The Right Tool for the Job: Matching Model and Instance Complexities

We assume a series of $n$ trained models $m_{1},\dots,m_{n}$ for a given task, such that for each $1<i\leq n$, $m_{i}$ is both more accurate than $m_{i-1}$ (as measured by a performance on validation data) and more expensive to execute. Current practice in NLP, which favors accuracy rather than efficiency Schwartz et al. (2019), would typically run $m_{n}$ on each test instance, as it would likely lead to the highest test score. However, many of the test instances could be solved by simpler (and faster) models; if we had an oracle that identifies the smallest model that solves a given instance, we could use it to substantially speed up inference. Our goal is to create an automatic measure which approximates the behavior of such an oracle, and identify the cheapest accurate model for each instance.

To demonstrate our approach, we consider the BERT-large model Devlin et al. (2019), based on a transformer architecture Vaswani et al. (2017) with 24 layers. To apply BERT-large to some downstream task, an output layer is typically added to the final layer of the model, and the model is fine-tuned on training data for that task. To make a prediction using the classifier on the final layer, the computation goes through all the layers sequentially, requiring more computation than a shallower model with fewer layers, which would suffice in some cases.

Our approach leverages BERT’s multilayered structure by adding an output layer to intermediate layers of the model. For $k<\ell$, the output layer after $k$ BERT layers exits the model earlier than a deeper output layer $\ell$, and therefore yields a more efficient (but potentially less accurate) prediction.

To make early exit decisions, we calculate the layer-wise BERT representations sequentially. As we reach a classification layer, we use it to make predictions. We interpret the label scores output by softmax as confidence scores. We use these confidence scores to decide whether to exit early or continue to the next (more expensive and more accurate) classifier. See Figure 1 for an illustration.

To train the model, we use the standard way of applying BERT to downstream tasks—fine-tuning the pre-trained weights, while learning the weights of the randomly initialized classifier, where here we learn multiple classifiers instead of one. As our loss function, we sum the losses of all classification layers, such that lower layers are trained to both be useful as feature generators for the higher layers, and as input to their respective classifiers. This also means that every output layer is trained to perform well on all instances. Importantly, we do not perform early exits during training, but only during inference.

To encourage monotonicity in performance of the different classifiers, each classifier at layer $k$ is given as input a weighted sum of all the layers up to and including $k$, such that the weight is learned during fine-tuning Peters et al. (2018).⁷⁷7We also considered feeding the output of previous classifiers as additional features to subsequent classifiers, known as stacking (Wolpert, 1992). Preliminary experiments did not yield any benefits, so we did not further pursue this direction.

Classifiers’ confidence scores are not always reliable Jiang et al. (2018). One way to mitigate this concern is to use calibration, which encourages the confidence level to correspond to the probability that the model is correct DeGroot and Fienberg (1983). In this paper we use temperature calibration, which is a simple technique that has been shown to work well in practice Guo et al. (2017), in particular for BERT fine-tuning Desai and Durrett (2020). The method learns a single parameter, denoted temperature or $T$, and divides each of the logits $\{z_{i}\}$ by $T$ before applying the softmax function:

We select $T$ to maximize the log-likelihood of the development dataset. Note that temperature calibration is monotonic and thus does not influence predictions. It is only used in our model to make early-exit decisions.

Our approach has several attractive properties. First, if $m_{i}$ is not sufficiently confident in its prediction, we reuse the computation and continue towards $m_{i+1}$ without recomputing the BERT layers up to $m_{i}$. Second, while our model is larger in terms of parameters compared to the standard approach due to the additional classification layers, this difference is marginal compared to the total number of trainable parameters: our experiments used 4 linear output layers instead of 1, which results in an increase of 6K (binary classification) to 12K (4-way classification) parameters. For the BERT-large model with 335M trainable parameters, this is less than 0.005% of the parameters. Third, as our experiments show (Section 5), while presenting a much better inference time/accuracy tradeoff, fine-tuning our model is as fast as fine-tuning the standard model with a single output layer. Moreover, our model allows for controlling this tradeoff by setting the confidence threshold at inference time, allowing users to better utilize the model for their inference budget.

For text classification, we experiment with the AG news topic identification dataset Zhang et al. (2015) and two sentiment analysis datasets: IMDB Maas et al. (2011) and the binary Stanford sentiment treebank (SST; Socher et al., 2013).⁸⁸8For SST, we only used full sentences, not phrases. For NLI, we experiment with the SNLI Bowman et al. (2015) and MultiNLI (MNLI; Williams et al., 2018) datasets. We use the standard train-development-test splits for all datasets except for MNLI, for which there is no public test set. As MNLI contains two validation sets (matched and mismatched), we use the matched validation set as our validation set and the mismatched validation set as our test set. See Table 1 for dataset statistics.

We use two types of baselines: running BERT-large in the standard way, with a single output layer on top of the last layer, and three efficient baselines of increasing size (Figure 2). Each is a fine-tuned BERT model with a single output layer after some intermediate layer. Importantly, these baselines offer a speed/accuracy tradeoff, but not within a single model like our approach.

