Framework

• Added GPU timer to ONNX inference for profiling
• Added deconvolution flags to NN inference for exact matching with GPU CF

Physics

• Cluster attachment efficiency vs. fake rate for different network inputs and thresholds
  • Attachment efficiency = (correctly attached cls NN / total cls) * (correctly attached cls NN / correctly attached cls GPU CF)

• Network outperforms GPU CF under all thresholds and input sizes. Choice for threshold is determined by number of correctly attached clusters in the next plot
• Significant benefits from using 3D networks
  
  
• Number of correctly attached clusters

• Threshold choice for classification network:
  • <= 0.01: Almost no loss in number of correctly attached clusters
  • >0.01 && <0.1: Maximum loss of 5% correctly attached clusters, but can lead to 18% savings in total clusters (see next plot)
    
    
• Number of total clusters

• CoG (pad) resolution as a function of occupancy for different network sizes (2 to 5 hidden layers; 16, 32, 64, 128 neurons per layer)

• More layers work better
• Network with L5 and N128 -> Not great performance, reason: Overtraining! Immediately visible in the logs. Validation loss goes up while training loss goes down / remains constant.
  -> Improvement for the future: Save network at best training loss, best validation loss and network after all epochs are done.

A cool thing to look at... and more

Neural network loss landscape:

• Take 1024 elements from the training data sample and perform PCA
  • Finds the axes that maximise the variance when projecting the data onto it, i.e. the most relevant axes to describe the data
• Take first two principal components and add them to the data as X_new = X + a*PCA1 + b*PCA2, where a and b are scale factors
• Choose a regular grid for a and b of arbitrary size, calculate the loss for each grid point using the training data output and network output
• Color = z = MSE loss; Smoothed with cubic splines, 400 grid points per direction

• Interpretation: This loss landscape is (almost) convex! Networks are (almost) guaranteed to land in the global optimum! This makes the method reliable.

Addendum