Haldane Bundles: A Dataset for Learning to Predict the Chern Number of Line Bundles on the Torus

Characteristic classes, which are abstract topological invariants associated with vector bundles, have become an important notion in modern physics with surprising real-world consequences. As a representative example, the incredible properties of topological insulators, which are insulators in their bulk but conductors on their surface, can be completely characterized by a specific characteristic class associated with their electronic band structure, the first Chern class. Given their importance to next generation computing and the computational challenge of calculating them using first-principles approaches, there is a need to develop machine learning approaches to predict the characteristic classes associated with a material system. To aid in this program we introduce the {\emph{Haldane bundle dataset}}, which consists of synthetically generated complex line bundles on the $2$-torus. We envision this dataset, which is not as challenging as noisy and sparsely measured real-world datasets but (as we show) still difficult for off-the-shelf architectures, to be a testing ground for architectures that incorporate the rich topological and geometric priors underlying characteristic classes.

Understanding the Inner Workings of Language Models Through Representation Dissimilarity

As language models are applied to an increasing number of real-world applications, understanding their inner workings has become an important issue in model trust, interpretability, and transparency. In this work we show that representation dissimilarity measures, which are functions that measure the extent to which two model's internal representations differ, can be a valuable tool for gaining insight into the mechanics of language models. Among our insights are: (i) an apparent asymmetry in the internal representations of model using SoLU and GeLU activation functions, (ii) evidence that dissimilarity measures can identify and locate generalization properties of models that are invisible via in-distribution test set performance, and (iii) new evaluations of how language model features vary as width and depth are increased. Our results suggest that dissimilarity measures are a promising set of tools for shedding light on the inner workings of language models.

Attributing Learned Concepts in Neural Networks to Training Data

By now there is substantial evidence that deep learning models learn certain human-interpretable features as part of their internal representations of data. As having the right (or wrong) concepts is critical to trustworthy machine learning systems, it is natural to ask which inputs from the model's original training set were most important for learning a concept at a given layer. To answer this, we combine data attribution methods with methods for probing the concepts learned by a model. Training network and probe ensembles for two concept datasets on a range of network layers, we use the recently developed TRAK method for large-scale data attribution. We find some evidence for convergence, where removing the 10,000 top attributing images for a concept and retraining the model does not change the location of the concept in the network nor the probing sparsity of the concept. This suggests that rather than being highly dependent on a few specific examples, the features that inform the development of a concept are spread in a more diffuse manner across its exemplars, implying robustness in concept formation.

ICML 2023 Topological Deep Learning Challenge : Design and Results

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

SCITUNE: Aligning Large Language Models with Scientific Multimodal Instructions

Instruction finetuning is a popular paradigm to align large language models (LLM) with human intent. Despite its popularity, this idea is less explored in improving the LLMs to align existing foundation models with scientific disciplines, concepts and goals. In this work, we present SciTune as a tuning framework to improve the ability of LLMs to follow scientific multimodal instructions. To test our methodology, we use a human-generated scientific instruction tuning dataset and train a large multimodal model LLaMA-SciTune that connects a vision encoder and LLM for science-focused visual and language understanding. In comparison to the models that are finetuned with machine generated data only, LLaMA-SciTune surpasses human performance on average and in many sub-categories on the ScienceQA benchmark.

ColMix -- A Simple Data Augmentation Framework to Improve Object Detector Performance and Robustness in Aerial Images

In the last decade, Convolutional Neural Network (CNN) and transformer based object detectors have achieved high performance on a large variety of datasets. Though the majority of detection literature has developed this capability on datasets such as MS COCO, these detectors have still proven effective for remote sensing applications. Challenges in this particular domain, such as small numbers of annotated objects and low object density, hinder overall performance. In this work, we present a novel augmentation method, called collage pasting, for increasing the object density without a need for segmentation masks, thereby improving the detector performance. We demonstrate that collage pasting improves precision and recall beyond related methods, such as mosaic augmentation, and enables greater control of object density. However, we find that collage pasting is vulnerable to certain out-of-distribution shifts, such as image corruptions. To address this, we introduce two simple approaches for combining collage pasting with PixMix augmentation method, and refer to our combined techniques as ColMix. Through extensive experiments, we show that employing ColMix results in detectors with superior performance on aerial imagery datasets and robust to various corruptions.

