In machine learning, knowledge distillation or model distillation is the process of transferring knowledge from a large model to a smaller one. While large models (such as very deep neural networks or ensembles of many models ) have more knowledge capacity than small models, this capacity might not be fully utilized. It can be just as computationally expensive to evaluate a model even if it utilizes little of its knowledge capacity. Knowledge distillation transfers knowledge from a large model to a smaller one without loss of validity. As smaller models are less expensive to evaluate, they can be deployed on less powerful hardware (such as a mobile device). There is also a less common technique called Reverse Knowledge Distillation, where knowledge is transferred from a smaller model to a larger one. Model distillation is not to be confused with model compression, which describes methods to decrease the size of a large model itself, without training a new model. Model compression generally preserves the architecture and the nominal parameter count of the model, while decreasing the bits-per-parameter. Knowledge distillation has been successfully used in several applications of machine learning such as object detection, acoustic models, and natural language processing. Recently, it has also been introduced to graph neural networks applicable to non-grid data.
Methods Knowledge transfer from a large model to a small one somehow needs to teach the latter without loss of validity. If both models are trained on the same data, the smaller model may have insufficient capacity to learn a concise knowledge representation compared to the large model. However, some information about a concise knowledge representation is encoded in the pseudolikelihoods assigned to its output: when a model correctly predicts a class, it assigns a large value to the output variable corresponding to such class, and smaller values to the other output variables. The distribution of values among the outputs for a record provides information on how the large model represents knowledge. Therefore, the goal of economical deployment of a valid model can be achieved by training only the large model on the data, exploiting its better ability to learn concise knowledge representations, and then distilling such knowledge into the smaller model, by training it to learn the soft output of the large model.
Mathematical formulation Given a large model as a function of the vector variable x {\displaystyle \mathbf {x} } , trained for a specific classification task, typically the final layer of classification networks is a softmax in the form
y i ( x | t ) = e z i ( x ) t ∑ j e z j ( x ) t {\displaystyle y_{i}(\mathbf {x} |t)={\frac {e^{\frac {z_{i}(\mathbf {x} )}{t}}}{\sum _{j}e^{\frac {z_{j}(\mathbf {x} )}{t}}}}}
where t {\displaystyle t} is the temperature, a parameter which is set to 1 for a standard softmax. The softmax operator converts the logit values z i ( x ) {\displaystyle z_{i}(\mathbf {x} )} to pseudo-probabilities: higher temperature values generate softer distributions of pseudo-probabilities among the output classes. Knowledge distillation consists of training a smaller network, called the distilled model, on a data set called the transfer set which could correspond to the original training set or consist of new, possibly unlabeled data. A cross-entropy loss function is typically used, computed between the output of the distilled model y ( x | t ) {\displaystyle \mathbf {y} (\mathbf {x} |t)} and the output of the large model y ^ ( x | t ) {\displaystyle {\hat {\mathbf {y} }}(\mathbf {x} |t)} on the same record (or the average of the individual outputs, if the large model is an ensemble), using a high value of softmax temperature t {\displaystyle t} for both models:
E ( x | t ) = − ∑ i y ^ i ( x | t ) log y i ( x | t ) . {\displaystyle E(\mathbf {x} |t)=-\sum _{i}{\hat {y}}_{i}(\mathbf {x} |t)\log y_{i}(\mathbf {x} |t).}
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