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Empirical studies have identified a range of learnability biases and limitations of transformers, such as a persistent difficulty in learning to compute simple formal languages such as PARITY, and a bias towards low-degree functions.…

Transformer architectures show significant promise for natural language processing. Given that a single pretrained model can be fine-tuned to perform well on many different tasks, these networks appear to extract generally useful linguistic…

Current neural network (NN) models can learn patterns from data points with historical dependence. Specifically, in natural language processing (NLP), sequential learning has transitioned from recurrence-based architectures to…

Representation learning for text via pretraining a language model on a large corpus has become a standard starting point for building NLP systems. This approach stands in contrast to autoencoders, also trained on raw text, but with the…

Neural networks can accurately forecast complex dynamical systems, yet how they internally represent underlying latent geometry remains poorly understood. We study neural forecasters through the lens of representational alignment,…

Transformers are theoretically reversal-invariant: their function class does not prefer left-to-right over right-to-left mappings. Yet empirical studies on natural language repeatedly report a "reversal curse," and recent work on temporal…

Encoder-decoder networks using convolutional neural network (CNN) architecture have been extensively used in deep learning literatures thanks to its excellent performance for various inverse problems. However, it is still difficult to…

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared…

The process by which Large Language Models (LLMs) acquire complex capabilities during training remains a key open question in mechanistic interpretability. This project investigates whether these learning dynamics can be characterized…

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…

Linguistic representation learning in deep neural language models (LMs) has been studied for decades, for both practical and theoretical reasons. However, finding representations in LMs remains an unsolved problem, in part due to a dilemma…

Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the…

How related are the representations learned by neural language models, translation models, and language tagging tasks? We answer this question by adapting an encoder-decoder transfer learning method from computer vision to investigate the…

While the last five years have seen considerable progress in understanding the internal representations of deep learning models, many questions remain. This is especially true when trying to understand the impact of model design choices,…

Graph Neural Networks (GNNs) are the dominant architecture for molecular machine learning, particularly for molecular property prediction and machine learning interatomic potentials (MLIPs). GNNs perform message passing on predefined graphs…

Autoencoders exhibit impressive abilities to embed the data manifold into a low-dimensional latent space, making them a staple of representation learning methods. However, without explicit supervision, which is often unavailable, the…

Existing interpretability methods for Large Language Models (LLMs) predominantly capture linear directions or isolated features. This overlooks the high-dimensional, relational, and nonlinear geometry of model representations. We apply…

Transformers have evolved with great success in various artificial intelligence tasks. Thanks to our recent prevalence of self-attention mechanisms, which capture long-term dependency, phenomenal outcomes in speech processing and…

The remarkable capability of Transformers to do reasoning and few-shot learning, without any fine-tuning, is widely conjectured to stem from their ability to implicitly simulate a multi-step algorithms -- such as gradient descent -- with…

Transformer-based models are now predominant in NLP. They outperform approaches based on static models in many respects. This success has in turn prompted research that reveals a number of biases in the language models generated by…