  Although deep feedforward neural networks share some characteristics with the
primate visual system, a key distinction is their dynamics. Deep nets typically
operate in serial stages wherein each layer completes its computation before
processing begins in subsequent layers. In contrast, biological systems have
cascaded dynamics: information propagates from neurons at all layers in
parallel but transmission occurs gradually over time, leading to speed-accuracy
trade offs even in feedforward architectures. We explore the consequences of
biologically inspired parallel hardware by constructing cascaded ResNets in
which each residual block has propagation delays but all blocks update in
parallel in a stateful manner. Because information transmitted through skip
connections avoids delays, the functional depth of the architecture increases
over time, yielding anytime predictions that improve with internal-processing
time. We introduce a temporal-difference training loss that achieves a strictly
superior speed-accuracy profile over standard losses and enables the cascaded
architecture to outperform state-of-the-art anytime-prediction methods. The
cascaded architecture has intriguing properties, including: it classifies
typical instances more rapidly than atypical instances; it is more robust to
both persistent and transient noise than is a conventional ResNet; and its
time-varying output trace provides a signal that can be exploited to improve
information processing and inference.