As all baselines have a single output layer, they all have a single loss term, such that BERT layers $1,\dots,k$ only focus on a single classification layer, rather than multiple ones as in our approach. As with our model, the single output layer in each of our baselines is given as input a learned weighted sum of all BERT layers up to the current layer.

As an upper bound to our approach, we consider a variant of our model that uses the exact amount of computation required to solve a given instance. It does so by replacing the confidence-based early-exit decision function with an oracle that returns the fastest classifier that is able to solve that instance, or the fastest classifier for instances that are not correctly solved by any of the classifiers.

We experiment with BERT-large-uncased (24 layers). We add output layers to four layers: 0, 4, 12 and 23.⁹⁹9Preliminary experiments with other configurations, including ones with more layers, led to similar results. We use the first three layer indices for our efficient baselines (the last one corresponds to our standard baseline). See Appendix A for implementation details.

For training, we use the largest batch size that fits in our GPU memory for each dataset, for both our baselines and our model. Our approach relies on discrete early-exit decisions that might differ between instances in a batch. For the sake of simplicity, we use a batch size of 1 during inference. This is useful for production setups where instances arrive one by one. Larger batch sizes can be applied using methods such as budgeted batch classification Huang et al. (2018), which specify a budget for the batch and select a subset of the instances to fit that budget, while performing early exit for the rest of the instances. We defer the technical implementation of this idea to future work.

To measure efficiency, we compute the average runtime of a single instance, across the test set. We repeat each validation and test experiment five times and report the mean and standard deviation.

At prediction time, our method takes as an input a threshold between 0 and 1, which is applied to each confidence score to decide whether to exit early. Lower thresholds result in earlier exits, with 0 implying the most efficient classifier is always used. A threshold of 1 always uses the most expensive and accurate classifier.

Figure 3 presents our test results.¹⁰¹⁰10For increased reproduciblity Dodge et al. (2019a), we also report validation results in Appendix B. The blue line shows our model, where each point corresponds to an increasingly large confidence threshold. The leftmost (rightmost) point is threshold 0 (1), with $x$-value showing the fraction of processing time relative to the standard baseline.

Our first observation is that our efficient baselines constitute a fast alternative to the standard BERT-large model. On AG, a classifier trained on layer 12 of BERT-large is 40% faster and within 0.5% of the standard model. On SNLI and IMDB a similar speedup results in 2% loss in performance.

Most notably, our approach presents a similar or better tradeoff in almost all cases. Our model is within 0.5% of the standard model while being 40% (IMDB) and 80% (AG) faster. For SST, our curve is strictly above two of the efficient baselines, while being below the standard one. In the two NLI datasets, our curve is slightly above the curve for the medium budgets, and below it for lower ones.

Finally, the results of the oracle baseline indicate the further potential of our approach: in all cases, the oracle outperforms the original baseline by 1.8% (AG) to 6.9% (MNLI), while being 4–6 times faster. These results motivate further exploration of better early-exit criteria (see Section 6). They also highlight the diversity of the different classifiers. One might expect that the set of correct predictions by the smaller classifiers will be contained in the corresponding sets of the larger classifiers. The large differences between the original baseline and our oracle indicate that this is not the case, and motivate future research on efficient ensemble methods which reuse much of the computation across different models.

Our results hint that combining the loss terms of each of our classifiers hurts their performance compared to our baselines, which use a single loss term. For the leftmost point in our graphs—always selecting the most efficient classifier—we observe a substantial drop in performance compared to the corresponding most efficient baseline, especially for the NLI datasets. For our rightmost point (always selecting the most accurate classifier), we observe a smaller drop, mostly in SST and MNLI, compared to the corresponding baseline, but also slower runtime, probably due to the overhead of running the earlier classifiers.

These trends further highlight the potential of our method, which is able to outperform the baseline speed-accuracy curves despite the weaker starting point. It also suggests ways to further improve our method by studying more sophisticated methods to combine the loss functions of our classifiers, and encourage them to be as precise as our baselines. We defer this to future work.

Fine-tuning BERT-large with our approach has a similar cost to fine-tuning the standard BERT-large model, with a single output layer. Table 2 shows the fine-tuning time of our model and the standard BERT-large baseline. Our model is not slower to fine-tune in four out of five cases, and is even slightly faster in three of them.¹¹¹¹11We note that computing the calibration temperature requires additional time, which ranges between 3 minutes (SST) to 24 minutes (MNLI).

This property makes our approach appealing compared to other approaches for reducing runtime such as pruning or model distillation (Section 7). These require, in addition to training the full model, also training another model for each point along the speed/accuracy curve, therefore substantially increasing the overall training time required to generate a full speed/accuracy tradeoff. In contrast, our single model allows for full control over this tradeoff by adjusting the confidence threshold, without increasing the training time compared to the standard, most accurate model.

A key property of our approach is that it can be applied to any multi-layer model. Particularly, it can be combined with other methods for making models more efficient, such as model distillation. To demonstrate this, we repeat our IMDB experiments with tinyBERT Jiao et al. (2019), which is a distilled version of BERT-base.¹²¹²12While we experimented with BERT-large and not BERT-base, the point of this experiment is to illustrate the potential of our method to be combined with distillation, and not to directly compare to our main results. We experiment with the tinyBERT v2 6-layer-768dim version.¹³¹³13Jiao et al. (2019) also suggested a task-specific version of tinyBERT which distills the model based on the downstream task. For consistency with our BERT-large experiments, we use the general version.

