SpanDrop: Simple and Effective Counterfactual Learning for Long Sequences

1 INTRODUCTION . Building effective machine learning systems for long sequences is a challenging and important task , which helps us better understand underlying patterns in naturally occurring sequential data like long texts ( Radford et al. , 2019 ) , protein sequences ( Jumper et al. , 2021 ) , financial time series ( Bao et al. , 2017 ) , etc . Recently , there is growing interest in studying neural network models that can capture long-range correlations in sequential data with high computational , memory , and statistical efficiency , especially widely adopted Transformer models ( Vaswani et al. , 2017 ) . Previous work approach long-sequence learning in Transformers largely by introducing computational approaches to replace the attention mechanism with more efficient counterparts . These approaches include limiting the input range over which the attention mechanism is applied ( Kitaev et al. , 2019 ) to limiting sequence-level attention to only a handful of positions ( Beltagy et al. , 2020 ; Zaheer et al. , 2020 ) . Other researchers make use of techniques akin to the kernel trick to eliminate the need to compute or instantiate the costly attention matrix ( Peng et al. , 2020 ; Katharopoulos et al. , 2020 ; Choromanski et al. , 2020 ) . Essentially , these approaches aim to approximate the original pairwise interaction with lower cost , and are often interested in still capturing the interactions between every pair of input elements ( e.g. , the long sequence benchmark proposed by Tay et al. , 2020 ) . In this paper , we instead investigate learning problems for long sequences where not all input elements contribute equally to the desired output . Natural examples that take this form include sentiment classification for long customer review documents ( where a few salient sentiment words contribute the most ) , question answering from a large document ( where each question typically requires a small number of supporting sentences to answer ) , key phrase detection in audio processing ( where a small number of recorded frames actually determine the prediction ) , as well as detecting a specific object from a complex scene ( where , similarly , a small amount of pixels determine the outcome ) , to name a few . In these problems , it is usually counterproductive to try and make direct use of the entire input if the contributing portion is small or sparse , which results in a problem of underspecification ( i.e. , the data does not sufficiently define the goal for statistical models ) . One approach to address this problem is annotating the segments or neighborhoods that directly contribute to the outcome in the entire input . This could take the form of a subset of sentences that answer a question or describe the relation between entities in a paragraph ( Yang et al. , 2018 ; Yao et al. , 2019 ) , which function as explainable evidence that supplements the answer . When such annotation is not feasible , researchers and practitioners often need to resort to either collecting more input-output pairs or designing problem-specific data augmentation techniques to make up for the data gap . For real-valued data , this often translates to random transformations ( e.g. , shifting or flipping an image ) ; for symbolic data like natural language , techniques like masking or substitution are more commonly used ( e.g. , randomly swapping words with a special mask token or other words ) . While these approaches have proven effective in some tasks , each has limitations that prevents it from being well-suited for the underspecification scenario . For instance , while global feature transformations enhance groupinvariance in learned representations , they do not directly help with better locating the underlying true stimulus . On the other hand , while replacement techniques like masking and substitution help ablate parts of the input , they are susceptible to the position bias of where the true stimulus might occur in the input . Furthermore , while substitution techniques can help create challenging contrastive examples , it is significantly more difficult to design them for complex symbolic sequences ( e.g. , replacing a phrase naturally in a sentence ) . To address these challenges , we propose SPANDROP , a simple and effective technique that helps models distill sparse supervision signal from long sequences when the problem is underspecified . Similar to replacement-based techniques such as masking and substitution , SPANDROP directly ablates parts of the input at random to construct counterfactual examples that preserve the original supervision signal with high probability . Instead of preserving the original sequence positions , however , SPANDROP directly removes ablated elements from the input to mitigate any bias that is related to the absolute positions of elements ( rather than the relative positions between them ) in the input . Upon closer examination of its theoretical and empirical properties , we further propose a more effective variant of SPANDROP based on the Beta-Bernoulli distribution that enhances the consistency of the augmented objective function with the original one . We demonstrate via carefully designed toy experiments that SPANDROP not only helps models achieve up to 20⇥ sample-efficiency in low-data settings , but also further reduces overfitting even when training data is abundant . We find that it is very effective at mitigating position bias compared to replacement-based counterfactual approaches , and enhances out-of-distribution generalization effectively . We further experiments on four natural language processing tasks that require models to answer question or extract entity relations from long texts , and demonstrate that SPANDROP can improve the performance of already competitive neural models without any change in model architecture . 