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Current Research Questions, Pruning the network, Testing redundancy, ITAC…

- - - - Sanity-check
        Add some representations that are noise only and don't contribute to the downstream performance.
        
        See how the similarities change.
        Maybe also check how dimensionality influences the metrics!
        
        Add some random noise channels --> Visualize how the similarity degrades
        
        Add redundancy by adding noise to the representations somewhat related.
      - Calculate the similarities between many pruned and many unpruned models.
        
        Pruning is supposed to remove redundancy / useless information.
        This should increase the representation wise relevance.
        The similarities should not change though since the "original representations" should be maintained
      - Potentially: Similarity beteween the unpruned original and the corresponding highly pruned model.
        
        When pruning would work perfectly the similarity should be 1 as we only remove redundant information. However that will probably not be the case.
        
        Maybe interesting insights on how the pruning process changes behavior itself?
      - Sanity-check
        Super low complexity model + Known task solution
        Show the issues I want to highlight
    - - Relevance Metrics
        
        Currently quantified models by Truncated Shapley. (Only an approximation of the relevance of the channels.)
        
        Speed: Slow AF
        Takes 3x longer than training the model ... (but can be done for small datasets)
        
        Might get infeasible for models with 1000+ channels and big datasets!
        
        L1 Magnitude of Weights+Biases
        
        Speed: Basically instant
        
        Heuristic
        
        Leave-One-Out sampling:
        Not really nice metric but measures downstream change at least.
        
        Easy to compute
        
        Speed: Faster (but still requires validation/merge set evaluations)
      - Calculation of the metrics for the representations of the original models
        
        Show the histograms --> Many models with 0 relevance
        
        Calculate correlations between different metrics. (Shapley should be gold-standard)
        
        Given that a representation wise similarity value can be calculated the correlation between the similarity and the relevance (if there is one) is evaluateable
      - Potentially: Show sanity-check relevance of random channels will be 0.
        
        Given by design that these channels don't have a relevance. Might seem like constructed for my own metrics?
      - Compare the metrics between the pruned and unpruned models.
        
        The relevance should indicate that the pruned models have higher relevance (on average) as we relevance should be condensed into fewer representation.
    - - Create a metrics that is f(similarity, relevance)
        
        A simple relevance weighted similarity might work. BUT the relevance is given by the downstream
        
        Just drop the similarity metric all together and go to the downstream task evaluation?
      - (hopefully) Show the f(similarity, relevance) for the pruned and original model is in the same ball-park (has to be better than 'raw' similarity values
    - - Show the similarity progression over the process of pruning the network (with itself)
      - Show the Inter-model similarity as pruning happens
        
        When this grows it indicates the relevant representations are similar across models
        
        When it stays constant the Similarity seems to take relevance of the channels into account and seems to be independent to dimensionality.
        
        When it decreases it's shows relevant representations differ between models.
      - Show different pruning methods:
        Unstructed: (Lottery-ticket)
        Structured: (Bottlenecks)
  - - - Argument 1: Increases the portion of relevant signal in these activations --> less noise parts?
- - - - Use it for error detection or potentially error correction
  - - - Use the existing Least Squares method to align the representations
        
        Cifar10/100 & ImageNet
        
        Between Architecture maybe?
        
        Filter the representations in such a way that both models predicted correctly! --> This is currently not done
      - Qualitatively show that the semantics / most activating inputs are similar
      - Quantify if relevant representations are more similar than irrelevant representations
    - - Calculate the similarity between models when predicting correctly and not correctly
    - - Fit GMM on approximation error for positive samples. And one on approximation error for disagreeing models.
      - Evaluate if dropping out the channels improves the overall ensemble performance
      - Maybe use it for uncertainty quantification to flag a prediction as unreliable?
- - - - 1. No joint training necessary to evaluate task groupings.
        (single architectures are enough)
      - 2. Iteratively extend only necessary to evaluate new representations and compare to old ones
      - 3. Possibly better at identifying matching groupings?
    - - 1. Evaluate Reps of single trained models and inter task similarities
        
        Maybe do so over the course of the training process?
      - Create method that selects groupings by highest avg. rep. similarity.