arXiv subjects

Mark Hamilton

Publications and source records attributed to Mark Hamilton.

At least 19 recordsLinked to original sources

arXiv2026

MathNet: a Global Multimodal Benchmark for Mathematical Reasoning and Retrieval

Mathematical problem solving remains a challenging test of reasoning for large language and multimodal models, yet existing benchmarks are limited in size, language coverage, and task diversity. We introduce MathNet, a high-quality, large-scale, multimodal, and multilingual dataset of Olympiad-level math problems together with a benchmark for evaluating mathematical reasoning in generative models and mathematical retrieval in embedding-based systems. MathNet spans 47 countries, 17 languages, and two decades of competitions, comprising 30,676 expert-authored problems with solutions across diverse domains. In addition to the core dataset, we construct a retrieval benchmark consisting of mathematically equivalent and structurally similar problem pairs curated by human experts. MathNet supports three tasks: (i) Problem Solving, (ii) Math-Aware Retrieval, and (iii) Retrieval-Augmented Problem Solving. Experimental results show that even state-of-the-art reasoning models (78.4% for Gemini-3.1-Pro and 69.3% for GPT-5) remain challenged, while embedding models struggle to retrieve equivalent problems. We further show that retrieval-augmented generation performance is highly sensitive to retrieval quality; for example, DeepSeek-V3.2-Speciale achieves gains of up to 12%, obtaining the highest scores on the benchmark. MathNet provides the largest high-quality Olympiad dataset together with the first benchmark for evaluating mathematical problem retrieval, and we publicly release both the dataset and benchmark at https://mathnet.mit.edu.

cs.AI↗

arXiv2025

Upsample Anything: A Simple and Hard to Beat Baseline for Feature Upsampling

We present \textbf{Upsample Anything}, a lightweight test-time optimization (TTO) framework that restores low-resolution features to high-resolution, pixel-wise outputs without any training. Although Vision Foundation Models demonstrate strong generalization across diverse downstream tasks, their representations are typically downsampled by 14x/16x (e.g., ViT), which limits their direct use in pixel-level applications. Existing feature upsampling approaches depend on dataset-specific retraining or heavy implicit optimization, restricting scalability and generalization. Upsample Anything addresses these issues through a simple per-image optimization that learns an anisotropic Gaussian kernel combining spatial and range cues, effectively bridging Gaussian Splatting and Joint Bilateral Upsampling. The learned kernel acts as a universal, edge-aware operator that transfers seamlessly across architectures and modalities, enabling precise high-resolution reconstruction of features, depth, or probability maps. It runs in only $\approx0.419 \text{s}$ per 224x224 image and achieves state-of-the-art performance on semantic segmentation, depth estimation, and both depth and probability map upsampling. \textbf{Project page:} \href{https://seominseok0429.github.io/Upsample-Anything/}{https://seominseok0429.github.io/Upsample-Anything/}

cs.CV↗

arXiv2025

Beyond I-Con: Exploring New Dimension of Distance Measures in Representation Learning

The Information Contrastive (I-Con) framework revealed that over 23 representation learning methods implicitly minimize KL divergence between data and learned distributions that encode similarities between data points. However, a KL-based loss may be misaligned with the true objective, and properties of KL divergence such as asymmetry and unboundedness may create optimization challenges. We present Beyond I-Con, a framework that enables systematic discovery of novel loss functions by exploring alternative statistical divergences. Key findings: (1) on unsupervised clustering of DINO-ViT embeddings, we achieve state-of-the-art results by modifying the PMI algorithm to use total variation (TV) distance; (2) supervised contrastive learning with Euclidean distance as the feature space metric is improved by replacing the standard loss function with Jenson-Shannon divergence (JSD); (3) on dimensionality reduction, we achieve superior qualitative results and better performance on downstream tasks than SNE by replacing KL with a bounded $f$-divergence. Our results highlight the importance of considering divergence choices in representation learning optimization.

cs.LG↗

arXiv2025

I-Con: A Unifying Framework for Representation Learning

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of modern loss functions in machine learning. In particular, we introduce a framework that shows that several broad classes of machine learning methods are precisely minimizing an integrated KL divergence between two conditional distributions: the supervisory and learned representations. This viewpoint exposes a hidden information geometry underlying clustering, spectral methods, dimensionality reduction, contrastive learning, and supervised learning. This framework enables the development of new loss functions by combining successful techniques from across the literature. We not only present a wide array of proofs, connecting over 23 different approaches, but we also leverage these theoretical results to create state-of-the-art unsupervised image classifiers that achieve a +8% improvement over the prior state-of-the-art on unsupervised classification on ImageNet-1K. We also demonstrate that I-Con can be used to derive principled debiasing methods which improve contrastive representation learners.