2 METHOD . In this section , we first formulate the problem of sequence inference , where the model takes sequential data as input to make predictions . Then , we introduce SPANDROP , a simple and effective data augmentation technique for long sequence inference , and analyze its theoretical properties . 2.1 PROBLEM DEFINITION . Sequence Inference . We consider a task where a model takes a sequence S as input and predicts the output y . We assume that S consists of n disjoint but contiguous spans , each representing a part of the sequence in order S = ( s1 , . . . , sn ) . One example of sequence inference is sentiment classification from a paragraph of text , where S is the paragraph and y the desired sentiment label . Spans could be words , phrases , sentences , or a mixture of these in the paragraph . Another example is time series prediction , where S is historical data , y is the value at the next time step . Supporting facts . Given an input-output pair ( S , y ) for sequence prediction , we assume that y is truly determined by only a subset of spans in S. More formally , we assume that there is a subset of spans Ssup ⇢ { s1 , s2 , . . . , sn } such that y is independent of si , if si /2 Ssup . In sentiment classification , Ssup could consist of important sentiment words or conjunctions ( like “ good ” , “ bad ” , “ but ” ) ; in time series prediction , it could reflect the most recent time steps as well as those a few cycles away if the series is periodic . For simplicity , we will denote the size of this set m = |Ssup| , and restrict our attention to tasks where m ⌧ n , such as those described in the previous section . 2.2 SPANDROP . In a long sequence inference task with sparse support facts ( m ⌧ n ) , most of the spans in the input sequence will not contribute to the prediction of y , but they will introduce spurious correlation in a low-data scenario . SPANDROP generates new data instances ( S̃ , y ) by ablating these spans at random , while preserving the supporting facts with high probability so that the model is still trained to make the correct prediction y . This is akin to counterfactually determining whether each span truly determines the outcome y by asking what the prediction would have been without it . Definition 1 ( SPANDROP ) . Formally , given a sequence S that consists of spans ( s1 , s2 , · · · sn ) , SPANDROP generates a new sequence S̃ as follows : i i.i.d.⇠ Bernoulli ( 1 p ) , S̃ = ( si ) ni=1 , i=1 , ( 1 ) where p is the hyperparameter that determines the probability to drop a span . Note that SPANDROP does not require introducing substitute spans or artificial symbols when ablating spans from the input sequence . It makes the most of the natural sequence as it occurs in the original training data , and preserves the relative order between spans that are not dropped , which is often helpful in understanding sequential data ( e.g. , time series or text ) . It is also not difficult to establish that the resulting sequence S̃ can preserve all of the m supporting facts with high probability regardless of how large n is . Remark 1 . The new sequence length n0 = |S̃| and the number of preserved supporting facts m0 = |S̃ \ Ssup| follow binomial distributions with parameters ( n , 1 p ) and ( m , 1 p ) , respectively : P ( n0|n , p ) = ✓ n n0 ◆ ( 1 p ) n 0 pn n 0 , P ( m0|m , p ) = ✓ m m0 ◆ ( 1 p ) m 0 pm m 0 . ( 2 ) Therefore , the proportion of sequences where all supporting facts are retained ( i.e. , m0 = m ) is ( 1 p ) m , which is independent of n. This means that as long as the total number of supporting facts in the sequence is bounded , then regardless of the sequence length , we can always choose p carefully such that we end up with many valid new examples with bounded noise introduced to supporting facts . Note that our analysis so far relies only on the assumption that m is known or can be estimated , and thus it can be applied to tasks where the precise set of supporting facts Ssup is unknown . More formally , the amount of new examples can be characterized by the size of the typical set of S̃ , i.e.the set of sequences that the randomly ablated sequence will fall into with high probability . The size of the typical set for SPANDROP is approximately 2nH ( p ) , where H ( p ) is the binary entropy of a Bernoulli random variable with probability p. Intuitively , these results indicate that the amount of total counterfactual examples generated by SPANDROP scales exponentially in n , but the level of supporting fact noise can be bounded as long as m is small . However , this formulation of SPANDROP does have a notable drawback that could potentially hinder its efficacy . Because the new sequence length n0 follows a binomial distribution , its mean is n ( 1 p ) and its variance is np ( 1 p ) . For sufficiently large n , most of the resulting S̃ will have lengths that concentrate around the mean with a width of O ( p n ) , which creates an artificial and permanent distribution drift from the original length ( see Figure 1 ( a ) ) . Furthermore , if we know the identity of Ssup and keep these spans during training , this length reduction will bias the training set towards easier examples to locate spans in Ssup . In the next subsection , we will introduce a variant of SPANDROP based on the beta-Bernoulli distribution that alleviates this issue .

Summary: This paper proposes a data augmentation method, SpanDrop (and its variant Beta-SpanDrop), for long sequence data, especially where supporting facts take small portions. They provide a theoretical background on their method and evaluate the method on a synthetic task (FindCats) and four real natural language processing tasks requiring reasoning over long texts. SpanDrop is effectively improves the accuracy in both low-resource and abundant-resource settings.