Optimizing inference

Neural networks pose unique challenges with regards to encrypted inference. Each neuron in a network applies an activation function that requires a PBS operation. The latency of a single PBS depends on the bit-width of the input of the PBS.

Several approaches can be used to reduce the overall latency of a neural network.

Circuit bit-width optimization

Quantization Aware Training and pruning introduce specific hyper-parameters that influence the accumulator sizes. It is possible to chose quantization and pruning configurations that reduce the accumulator size. A trade-off between latency and accuracy can be obtained by varying these hyper-parameters as described in the deep learning design guide.

Structured pruning

While un-structured pruning is used to ensure the accumulator bit-width stays low, structured pruning can eliminate entire neurons from the network. Many neural networks are over-parametrized (since this enables easier training) and some neurons can be removed. Structured pruning, applied to a trained network as a fine-tuning step, can be applied to built-in neural networks using the prune helper function as shown in this example. To apply structured pruning to custom models, it is recommended to use the torch-pruning package.

Rounded activations and quantizers

Reducing the bit-width of the inputs to the Table Lookup (TLU) operations is a major source of improvements in the latency. Post-training, it is possible to leverage some properties of the fused activation and quantization functions expressed in the TLUs to further reduce the accumulator. This is achieved through the rounded PBS feature as described in the rounded activations and quantizers reference. Adjusting the rounding amount, relative to the initial accumulator size, can bring large improvements in latency while maintaining accuracy.

TLU error tolerance adjustment

Finally, the TFHE scheme exposes a TLU error tolerance parameter that has an impact on crypto-system parameters that influence latency. A higher tolerance of TLU off-by-one errors results in faster computations but may reduce accuracy. One can think of the error of obtaining $T[x]$ as a Gaussian distribution centered on $x$: $TLU[x]$ is obtained with probability of 1 - p_error, while $T[x-1]$, $T[x+1]$ are obtained with much lower probability, etc. In Deep NNs, these type of errors can be tolerated up to some point. See the p_error documentation for details and more specifically the usage example of the API for finding the best p_error.