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Transformers trained on huge text corpora exhibit a remarkable set of capabilities. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities, potentially yielding a combinatorial explosion of what operations it can perform on an input. Motivated by the above, we aim to assess in this paper “how capable can a transformer become?”. In this work, we train Transformer models on a data-generating process that involves compositions of a set of well-defined monolithic capabilities and show that: (1) Transformers generalize to exponentially or even combinatorially many functions not seen in the training data; (2) composing functions by generating intermediate outputs is more effective at generalizing to unseen compositions; (3) the training data has a significant impact on the model’s ability to compose functions (4) Attention layers in the latter half of the model seem critical to compositionality. 

Transformers trained on huge text corpora exhibit a remarkable set of capabilities, e.g., performing simple logical operations. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities, potentially yielding a combinatorial explosion of what operations it can perform on an input. Motivated by the above, we aim to assess in this paper “how capable can a transformer become?”. Specifically, we train autoregressive Transformer models on a data-generating process that involves compositions of a set of well-defined monolithic capabilities. Through a series of extensive and systematic experiments on this data-generating process, we show that: (1) Autoregressive Transformers can learn compositional structures from the training data and generalize to exponentially or even combinatorially many functions; (2) composing functions by generating intermediate outputs is more effective at generalizing to unseen compositions, compared to generating no intermediate outputs; (3) the training data has a significant impact on the model’s ability to compose unseen combinations of functions; and (4) the attention layers in the latter half of the model are critical to compositionality 

Description of the DISCo facility and adaptive control experiments