Figure 4 shows our IMDB results. Much like for BERT-large, our method works well for tinyBERT, providing a better speed/accuracy tradeoff compared to the standard tinyBERT baseline and the efficient tinyBERT baselines.

Second, while tinyBERT is a distilled version of BERT-base, its speed-accuracy tradeoff is remarkably similar to our BERT-large efficient baselines, which hints that our efficient baselines are a simpler alternative to tinyBERT, and as effective for model compression. Finally, our method applied to BERT-large provides the best overall speed-accuracy tradeoff, especially with higher budgets.

We first consider the length of instances: is our model more confident in its decisions on short documents compared to longer ones? To address this we compute Spearman’s $\rho$ correlation between the confidence level of our most efficient classifier and the document’s length.

The results in Table 3 show that the correlations across all datasets are generally low ($|\rho|<0.2$). Moreover, as expected, across four out of five datasets, the (weak) correlation between confidence and length is negative; our model is somewhat more confident in its prediction on shorter documents. The fifth dataset (AG), shows the opposite trend: confidence is positively correlated with length. This discrepancy might be explained by the nature of the tasks we consider. For instance, IMDB and SST are sentiment analysis datasets, where longer texts might include conflicting evidence and thus be harder to classify. In contrast, AG is a news topic detection dataset, where a conflict between topics is uncommon, and longer documents provide more opportunities to find the topic.

Our next criterion for “difficulty” is the consistency of model predictions. Toneva et al. (2019) proposed a notion of “unforgettable” training instances, which once the model has predicted correctly, it never predicts incorrectly for the remainder of training iterations. Such instances can be thought of as “easy” or memorable examples. Similarly, Sakaguchi et al. (2019) defined test instances as “predictable” if multiple simple models predict them correctly. Inspired by these works, we define the criterion of consistency: whether all classifiers in our model agree on the prediction of a given instance, regardless of whether it is correct or not. Table 3 shows Spearman’s $\rho$ correlation between the confidence of the most efficient classifier and this measure of consistency. Our analysis reveals a medium correlation between confidence and consistency across all datasets ($0.37\leq\rho\leq 0.47$), which indicates that the measure of confidence generally agrees with the measure of consistency.

Gururangan et al. (2018) and Poliak et al. (2018) showed that some NLI instances can be solved by only looking at the hypothesis—these were artifacts of the annotation process. They argued that such instances are “easier” for machines, compared to those which required access to the full input, which they considered “harder.” Table 4 shows the correlation between the confidence of each of our classifiers on the SNLI and MNLI dataset with the confidence of a hypothesis-only classifier. Similarly to the consistency results, we see that the confidence of our most efficient classifier is reasonably correlated with the predictions of the hypothesis-only classifier. As expected, as we move to larger, more accurate classifiers, which presumably are able to make successful predictions on harder instances, this correlation decreases.

Both NLI datasets include labels from five different annotators. We treat the inter-annotator consensus (IAC) as another measure of difficulty: the higher the consensus is, the easier the instance. We compute IAC for each example as the fraction of annotators who agreed on the majority label, hence this number ranges from 0.6 to 1.0 for five annotators. Table 4 shows the correlation between the confidence of our classifiers with the IAC measure on SNLI and MNLI. The correlation with our most efficient classifiers is rather weak, only 0.08 and 0.14. Surprisingly, as we move to larger models, the correlation increases, up to 0.32 for the most accurate classifiers. This indicates that the two measures perhaps capture a different notion of difficulty.

Figure 5 shows the proportion of instances in our validation set that are predicted with high confidence by our calibrated model (90% threshold) for each dataset, label, and model size. We first note that across all datasets, and almost all model sizes, different labels are not predicted with the same level of confidence. For instance, for AG, the layer 0 model predicts the tech label with 87.8% average confidence, compared to 96.8% for the sports label. Moreover, in accordance with the overall performance, across almost all datasets and model sizes, the confidence levels increase as the models get bigger in size. Finally, in some cases, as we move towards larger models, the gaps in confidence close (e.g., IMDB and SST), although the relative ordering hardly ever changes.

Two potential explanations come up when observing these results; either some labels are easier to predict than others (and thus the models are more confident when predicting them), or the models are biased towards some classes compared to others. To help differentiate between these two hypotheses, we plot in Figure 6 the average confidence level and the average $F_{1}$ score of the most efficient classifier across labels and datasets.

The plot indicates that both hypotheses are correct to some degree. Some labels, such as sports for AG and positive for IMDB, are both predicted with high confidence, and solved with high accuracy. In contrast, our model is overconfident in its prediction of some labels (business for AG, positive for SST), and underconfident in others (tech for AG, entailment for MNLI). These findings might indicate that while our method is designed to be globally calibrated, it is not necessarily calibrated for each label individually. Such observations relate to existing concerns regarding fairness when using calibrated classifiers Pleiss et al. (2017).