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This thesis will address the fusion of multiple data sources arising in remote sensing, such as hyperspectral and LIDAR. Fusing of multiple data sources provides better data representation and classification results than any of the independent data sources would alone. We begin our investigation with the well-studied Laplacian Eigenmap (LE) algorithm. This algorithm offers a rich template to which fusion concepts can be added. For each phase of the LE algorithm (graph, operator, and feature space) we develop and test different data fusion techniques. We also investigate how partially labeled data and approximate LE preimages can used to achieve data fusion. Lastly, we study several numerical acceleration techniques that can be used to augment the developed algorithms, namely the Nystrom extension, Random Projections, and Approximate Neighborhood constructions. The Nyström extension is studied in detail and the application of Frame Theory and Sigma-Delta Quantization is proposed to enrich the Nyström extension.

Machine unlearning (MU) is a promising cost-effective method to cleanse undesired information (generated concepts, biases, or patterns) from foundational diffusion models. While MU is orders of magnitude less costly than retraining a diffusion model without the undesired information, it can be challenging and labor-intensive to prove that the information has been fully removed from the model. Moreover, MU can damage diffusion model performance on surrounding concepts that one would like to retain, making it unclear if the diffusion model is still fit for deployment. We introduce autoeval-dmun, an automated tool which leverages (vision-) language models to thoroughly assess unlearning in diffusion models. Given a target concept, autoeval-dmun extracts structured, relevant world knowledge from the language model to identify nearby concepts which are likely damaged by unlearning and to circumvent unlearning with adversarial prompts. We use our automated tool to evaluate popular diffusion model unlearning methods, revealing that language models (1) impose semantic orderings of nearby concepts which correlate well with unlearning damage and (2) effectively circumvent unlearning with synthetic adversarial prompts.

Collecting high quality data for object detection tasks is challenging due to the inherent subjectivity in labeling the boundaries of an object. This makes it difficult to not only collect consistent annotations across a dataset but also to validate them, as no two annotators are likely to label the same object using the exact same coordinates. These challenges are further compounded when object boundaries are partially visible or blurred, which can be the case in many domains. Training on noisy annotations significantly degrades detector performance, rendering them unusable, particularly in few-shot settings, where just a few corrupted annotations can impact model performance. In this work, we propose FMG-Det, a simple, efficient methodology for training models with noisy annotations. More specifically, we propose combining a multiple instance learning (MIL) framework with a pre-processing pipeline that leverages powerful foundation models to correct labels prior to training. This pre-processing pipeline, along with slight modifications to the detector head, results in state-of-the-art performance across a number of datasets, for both standard and few-shot scenarios, while being much simpler and more efficient than other approaches.

Hyperspectral measurements from long range sensors can give a detailed picture of the items, materials, and chemicals in a scene but analysis can be difficult, slow, and expensive due to high spatial and spectral resolutions of state-of-the-art sensors. As such, sparsity is important to enable the future of spectral compression and analytics. It has been observed that environmental and atmospheric effects, including scattering, can produce nonlinear effects posing challenges for existing source separation and compression methods. We present a novel transformation into Hilbert spaces for pruning and constructing sparse representations via non-negative least squares minimization. Then we introduce max likelihood compression vectors to decrease information loss. Our approach is benchmarked against standard pruning and least squares as well as deep learning methods. Our methods are evaluated in terms of overall spectral reconstruction error and compression rate using real and synthetic data. We find that pruning least squares methods converge quickly unlike matching pursuit methods. We find that Hilbert space pruning can reduce error by as much as 40% of the error of standard pruning and also outperform neural network autoencoders.

We present a framework for inferring an atmospheric transmission profile from a spectral scene. This framework leverages a lightweight, physics-based simulator that is automatically tuned - by virtue of autodifferentiation and differentiable programming - to construct a surrogate atmospheric profile to model the observed data. We demonstrate utility of the methodology by (i) performing atmospheric correction, (ii) recasting spectral data between various modalities (e.g. radiance and reflectance at the surface and at the sensor), and (iii) inferring atmospheric transmission profiles, such as absorbing bands and their relative magnitudes.

