Recent advances in deep learning have relied heavily on the use of large Transformers due to their ability to learn at scale. However, the core building block of Transformers, the attention operator, exhibits quadratic cost in sequence length, limiting the amount of context accessible. Existing subquadratic methods based on low-rank and sparse approximations need to be combined with dense attention layers to match Transformers, indicating a gap in capability. In this work, we propose Hyena, a subquadratic drop-in replacement for attention constructed by interleaving implicitly parametrized long convolutions and data-controlled gating. In recall and reasoning tasks on sequences of thousands to hundreds of thousands of tokens, Hyena improves accuracy by more than 50 points over operators relying on state-spaces and other implicit and explicit methods, matching attention-based models. We set a new state-of-the-art for dense-attention-free architectures on language modeling in standard datasets (WikiText103 and The Pile), reaching Transformer quality with a 20% reduction in training compute required at sequence length 2K. Hyena operators are twice as fast as highly optimized attention at sequence length 8K, and 100x faster at sequence length 64K.

A central challenge in sensory neuroscience is to understand neural computations and circuit mechanisms that underlie the encoding of ethologically relevant, natural stimuli. In multilayered neural circuits, nonlinear processes such as synaptic transmission and spiking dynamics present a significant obstacle to the creation of accurate computational models of responses to natural stimuli. Here we demonstrate that deep convolutional neural networks (CNNs) capture retinal responses to natural scenes nearly to within the variability of a cell's response, and are markedly more accurate than linear-nonlinear (LN) models and Generalized Linear Models (GLMs). Moreover, we find two additional surprising properties of CNNs: they are less susceptible to overfitting than their LN counterparts when trained on small amounts of data, and generalize better when tested on stimuli drawn from a different distribution (e.g. between natural scenes and white noise). An examination of the learned CNNs reveals several properties. First, a richer set of feature maps is necessary for predicting the responses to natural scenes compared to white noise. Second, temporally precise responses to slowly varying inputs originate from feedforward inhibition, similar to known retinal mechanisms. Third, the injection of latent noise sources in intermediate layers enables our model to capture the sub-Poisson spiking variability observed in retinal ganglion cells. Fourth, augmenting our CNNs with recurrent lateral connections enables them to capture contrast adaptation as an emergent property of accurately describing retinal responses to natural scenes. These methods can be readily generalized to other sensory modalities and stimulus ensembles. Overall, this work demonstrates that CNNs not only accurately capture sensory circuit responses to natural scenes, but also can yield information about the circuit's internal structure and function.