How many dimensions are required to find an adversarial example?

Past work exploring adversarial vulnerability have focused on situations where an adversary can perturb all dimensions of model input. On the other hand, a range of recent works consider the case where either (i) an adversary can perturb a limited number of input parameters or (ii) a subset of modalities in a multimodal problem. In both of these cases, adversarial examples are effectively constrained to a subspace $V$ in the ambient input space $\mathcal{X}$. Motivated by this, in this work we investigate how adversarial vulnerability depends on $\dim(V)$. In particular, we show that the adversarial success of standard PGD attacks with $\ell^p$ norm constraints behaves like a monotonically increasing function of $\epsilon (\frac{\dim(V)}{\dim \mathcal{X}})^{\frac{1}{q}}$ where $\epsilon$ is the perturbation budget and $\frac{1}{p} + \frac{1}{q} =1$, provided $p > 1$ (the case $p=1$ presents additional subtleties which we analyze in some detail). This functional form can be easily derived from a simple toy linear model, and as such our results land further credence to arguments that adversarial examples are endemic to locally linear models on high dimensional spaces.

Fast computation of permutation equivariant layers with the partition algebra

Linear neural network layers that are either equivariant or invariant to permutations of their inputs form core building blocks of modern deep learning architectures. Examples include the layers of DeepSets, as well as linear layers occurring in attention blocks of transformers and some graph neural networks. The space of permutation equivariant linear layers can be identified as the invariant subspace of a certain symmetric group representation, and recent work parameterized this space by exhibiting a basis whose vectors are sums over orbits of standard basis elements with respect to the symmetric group action. A parameterization opens up the possibility of learning the weights of permutation equivariant linear layers via gradient descent. The space of permutation equivariant linear layers is a generalization of the partition algebra, an object first discovered in statistical physics with deep connections to the representation theory of the symmetric group, and the basis described above generalizes the so-called orbit basis of the partition algebra. We exhibit an alternative basis, generalizing the diagram basis of the partition algebra, with computational benefits stemming from the fact that the tensors making up the basis are low rank in the sense that they naturally factorize into Kronecker products. Just as multiplication by a rank one matrix is far less expensive than multiplication by an arbitrary matrix, multiplication with these low rank tensors is far less expensive than multiplication with elements of the orbit basis. Finally, we describe an algorithm implementing multiplication with these basis elements.

Robustness of edited neural networks

Successful deployment in uncertain, real-world environments requires that deep learning models can be efficiently and reliably modified in order to adapt to unexpected issues. However, the current trend toward ever-larger models makes standard retraining procedures an ever-more expensive burden. For this reason, there is growing interest in model editing, which enables computationally inexpensive, interpretable, post-hoc model modifications. While many model editing techniques are promising, research on the properties of edited models is largely limited to evaluation of validation accuracy. The robustness of edited models is an important and yet mostly unexplored topic. In this paper, we employ recently developed techniques from the field of deep learning robustness to investigate both how model editing affects the general robustness of a model, as well as the robustness of the specific behavior targeted by the edit. We find that edits tend to reduce general robustness, but that the degree of degradation depends on the editing algorithm chosen. In particular, robustness is best preserved by more constrained techniques that modify less of the model. Motivated by these observations, we introduce two new model editing algorithms, direct low-rank model editing and 1-layer interpolation (1-LI), which each exhibit strong generalization performance.

Exploring the Representation Manifolds of Stable Diffusion Through the Lens of Intrinsic Dimension

Prompting has become an important mechanism by which users can more effectively interact with many flavors of foundation model. Indeed, the last several years have shown that well-honed prompts can sometimes unlock emergent capabilities within such models. While there has been a substantial amount of empirical exploration of prompting within the community, relatively few works have studied prompting at a mathematical level. In this work we aim to take a first step towards understanding basic geometric properties induced by prompts in Stable Diffusion, focusing on the intrinsic dimension of internal representations within the model. We find that choice of prompt has a substantial impact on the intrinsic dimension of representations at both layers of the model which we explored, but that the nature of this impact depends on the layer being considered. For example, in certain bottleneck layers of the model, intrinsic dimension of representations is correlated with prompt perplexity (measured using a surrogate model), while this correlation is not apparent in the latent layers. Our evidence suggests that intrinsic dimension could be a useful tool for future studies of the impact of different prompts on text-to-image models.