Cluster error parameterization

• Continued with grid searches + interpolation:
  • New procedure for finding minima:
    • Run approximate grid ranges (parallelizable)
    • Fit small NN to surface (interpolation, 2D)
    • Use gradient descent to find extremum
    • Sample Latin hypercube grid around extremum
    • Iterate until satisfaction

1. NN trained with mC[0] < 0.5 && mC[2] < 0.5 && abs(dy) < 2 && abs(dz) < 2, optimization strategy: maximizes number of correctly attached clusters

Plot number of correctly attached clusters as a function of scale parameters, interpolated by NN

(sampling from regular grid by LHS (Latin Hypercube sampling) visible around predicted minimum)

Using config close to minimum

Efficiency worse, but better fake and clone rate. And much longer tracks compared to default reco -> Less clones?!
Finds less tracks than default reco, but above NCl > 60 it finds more tracks than the default reco

2. NN trained with mC[0] < 0.25 && mC[2] < 0.25 && abs(dy) < 1.5 && abs(dz) < 1.5, optimization strategy: maximizes number of correctly attached clusters

• Similar picture
• Correctly attached clusters, default reco: 18.06 mio. ; ..., closest NN config : 18.39 mio..

3. NN trained with mC[0] < 0.25 && mC[2] < 0.25 && abs(dy) < 1.5 && abs(dz) < 1.5, Change of optimization strategy: Optimize for "correctly attached non-fake clusters"

• Best configurations:
  • y = 0.252811, z = 2.21427 (correctly attached opt. from previous bullet point)
  • y = 0.177332, z = 2.91026 (correctly attached, non-fake opt.)
• Clearly differ between both optimization strategies...

• Seems to work a lot better to reduce fake-rates
• NCl peak behaviour at 120 much closer to current reco.
• Significantly reduced short tracks

4. NN trained with mC[0] < 0.25 && mC[2] < 0.25 && abs(dy) < 1.5 && abs(dz) < 1.5, Change of optimization strategy: Maximize "correctly attached non-fake clusters - fake attached clusters"

Using the same data as above:

This means, the optimization objective has shifted towards higher scaleZ and lower scaleY factors than previously!

Extend the grid.

Take one direction through phase-space:

vs local Y:

vs pT:

Similar pictures vs. Eta, Phi and Z -> Its not a random spike somewhere, it's rather a lower efficiency, clone and fake rate across the phase-space

Effect of increasing scaleZ parameter:

• Lower efficiency
• Lower fake rate
• Lower clone rate

Now the other direction:

Effect of increasing scaleY parameter:

• Lower efficiency
• Higher fake-rate
• Lower clone-rate

Lessons learned:

• Fake and clone rate can be optimised with the shown optimization strategies
• Efficiency is not well optimized with the taken metrics -> New metric needed?! What to take?

Best configurations overview:

• y = 0.252811, z = 2.21427 (correctly attached, tighter cuts)
• y = 0.177332, z = 2.91026 (correctly attached non-fake)
• y = 0.148339, z = 4.30489 (correctly attached non-fake - fake attached)

One more study: Effect of network size

Use networks:

1. 2 layers, 32 neurons per layer
2. 4 layers, 32 NpL
3. 8 layers, 32 NpL
4. 16 layers, 32 NpL (all cases from studies above)

1.

2.

3.

4.

-> Scale factors need to be tuned individually per network and might be somewhat sensitive to networks ability to fit the underlying data

1. scaleY = 0.104, scaleZ = 3.96
2. scaleY = 0.124, scaleZ = 2.776
3. scaleY = 0.171, scaleZ = 2.30
4. scaleY = 0.141, scaleZ = 6.45 (and previous: scaleY = 0.148, scaleZ = 4.30)

Lesson learnt:

• ScaleZ (= scaling in time / Z direction) is quite volatile...

Caveats and further development:

• This is now tuned with dataset from centrality enforced 38 kHz simulations (LHC24ar apass2 anchored) -> Maybe switch to dataset of lower occupancy or combine different datasets
• Optimization strategies (correctly attached clusters) is only available in MC data, would prefer metric for real data tuning
• To be seen how well this would extrapolate to real data (future development)

Final Q:

• In GPUQA: "Correctly attached clusters" and "Correctly Attached all-trk normalized" are not identical