cs.LG↗

arXiv2024

Integral-integral affine geometry, geometric quantization, and Riemann-Roch

We give a simple proof that, for a pre-quantized compact symplectic manifold with a Lagrangian torus fibration, its Riemann-Roch number coincides with its number of Bohr-Sommerfeld fibres. This can be viewed as an instance of the "independence of polarization" phenomenon of geometric quantization. The base space for such a fibration acquires a so-called integral-integral affine structure. The proof uses the following simple fact, whose proof is trickier than we expected: on a compact integral-integral affine manifold, the total volume is equal to the number of integer points.

math.SG↗

arXiv2024

Seeing Faces in Things: A Model and Dataset for Pareidolia

The human visual system is well-tuned to detect faces of all shapes and sizes. While this brings obvious survival advantages, such as a better chance of spotting unknown predators in the bush, it also leads to spurious face detections. ``Face pareidolia'' describes the perception of face-like structure among otherwise random stimuli: seeing faces in coffee stains or clouds in the sky. In this paper, we study face pareidolia from a computer vision perspective. We present an image dataset of ``Faces in Things'', consisting of five thousand web images with human-annotated pareidolic faces. Using this dataset, we examine the extent to which a state-of-the-art human face detector exhibits pareidolia, and find a significant behavioral gap between humans and machines. We find that the evolutionary need for humans to detect animal faces, as well as human faces, may explain some of this gap. Finally, we propose a simple statistical model of pareidolia in images. Through studies on human subjects and our pareidolic face detectors we confirm a key prediction of our model regarding what image conditions are most likely to induce pareidolia. Dataset and Website: https://aka.ms/faces-in-things

cs.CV↗

arXiv2024

Separating the "Chirp" from the "Chat": Self-supervised Visual Grounding of Sound and Language

We present DenseAV, a novel dual encoder grounding architecture that learns high-resolution, semantically meaningful, and audio-visually aligned features solely through watching videos. We show that DenseAV can discover the ``meaning'' of words and the ``location'' of sounds without explicit localization supervision. Furthermore, it automatically discovers and distinguishes between these two types of associations without supervision. We show that DenseAV's localization abilities arise from a new multi-head feature aggregation operator that directly compares dense image and audio representations for contrastive learning. In contrast, many other systems that learn ``global'' audio and video representations cannot localize words and sound. Finally, we contribute two new datasets to improve the evaluation of AV representations through speech and sound prompted semantic segmentation. On these and other datasets we show DenseAV dramatically outperforms the prior art on speech and sound prompted semantic segmentation. DenseAV outperforms the previous state-of-the-art, ImageBind, on cross-modal retrieval using fewer than half of the parameters. Project Page: \href{https://aka.ms/denseav}{https://aka.ms/denseav}

cs.CV↗

arXiv2024

FeatUp: A Model-Agnostic Framework for Features at Any Resolution

Deep features are a cornerstone of computer vision research, capturing image semantics and enabling the community to solve downstream tasks even in the zero- or few-shot regime. However, these features often lack the spatial resolution to directly perform dense prediction tasks like segmentation and depth prediction because models aggressively pool information over large areas. In this work, we introduce FeatUp, a task- and model-agnostic framework to restore lost spatial information in deep features. We introduce two variants of FeatUp: one that guides features with high-resolution signal in a single forward pass, and one that fits an implicit model to a single image to reconstruct features at any resolution. Both approaches use a multi-view consistency loss with deep analogies to NeRFs. Our features retain their original semantics and can be swapped into existing applications to yield resolution and performance gains even without re-training. We show that FeatUp significantly outperforms other feature upsampling and image super-resolution approaches in class activation map generation, transfer learning for segmentation and depth prediction, and end-to-end training for semantic segmentation.