Score-based generative models require guidance in order to generate plausible, on-manifold samples. The most popular guidance method, Classifier-Free Guidance (CFG), is only applicable in settings with labeled data and requires training an additional unconditional score-based model. More recently, Auto-Guidance adopts a smaller, less capable version of the original model to guide generation. While each method effectively promotes the fidelity of generated data, each requires labeled data or the training of additional models, making it challenging to guide score-based models when (labeled) training data are not available or training new models is not feasible. We make the surprising discovery that the positive curvature of log density estimates in saddle regions provides strong guidance for score-based models. Motivated by this, we develop saddle-free guidance (SFG) which maintains estimates of maximal positive curvature of the log density to guide individual score-based models. SFG has the same computational cost of classifier-free guidance, does not require additional training, and works with off-the-shelf diffusion and flow matching models. Our experiments indicate that SFG achieves state-of-the-art FID and FD-DINOv2 metrics in single-model unconditional ImageNet-512 generation. When SFG is combined with Auto-Guidance, its unconditional samples achieve general state-of-the-art in FD-DINOv2 score. Our experiments with FLUX.1-dev and Stable Diffusion v3.5 indicate that SFG boosts the diversity of output images compared to CFG while maintaining excellent prompt adherence and image fidelity.

The local intrinsic dimension (LID) of data is a fundamental quantity in signal processing and learning theory, but quantifying the LID of high-dimensional, complex data has been a historically challenging task. Recent works have discovered that diffusion models capture the LID of data through the spectra of their score estimates and through the rate of change of their density estimates under various noise perturbations. While these methods can accurately quantify LID, they require either many forward passes of the diffusion model or use of gradient computation, limiting their applicability in compute- and memory-constrained scenarios. We show that the LID is a lower bound on the denoising score matching loss, motivating use of the denoising score matching loss as a LID estimator. Moreover, we show that the equivalent implicit score matching loss also approximates LID via the normal dimension and is closely related to a recent LID estimator, FLIPD. Our experiments on a manifold benchmark and with Stable Diffusion 3.5 indicate that the denoising score matching loss is a highly competitive and scalable LID estimator, achieving superior accuracy and memory footprint under increasing problem size and quantization level.

Multimodal large language models (MLLMs) have altered the landscape of computer vision, obtaining impressive results across a wide range of tasks, especially in zero-shot settings. Unfortunately, their strong performance does not always transfer to out-of-distribution domains, such as earth observation (EO) imagery. Prior work has demonstrated that MLLMs excel at some EO tasks, such as image captioning and scene understanding, while failing at tasks that require more fine-grained spatial reasoning, such as object localization. However, MLLMs are advancing rapidly and insights quickly become out-dated. In this work, we analyze more recent MLLMs that have been explicitly trained to include fine-grained spatial reasoning capabilities, benchmarking them on EO object localization tasks. We demonstrate that these models are performant in certain settings, making them well suited for zero-shot scenarios. Additionally, we provide a detailed discussion focused on prompt selection, ground sample distance (GSD) optimization, and analyzing failure cases. We hope that this work will prove valuable as others evaluate whether an MLLM is well suited for a given EO localization task and how to optimize it.

To create usable and deployable Artificial Intelligence (AI) systems, there requires a level of assurance in performance under many different conditions. Many times, deployed machine learning systems will require more classic logic and reasoning performed through neurosymbolic programs jointly with artificial neural network sensing. While many prior works have examined the assurance of a single component of the system solely with either the neural network alone or entire enterprise systems, very few works have examined the assurance of integrated neurosymbolic systems. Within this work, we assess the assurance of end-to-end fully differentiable neurosymbolic systems that are an emerging method to create data-efficient and more interpretable models. We perform this investigation using Scallop, an end-to-end neurosymbolic library, across classification and reasoning tasks in both the image and audio domains. We assess assurance across adversarial robustness, calibration, user performance parity, and interpretability of solutions for catching misaligned solutions. We find end-to-end neurosymbolic methods present unique opportunities for assurance beyond their data efficiency through our empirical results but not across the board. We find that this class of neurosymbolic models has higher assurance in cases where arithmetic operations are defined and where there is high dimensionality to the input space, where fully neural counterparts struggle to learn robust reasoning operations. We identify the relationship between neurosymbolic models' interpretability to catch shortcuts that later result in increased adversarial vulnerability despite performance parity. Finally, we find that the promise of data efficiency is typically only in the case of class imbalanced reasoning problems.

We present a sensor-agnostic spectral transformer as the basis for spectral foundation models. To that end, we introduce a Universal Spectral Representation (USR) that leverages sensor meta-data, such as sensing kernel specifications and sensing wavelengths, to encode spectra obtained from any spectral instrument into a common representation, such that a single model can ingest data from any sensor. Furthermore, we develop a methodology for pre-training such models in a self-supervised manner using a novel random sensor-augmentation and reconstruction pipeline to learn spectral features independent of the sensing paradigm. We demonstrate that our architecture can learn sensor independent spectral features that generalize effectively to sensors not seen during training. This work sets the stage for training foundation models that can both leverage and be effective for the growing diversity of spectral data.