Neural network weight extraction

neural-network-weight-extraction

Summary

Extract weight matrices from trained multilayer perceptron neural networks across multiple cross-validation folds to compute microbe-metabolite feature attribution scores via Olden's method. This enables downstream biclustering and module discovery by quantifying how individual network weights contribute to metabolite abundance predictions.

When to use

You have trained MLPNN models on paired microbiome-metabolome data (via 10-fold cross-validation repeated across multiple iterations) and need to derive interpretable microbe-metabolite interaction scores rather than treating the network as a black box. Use this when your goal is to construct functional modules or interaction networks that group microbes and metabolites by their learned predictive relationships.

When NOT to use

• You have only a single trained neural network model; Olden's method requires an ensemble to compute a meaningful consensus attribution matrix.
• Your network output is a classification task or categorical prediction rather than regression of metabolite abundances; Olden's method is designed for continuous feature attribution in regression contexts.
• You lack a background distribution from shuffled-data cross-validation; the 97.5 percentile threshold depends on empirically estimated background statistics.

Inputs

• Trained MLPNN weight matrices (W_l) from all hidden layers
• Ensemble of trained neural network models (≥10 models from cross-validation)
• Background distribution of attribution scores (from shuffled-data cross-validation)
• List of well-predicted metabolites (filtered by correlation threshold)

Outputs

• Normalized microbe-metabolite attribution score matrix (values in [−1, 1])
• Mean attribution matrix S* (averaged across all trained models)
• List of significant microbes (those with ≥1 score above 97.5 percentile threshold)
• Module membership assignments (if biclustering is applied downstream)

How to apply

Load all trained MLPNN weight matrices W_l from hidden layers across the ensemble of models (e.g., 100 models from 10 iterations × 10-fold cross-validation). Apply Olden's method by multiplying weight matrices across all layers sequentially (S = ∏ W_l for l ∈ L) to produce one attribution score matrix per trained model. Average all score matrices to generate a consensus matrix S*, then flatten and apply a 97.5 percentile threshold (computed from the background distribution of shuffled-data models) to identify significant scores. Normalize all significant scores to the range [−1, 1] by dividing by the 97.5 percentile threshold, filter out microbes with no attribution scores above threshold across any well-predicted metabolite, and output the normalized score matrix for subsequent clustering or network analysis.

Related tools

• TensorFlow (Framework for loading and manipulating trained neural network weight matrices)
• scikit-learn (Hierarchical clustering and consensus clustering on normalized attribution scores)
• Seaborn clustermap (Visualization of normalized attribution score matrices)
• Cytoscape (Visualization of module-based interaction networks derived from attribution scores)

Examples

# Load 100 trained models and extract weight matrices; compute Olden attribution scores
import numpy as np
for model_i in range(100):
    W_layers = [model_weights[l] for l in range(num_layers)]
    S_i = np.ones(shape=(n_microbes, n_metabolites))
    for W_l in W_layers:
        S_i = S_i @ W_l.T
    S_matrices.append(S_i)
S_star = np.mean(S_matrices, axis=0)
thresh_95 = np.percentile(np.abs(S_background.flatten()), 97.5)
S_norm = S_star / thresh_95
S_norm = np.clip(S_norm, -1, 1)

Evaluation signals

• Mean attribution matrix S* is symmetric in structure and centered near zero (positive and negative contributions are both present).
• Normalized scores are bounded to [−1, 1]; any value outside this range indicates an error in the normalization step.
• Number of significant microbes (with ≥1 score above 97.5 percentile) is substantially smaller than total number of microbes in input data (e.g., 163 out of thousands), confirming that filtering is selective.
• Positive attribution scores correlate with microbes known to increase metabolite abundance; negative scores correlate with inhibitory microbes (validate against prior knowledge or external data).
• Downstream biclustering produces ≥2 and ≤20 consensus clusters (k* and k**), with silhouette coefficient or cumulative distribution function area indicating stable partitions.

Limitations

• Olden's method assumes multiplicative interactions across layers; complex non-linear pathways through skip connections or residual networks may not be fully captured.
• Attribution scores are relative, not absolute; interpretation depends on the magnitude of the background threshold, which can vary across datasets (e.g., higher threshold observed in longitudinal soil data).
• MiMeNet analysis is data-driven without incorporating mechanistic knowledge; high attribution scores do not prove causal relationships, only learned predictive correlations.
• Not all metabolites may be associated with microbes, resulting in lower prediction correlations for some metabolites and potentially unstable or uninformative attribution scores.
• Weight extraction and attribution computation are sensitive to network hyperparameter choices (number of layers, layer size, L2 penalty, dropout rate); results may differ substantially if architecture is changed.

Evidence

• [other] Calculate microbe-metabolite feature attribution scores S using Olden's method by multiplying weight matrices across layers (S = ∏ W_l for l ∈ L), producing one score matrix per trained model.: "Calculate microbe-metabolite feature attribution scores S using Olden's method by multiplying weight matrices across layers (S = ∏ W_l for l ∈ L)"
• [other] Generate mean attribution matrix S* by averaging all 100 S_i matrices, then flatten into a feature vector and apply 97.5 percentile threshold to identify significant attribution scores.: "Generate mean attribution matrix S* by averaging all 100 S_i matrices, then flatten into a feature vector and apply 97.5 percentile threshold to identify significant attribution scores"
• [other] Normalize all significant scores to range [-1, 1] by dividing by the 97.5 percentile threshold from background distribution.: "normalize all significant scores to range [-1, 1] by dividing by the 97.5 percentile threshold from background distribution"
• [other] Filter out non-significant microbes (those with no attribution scores above threshold with any well-predicted metabolite): "Filter out non-significant microbes (those with no attribution scores above threshold with any well-predicted metabolite)"
• [other] Load trained MLPNN models (100 models from 10 iterations of 10-fold cross-validation) and extract weight matrices W_l from all hidden layers.: "Load trained MLPNN models (100 models from 10 iterations of 10-fold cross-validation) and extract weight matrices W_l from all hidden layers"
• [other] Positive attribution scores indicate microbes that contribute positively to metabolite abundance prediction, while negative scores indicate negative contributions.: "Positive attribution scores indicate microbes that contribute positively to metabolite abundance prediction, while negative scores indicate negative contributions"
• [methods] Any feature attribution score in the observed dataset with an absolute value above the threshold was considered significant: "Any feature attribution score in the observed dataset with an absolute value above the threshold was considered significant"
• [results] We identified 163 microbes that had at least one significant attribution score with a well-predicted metabolite: "We identified 163 microbes that had at least one significant attribution score with a well-predicted metabolite"