to Implement Maximum Mutual Information Criterion for Rationalization (2025)

Abstract: Rationalization is a framework that aims to build self-explanatory NLP models by extracting a subset of human-intelligible pieces of their inputting texts. It involves a cooperative game where a selector selects the most human-intelligible parts of the input as the rationale, followed by a predictor that makes predictions based on these selected rationales. Existing literature uses the cross-entropy between the model’s predictions and the ground-truth labels to measure the informativeness of the selected rationales, guiding the selector to choose better ones. In this study, we first theoretically analyze the objective of rationalization by decomposing it into two parts: the model-agnostic informativeness of the rationale candidates and the predictor’s degree of fit. We then provide various empirical evidence to support that, under this framework, the selector tends to sample from a limited small region, causing the predictor to overfit these localized areas. This results in a significant mismatch between the cross-entropy objective and the informativeness of the rationale candidates, leading to suboptimal solutions. To address this issue, we propose a simple yet effective method that introduces random vicinal1 perturbations to the selected rationale candidates. This approach broadens the predictor’s assessment to a vicinity around the selected rationale candidate. Compared to recent competitive methods, our method significantly improves rationale quality (by up to 6.6%) across six widely used classification datasets. The term “vicinal” is borrowed from vicinal risk minimization (Chapelle et al., 2000); “vicinal” means neighboring or adjacent.

## introduction with the success of deep learning, there are growing concerns over interpretability @xcite . ideally, the explanation should be both faithful (reflecting the model's actual behavior) and plausible (aligning with human understanding) @xcite . post-hoc explanations, which are trained separately from the prediction process, may not faithfully represent an agent's decision, despite appearing plausible @xcite . in contrast to post-hoc methods, ante-hoc (or self-explaining) techniques typically offer increased transparency @xcite and faithfulness @xcite , as the prediction is made based on the explanation itself. there is a stream of research that has exposed the unreliability of post-hoc explanations and called for self-explanatory methods @xcite @xcite . in this study, our primary focus is on investigating a general model-agnostic self-explaining framework called rationalizing neural predictions (rnp, also known as rationalization) @xcite . rnp utilizes a cooperative game involving a selector and a predictor. this game is designed with a focus on ''data-centric'' (i.e., it is to explain the connection between a text and the model-agnostic task label, rather than explaining the output of a specific model) feature importance: the selector first identifies the most informative part of the input, termed the rationale (in practice, rationale selection is achieved through masking unuseful tokens). subsequently, the rationale is transmitted to the predictor to make predictions, as illustrated in figure 1 . the figure 1 : the standard rationalization framework rnp. the task is binary sentiment classification. x, z, ŷ , y represent the input, the selected rationale candidate, the prediction and the ground truth label; m is a sequence of binary masks. θ s , θ p are the parameters of the selector and the predictor; and h c denotes the cross-entropy. despite its strength, the cooperative game of rationalization is difficult to train if the selector and the predictor are not well coordinated @xcite . in this paper, we begin by analyzing the objective of cooperative rationalization, decomposing the practical assessment of rationale candidates by the selector (i.e., h c (y, ŷ |z)) into two parts: the model-agnostic informativeness of the rationale candidates (i.e., h(y |z)), and the degree to which the predictor fits the conditional distribution p (y |z) (i.e., d kl (p (y |z)||p ( ŷ |z))), as shown in §4.1. initially, due to random initialization, the selector samples all rationale candidate regions evenly, and all rationale candidates are fairly fitted by the predictor, resulting in similar d kl . therefore, the selector tends to choose candidates with relatively lower h(y |z). we then empirically observe that once the selector identifies some good (but not necessarily optimal) rationale candidates that have relatively low h(y |z), it dramatically increases the probability of selecting these candidates and decreases the probability of selecting others, sampling within a very small area (in fact, even a single point, as shown in empirical observation 1 of §4.2). this results in the predictor's perspective being limited to a small local area, only capable of reasonably fitting a narrow range of rationale candidates. consequently, the optimal rationale, despite having the lowest h(y |z), may be overlooked due to