Deep Neural Networks (DNNs) are currently used in many fields, including critical real-time applications. Due to its compute-intensive nature, speeding up DNNs has become an important topic in current research. We propose a hybrid opto-electronic computing architecture targeting the acceleration of DNNs based on the residue number system (RNS). In this novel architecture, we combine the use of Wavelength Division Multiplexing (WDM) and RNS for efficient execution. WDM is used to enable a high level of parallelism while reducing the number of optical components needed to decrease the area of the accelerator. Moreover, RNS is used to generate optical components with short optical critical paths. In addition to speed, this has the advantage of lowering the optical losses and reducing the need for high laser power. Our RNS compute modules use one-hot encoding and thus enable fast switching between the electrical and optical domains. In this work, we demonstrate how to implement the different DNN computational kernels using WDM-enabled RNS based integrated photonics. We provide an accelerator architecture that uses our designed components and perform design space exploration to select efficient architecture parameters. Compared to memristor crossbars, our residue matrix-vector multiplication unit has two orders of magnitude higher peak performance. Our experimental evaluation using DNN benchmarks illustrates that our architecture can perform more than 19 times faster than the state of the art GPUs under the same power budget. CCS CONCEPTS • Computer systems organization → Neural networks; Optical computing; • Computing methodologies → Parallel computing methodologies.