Adaptive wavelet distillation from neural networks through interpretations (2107.09145v2)

Abstract: Recent deep-learning models have achieved impressive prediction performance, but often sacrifice interpretability and computational efficiency. Interpretability is crucial in many disciplines, such as science and medicine, where models must be carefully vetted or where interpretation is the goal itself. Moreover, interpretable models are concise and often yield computational efficiency. Here, we propose adaptive wavelet distillation (AWD), a method which aims to distill information from a trained neural network into a wavelet transform. Specifically, AWD penalizes feature attributions of a neural network in the wavelet domain to learn an effective multi-resolution wavelet transform. The resulting model is highly predictive, concise, computationally efficient, and has properties (such as a multi-scale structure) which make it easy to interpret. In close collaboration with domain experts, we showcase how AWD addresses challenges in two real-world settings: cosmological parameter inference and molecular-partner prediction. In both cases, AWD yields a scientifically interpretable and concise model which gives predictive performance better than state-of-the-art neural networks. Moreover, AWD identifies predictive features that are scientifically meaningful in the context of respective domains. All code and models are released in a full-fledged package available on Github (https://github.com/Yu-Group/adaptive-wavelets).

Adaptive Wavelet Distillation from Neural Networks through Interpretations: A Synopsis

The paper under discussion introduces an innovative method, Adaptive Wavelet Distillation (AWD), which aims to convert the functionality of a trained neural network into an interpretable wavelet transform. AWD addresses the prevalent challenge in deep learning models, particularly their lack of interpretability and computational efficiency. By merging interpretability with high predictive performance, AWD creates a concise model that is computationally sustainable and scientifically interpretable, thus potentially enhancing applications in critical fields such as cosmological parameter inference and molecular-partner prediction.

Key Contributions

1. Wavelet Transform Interpretation: The crux of AWD lies in learning a wavelet transform that incorporates feature attributions from pre-trained neural networks, allowing the transformation to reflect not only input signal distributions but also target variable correlations and biases of the network.
2. Theoretical Foundation: The paper provides a robust framework for ensuring that the learned wavelet maintains invertibility and conforms to standard wavelet bases' conditions. This is crucial for ensuring that no significant input information is lost during the transformation and that the wavelets are mathematically valid.
3. Application to Real-World Problems: AWD's utility and effectiveness are validated through applications in two scientific domains:
   • Cosmological Parameter Inference: AWD significantly enhances the task of inferring cosmological parameters from weak gravitational lensing convergence maps by allowing the integration of multi-resolution wavelet structures, surpassing state-of-the-art neural networks in predictive performance.
   • Molecular-Partner Prediction: In cell biology, AWD offers a transparent model for predicting molecular interactions, where it not only achieves better predictive accuracy than existing methods but also aligns closely with domain experts' understanding of relevant biological processes.
4. Improvement Over State-of-the-Art Models: Across both application domains, AWD provides models that challenge and, in some cases, outperform contemporary deep learning techniques while offering the significant advantage of interpretability.

Methodology

AWD is characterized by its approach to wavelet model construction:

• Penalization Framework: It involves a regularization framework where the contribution of interpretation, wavelet, and reconstruction losses can be fine-tuned. The approach is grounded in rigorous mathematical principles that ensure viability as an orthonormal wavelet basis.
• Optimization: Optimization of the wavelet filters is meticulously performed using feature attributions from the DNN, encouraging a sparse and relevant wavelet representation of the data, which is crucial for interpretability and efficient computation.

Implications and Future Directions

The implications of AWD are multi-faceted:

• Practical Impact: In fields where interpretability is paramount, such as healthcare and scientific research, AWD offers a potent tool for model validation and hypothesis testing.
• Theoretical Advancement: By tackling the interpretability aspect in a mathematically grounded manner, AWD contributes to the broader discourse on how complex models can be distilled into forms comprehensible by human cognition and domain expertise.

Looking forward, there are several avenues for further research:

• Expansion to Other Domains: Extending AWD to other domains, like image and language processing, can open up new methodologies for processing complex data efficiently.
• Deeper Integration with Machine Learning Frameworks: Integrating AWD with advanced frameworks or combining it with other interpretability tools could enhance its robustness and applicability.
• Optimization Techniques: Improved algorithmic strategies for solving the AWD model's optimization problem can potentially reduce computational burdens and improve scalability.

Overall, AWD represents a pivotal step towards a more transparent and efficient utilization of deep learning, aligning complex predictive models more closely with human judgment and scientific inquiry.