a high to mitigate this issue, ensuring that the predictor equally fits any rationale candidates might be a viable solution. however, we also find the negative result that completely random sampling across all possible areas, to allow the predictor to fit all rationale candidates equally, renders the predictor ineffective due to an excessively low signal-to-noise ratio (see §4.3). as a result, we try to develop a compromise solution. given the continuity of textual semantics (''continuity'' does not refer to the adjacency of words, but rather to the gradual, smooth change in meaning when a small number of words are altered, rather than a sudden shift), an empirical conjecture is that if the selector identifies suboptimal rationale candidates with relatively low h(y |z), then the optimal rationale is likely within its vicinity. therefore, the predictor only needs to focus on fitting the rationale candidates within this vicinity. inspired by the philosophy of variational autoencoders (vae), we construct the vicinity by introducing random perturbations to the selected rationale candidates and use this new vicinity to train the predictor. the architecture of our method is shown in figure 7 , with figure 8 showing its intuition. through this approach, we significantly improved the rationale quality extracted by the standard rnp on six datasets from two widely used rationalization benchmarks, surpassing some recently published rnp variants. our contributions are summarized as follows: (1) problem identification: we formally analyze the objective of rationalization and identify the practical gap between the rationales' informativeness and the model's assessment of them, which is the primary contribution of this paper. (2) empirical evidence: we provide various empirical evidence to demonstrate how this gap can affect the quality of extracted rationales. (3) simple solution: we introduce a simple yet effective method named vicinal evaluation rationalization (ver) to mitigate this gap. empirical results on several widely used benchmarks demonstrate the effectiveness of the proposed method. additionally, our method is straightforward and does not require any additional auxiliary modules, preserving its potential to be combined with future methods. ## background of rationalization notations. we consider the text classification task. we use f s (•) and f p (•) to represent the selector and the predictor, with θ s , θ p being their parameters, respectively. upper case letters, such as x and y , represent randoms variables. and lower case letters represent variable values. for the sake of notation brevity, we do not distinguish between vectors and scalars. @xmath0:l represents the texts of length l and y represents the classes in a dataset d. generally, the dataset d is considered representing the distribution of p (y |x) such that it can be approximated by a predictor which produces p ( ŷ |x) (usually by minimizing the cross-entropy h c (y, ŷ |x)): then, we introduce the rationalization task. the overall target of the rationalization task is to find the evidence from x that best supports y (not the model predicted ŷ in ante-hoc explanation). based on this target, the intuition is that good rationales can be used to achieve high prediction accuracy. as a result, the practical way to identify rationales is to train a selector and a predictor that cooperatively maximize the prediction accuracy, as specified below. for each (x, y) ∈ d, the selector first outputs a sequence of binary mask @xmath1, • • • , m l ] ∈ {0, 1} l , where l is the sequence length. 2 then, it forms the rationale candidate z by the element-wise product: to simplify the notation, we denote f s (x) by z in the following sections, i.e., f s (x) = z (here f s (x) represents the whole dataset's rationale set, so we use upper case z to represent it). with the selector's sampling, we get a set of (z, y ) samples d z , which is generally considered to be represent the distribution p (y |z) and serve as the training data of the predictor. then, standard rationalization attempts to identify the rationale by minimizing the cross-entropy: compactness and coherence regularizer. to make the selected rationale human-intelligible, rationalization methods usually constrain the rationales by compact and coherent regularization terms. in this paper, we use the most widely used constraints proposed by @xcite : ## conclusion and limitations in this paper, we first theoretically analyze the common approximation of the mutual information maximization criterion, specifically the minimization of cross-entropy, and its shortcomings when applied to the cooperative self-explanatory framework. we provide extensive empirical evidence to verify the existence and negative impact of this issue in practice. subsequently, we propose a very simple method to mitigate this problem, achieving considerable improvements compared to existing methods. a potential limitation of our approach is that we only consider correlation, not causation, so a future direction may be to integrate our work with causal research studies.