We propose a novel approach based on modern deep artificial neural networks (DNNs) for understanding how the morpho-electrical complexity of neurons shapes their input/output (I/O) properties at the millisecond resolution in response to massive synaptic input. The I/O of integrate and fire point neuron is accurately captured by a DNN with a single unit and one hidden layer. A fully connected DNN with one hidden layer faithfully replicated the I/O relationship of a detailed model of Layer 5 cortical pyramidal cell (L5PC) receiving AMPA and GABAA synapses. However, when adding voltage-gated NMDA-conductances, a temporally-convolutional DNN with seven layers was required. Analysis of the DNN filters provides new insights into dendritic processing shaping the I/O properties of neurons. This work proposes a systematic approach for characterizing the functional “depth” of a biological neurons, suggesting that cortical pyramidal neurons and the networks they form are computationally much more powerful than previously assumed.