We propose using mechanistic interpretability – techniques for reverse engineering model weights into human-interpretable algorithms – to derive and compactly prove formal guarantees on model performance. We prototype this approach by formally proving accuracy lower bounds for a small transformer trained on Max-of-K, validating proof transferability across 151 random seeds and four values of K. We create 102 different computer-assisted proof strategies and assess their length and tightness of bound on each of our models. Using quantitative metrics, we find that shorter proofs seem to require and provide more mechanistic understanding. Moreover, we find that more faithful mechanistic understanding leads to tighter performance bounds. We confirm these connections by qualitatively examining a subset of our proofs. Finally, we identify compounding structureless errors as a key challenge for using mechanistic interpretability to generate compact proofs on model performance.

Foundation models are becoming valuable tools in medicine.

However, these parameters are often high-dimensional and hard to interpret.

Incorporating biological neuronal properties into Artificial Neural Networks (ANNs) to enhance computational capabilities is under active investigation in the field of deep learning. Inspired by recent findings indicating that dendrites adhere to quadratic integration rule for synaptic inputs, this study explores the computational benefits of quadratic neurons. We theoretically demonstrate that quadratic neurons inherently capture correlation within structured data, a feature that grants them superior generalization abilities over traditional neurons. This is substantiated by few-shot learning experiments. Furthermore, we integrate the quadratic rule into Convolutional Neural Networks (CNNs) using a biologically plausible approach, resulting in innovative architectures--Dendritic integration inspired CNNs (Dit-CNNs). Our Dit-CNNs compete favorably with state-of-the-art models across multiple classification benchmarks, e.g., ImageNet-1K, while retaining the simplicity and efficiency of traditional CNNs.

However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast sampling methods. In this work, we propose to train discrete EBMs with Energy Discrepancy, a loss function which only requires the evaluation of the energy function at data points and their perturbed counterparts, thus eliminating the need for Markov chain Monte Carlo.

"freely" into massive pre-training datasets to support large-scale pre-training.

To facilitate the algorithm's widespread adoption among

This unified model can quickly adapt to new tasks without the need to retrain a large model.