cs.CV↗

arXiv2023

Large-Scale Automatic Audiobook Creation

An audiobook can dramatically improve a work of literature's accessibility and improve reader engagement. However, audiobooks can take hundreds of hours of human effort to create, edit, and publish. In this work, we present a system that can automatically generate high-quality audiobooks from online e-books. In particular, we leverage recent advances in neural text-to-speech to create and release thousands of human-quality, open-license audiobooks from the Project Gutenberg e-book collection. Our method can identify the proper subset of e-book content to read for a wide collection of diversely structured books and can operate on hundreds of books in parallel. Our system allows users to customize an audiobook's speaking speed and style, emotional intonation, and can even match a desired voice using a small amount of sample audio. This work contributed over five thousand open-license audiobooks and an interactive demo that allows users to quickly create their own customized audiobooks. To listen to the audiobook collection visit \url{https://aka.ms/audiobook}.

cs.SD↗

arXiv2023

MultiEarth 2023 -- Multimodal Learning for Earth and Environment Workshop and Challenge

The Multimodal Learning for Earth and Environment Workshop (MultiEarth 2023) is the second annual CVPR workshop aimed at the monitoring and analysis of the health of Earth ecosystems by leveraging the vast amount of remote sensing data that is continuously being collected. The primary objective of this workshop is to bring together the Earth and environmental science communities as well as the multimodal representation learning communities to explore new ways of harnessing technological advancements in support of environmental monitoring. The MultiEarth Workshop also seeks to provide a common benchmark for processing multimodal remote sensing information by organizing public challenges focused on monitoring the Amazon rainforest. These challenges include estimating deforestation, detecting forest fires, translating synthetic aperture radar (SAR) images to the visible domain, and projecting environmental trends. This paper presents the challenge guidelines, datasets, and evaluation metrics. Our challenge website is available at https://sites.google.com/view/rainforest-challenge/multiearth-2023.

cs.CV↗

arXiv2023

Exploring Gender and Race Biases in the NFT Market

Non-Fungible Tokens (NFTs) are non-interchangeable assets, usually digital art, which are stored on the blockchain. Preliminary studies find that female and darker-skinned NFTs are valued less than their male and lighter-skinned counterparts. However, these studies analyze only the CryptoPunks collection. We test the statistical significance of race and gender biases in the prices of CryptoPunks and present the first study of gender bias in the broader NFT market. We find evidence of racial bias but not gender bias. Our work also introduces a dataset of gender-labeled NFT collections to advance the broader study of social equity in this emerging market.

cs.CY↗

arXiv2022

Developing a Series of AI Challenges for the United States Department of the Air Force

Through a series of federal initiatives and orders, the U.S. Government has been making a concerted effort to ensure American leadership in AI. These broad strategy documents have influenced organizations such as the United States Department of the Air Force (DAF). The DAF-MIT AI Accelerator is an initiative between the DAF and MIT to bridge the gap between AI researchers and DAF mission requirements. Several projects supported by the DAF-MIT AI Accelerator are developing public challenge problems that address numerous Federal AI research priorities. These challenges target priorities by making large, AI-ready datasets publicly available, incentivizing open-source solutions, and creating a demand signal for dual use technologies that can stimulate further research. In this article, we describe these public challenges being developed and how their application contributes to scientific advances.

cs.AI↗

arXiv2022

MultiEarth 2022 -- Multimodal Learning for Earth and Environment Workshop and Challenge

The Multimodal Learning for Earth and Environment Challenge (MultiEarth 2022) will be the first competition aimed at the monitoring and analysis of deforestation in the Amazon rainforest at any time and in any weather conditions. The goal of the Challenge is to provide a common benchmark for multimodal information processing and to bring together the earth and environmental science communities as well as multimodal representation learning communities to compare the relative merits of the various multimodal learning methods to deforestation estimation under well-defined and strictly comparable conditions. MultiEarth 2022 will have three sub-challenges: 1) matrix completion, 2) deforestation estimation, and 3) image-to-image translation. This paper presents the challenge guidelines, datasets, and evaluation metrics for the three sub-challenges. Our challenge website is available at https://sites.google.com/view/rainforest-challenge.

