Adam Tsou

Saad Qadeer, Andrew Engel, Amanda Howard et al.

Despite their immense promise in performing a variety of learning tasks, a theoretical understanding of the limitations of Deep Neural Networks (DNNs) has so far eluded practitioners. This is partly due to the inability to determine the closed forms of the learned functions, making it harder to study their generalization properties on unseen datasets. Recent work has shown that randomly initialized DNNs in the infinite width limit converge to kernel machines relying on a Neural Tangent Kernel (NTK) with known closed form. These results suggest, and experimental evidence corroborates, that empirical kernel machines can also act as surrogates for finite width DNNs. The high computational cost of assembling the full NTK, however, makes this approach infeasible in practice, motivating the need for low-cost approximations. In the current work, we study the performance of the Conjugate Kernel (CK), an efficient approximation to the NTK that has been observed to yield fairly similar results. For the regression problem of smooth functions and logistic regression classification, we show that the CK performance is only marginally worse than that of the NTK and, in certain cases, is shown to be superior. In particular, we establish bounds for the relative test losses, verify them with numerical tests, and identify the regularity of the kernel as the key determinant of performance. In addition to providing a theoretical grounding for using CKs instead of NTKs, our framework suggests a recipe for improving DNN accuracy inexpensively. We present a demonstration of this on the foundation model GPT-2 by comparing its performance on a classification task using a conventional approach and our prescription. We also show how our approach can be used to improve physics-informed operator network training for regression tasks as well as convolutional neural network training for vision classification tasks.

Max Vargas, Adam Tsou, Andrew Engel et al.

Sampling biases can cause distribution shifts between train and test datasets for supervised learning tasks, obscuring our ability to understand the generalization capacity of a model. This is especially important considering the wide adoption of pre-trained foundational neural networks -- whose behavior remains poorly understood -- for transfer learning (TL) tasks. We present a case study for TL on the Sentiment140 dataset and show that many pre-trained foundation models encode different representations of Sentiment140's manually curated test set $M$ from the automatically labeled training set $P$, confirming that a distribution shift has occurred. We argue training on $P$ and measuring performance on $M$ is a biased measure of generalization. Experiments on pre-trained GPT-2 show that the features learnable from $P$ do not improve (and in fact hamper) performance on $M$. Linear probes on pre-trained GPT-2's representations are robust and may even outperform overall fine-tuning, implying a fundamental importance for discerning distribution shift in train/test splits for model interpretation.

Andrew Engel, Nell Byler, Adam Tsou et al.

We present Mantis Shrimp, a multi-survey deep learning model for photometric redshift estimation that fuses ultra-violet (GALEX), optical (PanSTARRS), and infrared (UnWISE) imagery. Machine learning is now an established approach for photometric redshift estimation, with generally acknowledged higher performance in areas with a high density of spectroscopically identified galaxies over template-based methods. Multiple works have shown that image-based convolutional neural networks can outperform tabular-based color/magnitude models. In comparison to tabular models, image models have additional design complexities: it is largely unknown how to fuse inputs from different instruments which have different resolutions or noise properties. The Mantis Shrimp model estimates the conditional density estimate of redshift using cutout images. The density estimates are well calibrated and the point estimates perform well in the distribution of available spectroscopically confirmed galaxies with (bias = 1e-2), scatter (NMAD = 2.44e-2) and catastrophic outlier rate ($η$=17.53$\%$). We find that early fusion approaches (e.g., resampling and stacking images from different instruments) match the performance of late fusion approaches (e.g., concatenating latent space representations), so that the design choice ultimately is left to the user. Finally, we study how the models learn to use information across bands, finding evidence that our models successfully incorporates information from all surveys. The applicability of our model to the analysis of large populations of galaxies is limited by the speed of downloading cutouts from external servers; however, our model could be useful in smaller studies such as generating priors over redshift for stellar population synthesis.