I have not heard about the IBM paper until now. This is inspired by my personal experiments training (obviously classical) machine learning models.
Suppose that V0,…,Vn,W0,…,Wn are real or complex finite dimensional inner product spaces. Suppose that the training data consists of tuples of the form (v0,…,vn) where v0∈V0,…,vn∈Vn are vectors. Let W0=V0 and let Bj:Vj+1×Wj→Wj+1 be bilinear for all j. Then let
Lv(w)=Bj(v,w) whenever v∈Vj+1,w∈Wj. Then we define our polynomial by setting p(v0,…,vn)=Lvn…Lv1(v0). In other words, my machine learning models are just compositions of bilinear mappings. In addition to wanting TrU([p(v0,…,vn)]) to approximate the label, we also include regularization that makes the machine learning model pseudodeterministically trained so that if we train it twice with different initializations, we end up with the same trained model. Here, the machine learning model has n layers, but the addition of extra layers gives us diminishing returns since bilinearity is close to linearity, so I still want to figure out how to improve the performance of such a machine learning model to match deep neural networks (if that is even feasible).
I use quantum information theory for my experiments mainly because quantum information theory behaves well unlike neural networks.
I have not heard about the IBM paper until now. This is inspired by my personal experiments training (obviously classical) machine learning models.
Suppose that V0,…,Vn,W0,…,Wn are real or complex finite dimensional inner product spaces. Suppose that the training data consists of tuples of the form (v0,…,vn) where v0∈V0,…,vn∈Vn are vectors. Let W0=V0 and let Bj:Vj+1×Wj→Wj+1 be bilinear for all j. Then let
Lv(w)=Bj(v,w) whenever v∈Vj+1,w∈Wj. Then we define our polynomial by setting p(v0,…,vn)=Lvn…Lv1(v0). In other words, my machine learning models are just compositions of bilinear mappings. In addition to wanting TrU([p(v0,…,vn)]) to approximate the label, we also include regularization that makes the machine learning model pseudodeterministically trained so that if we train it twice with different initializations, we end up with the same trained model. Here, the machine learning model has n layers, but the addition of extra layers gives us diminishing returns since bilinearity is close to linearity, so I still want to figure out how to improve the performance of such a machine learning model to match deep neural networks (if that is even feasible).
I use quantum information theory for my experiments mainly because quantum information theory behaves well unlike neural networks.