cs.CV↗

arXiv2022

Unsupervised Semantic Segmentation by Distilling Feature Correspondences

Unsupervised semantic segmentation aims to discover and localize semantically meaningful categories within image corpora without any form of annotation. To solve this task, algorithms must produce features for every pixel that are both semantically meaningful and compact enough to form distinct clusters. Unlike previous works which achieve this with a single end-to-end framework, we propose to separate feature learning from cluster compactification. Empirically, we show that current unsupervised feature learning frameworks already generate dense features whose correlations are semantically consistent. This observation motivates us to design STEGO ($\textbf{S}$elf-supervised $\textbf{T}$ransformer with $\textbf{E}$nergy-based $\textbf{G}$raph $\textbf{O}$ptimization), a novel framework that distills unsupervised features into high-quality discrete semantic labels. At the core of STEGO is a novel contrastive loss function that encourages features to form compact clusters while preserving their relationships across the corpora. STEGO yields a significant improvement over the prior state of the art, on both the CocoStuff ($\textbf{+14 mIoU}$) and Cityscapes ($\textbf{+9 mIoU}$) semantic segmentation challenges.

cs.CV↗

arXiv2021

Axiomatic Explanations for Visual Search, Retrieval, and Similarity Learning

Visual search, recommendation, and contrastive similarity learning power technologies that impact billions of users worldwide. Modern model architectures can be complex and difficult to interpret, and there are several competing techniques one can use to explain a search engine's behavior. We show that the theory of fair credit assignment provides a $\textit{unique}$ axiomatic solution that generalizes several existing recommendation- and metric-explainability techniques in the literature. Using this formalism, we show when existing approaches violate "fairness" and derive methods that sidestep these shortcomings and naturally handle counterfactual information. More specifically, we show existing approaches implicitly approximate second-order Shapley-Taylor indices and extend CAM, GradCAM, LIME, SHAP, SBSM, and other methods to search engines. These extensions can extract pairwise correspondences between images from trained $\textit{opaque-box}$ models. We also introduce a fast kernel-based method for estimating Shapley-Taylor indices that require orders of magnitude fewer function evaluations to converge. Finally, we show that these game-theoretic measures yield more consistent explanations for image similarity architectures.

cs.LG↗

arXiv2020

Large-Scale Intelligent Microservices

Deploying Machine Learning (ML) algorithms within databases is a challenge due to the varied computational footprints of modern ML algorithms and the myriad of database technologies each with its own restrictive syntax. We introduce an Apache Spark-based micro-service orchestration framework that extends database operations to include web service primitives. Our system can orchestrate web services across hundreds of machines and takes full advantage of cluster, thread, and asynchronous parallelism. Using this framework, we provide large scale clients for intelligent services such as speech, vision, search, anomaly detection, and text analysis. This allows users to integrate ready-to-use intelligence into any datastore with an Apache Spark connector. To eliminate the majority of overhead from network communication, we also introduce a low-latency containerized version of our architecture. Finally, we demonstrate that the services we investigate are competitive on a variety of benchmarks, and present two applications of this framework to create intelligent search engines, and real-time auto race analytics systems.

cs.AI↗

arXiv2020

MosAIc: Finding Artistic Connections across Culture with Conditional Image Retrieval

We introduce MosAIc, an interactive web app that allows users to find pairs of semantically related artworks that span different cultures, media, and millennia. To create this application, we introduce Conditional Image Retrieval (CIR) which combines visual similarity search with user supplied filters or "conditions". This technique allows one to find pairs of similar images that span distinct subsets of the image corpus. We provide a generic way to adapt existing image retrieval data-structures to this new domain and provide theoretical bounds on our approach's efficiency. To quantify the performance of CIR systems, we introduce new datasets for evaluating CIR methods and show that CIR performs non-parametric style transfer. Finally, we demonstrate that our CIR data-structures can identify "blind spots" in Generative Adversarial Networks (GAN) where they fail to properly model the true data distribution.

cs.LG↗

arXiv2020

It Is Likely That Your Loss Should be a Likelihood

Many common loss functions such as mean-squared-error, cross-entropy, and reconstruction loss are unnecessarily rigid. Under a probabilistic interpretation, these common losses correspond to distributions with fixed shapes and scales. We instead argue for optimizing full likelihoods that include parameters like the normal variance and softmax temperature. Joint optimization of these "likelihood parameters" with model parameters can adaptively tune the scales and shapes of losses in addition to the strength of regularization. We explore and systematically evaluate how to parameterize and apply likelihood parameters for robust modeling, outlier-detection, and re-calibration. Additionally, we propose adaptively tuning $L_2$ and $L_1$ weights by fitting the scale parameters of normal and Laplace priors and introduce more flexible element-wise regularizers.

cs.LG↗