Soheil Kolouri

Soroush Abbasi Koohpayegani, KL Navaneet, Parsa Nooralinejad et al.

Fine-tuning Large Language Models (LLMs) and storing them for each downstream task or domain is impractical because of the massive model size (e.g., 350GB in GPT-3). Current literature, such as LoRA, showcases the potential of low-rank modifications to the original weights of an LLM, enabling efficient adaptation and storage for task-specific models. These methods can reduce the number of parameters needed to fine-tune an LLM by several orders of magnitude. Yet, these methods face two primary limitations: (1) the parameter count is lower-bounded by the rank one decomposition, and (2) the extent of reduction is heavily influenced by both the model architecture and the chosen rank. We introduce NOLA, which overcomes the rank one lower bound present in LoRA. It achieves this by re-parameterizing the low-rank matrices in LoRA using linear combinations of randomly generated matrices (basis) and optimizing the linear mixture coefficients only. This approach allows us to decouple the number of trainable parameters from both the choice of rank and the network architecture. We present adaptation results using GPT-2, LLaMA-2, and ViT in natural language and computer vision tasks. NOLA performs as well as LoRA models with much fewer number of parameters compared to LoRA with rank one, the best compression LoRA can archive. Particularly, on LLaMA-2 70B, our method is almost 20 times more compact than the most compressed LoRA without degradation in accuracy. Our code is available here: https://github.com/UCDvision/NOLA

Abihith Kothapalli, Ashkan Shahbazi, Xinran Liu et al.

Learning from set-structured data, such as point clouds, has gained significant attention from the machine learning community. Geometric deep learning provides a blueprint for designing effective set neural networks that preserve the permutation symmetry of set-structured data. Of our interest are permutation invariant networks, which are composed of a permutation equivariant backbone, permutation invariant global pooling, and regression/classification head. While existing literature has focused on improving equivariant backbones, the impact of the pooling layer is often overlooked. In this paper, we examine the interplay between permutation equivariant backbones and permutation invariant global pooling on three benchmark point cloud classification datasets. Our findings reveal that: 1) complex pooling methods, such as transport-based or attention-based poolings, can significantly boost the performance of simple backbones, but the benefits diminish for more complex backbones, 2) even complex backbones can benefit from pooling layers in low data scenarios, 3) surprisingly, the choice of pooling layers can have a more significant impact on the model's performance than adjusting the width and depth of the backbone, and 4) pairwise combination of pooling layers can significantly improve the performance of a fixed backbone. Our comprehensive study provides insights for practitioners to design better permutation invariant set neural networks. Our code is available at https://github.com/mint-vu/backbone_vs_pooling.

Megan M. Baker, Alexander New, Mario Aguilar-Simon et al.

Despite the advancement of machine learning techniques in recent years, state-of-the-art systems lack robustness to "real world" events, where the input distributions and tasks encountered by the deployed systems will not be limited to the original training context, and systems will instead need to adapt to novel distributions and tasks while deployed. This critical gap may be addressed through the development of "Lifelong Learning" systems that are capable of 1) Continuous Learning, 2) Transfer and Adaptation, and 3) Scalability. Unfortunately, efforts to improve these capabilities are typically treated as distinct areas of research that are assessed independently, without regard to the impact of each separate capability on other aspects of the system. We instead propose a holistic approach, using a suite of metrics and an evaluation framework to assess Lifelong Learning in a principled way that is agnostic to specific domains or system techniques. Through five case studies, we show that this suite of metrics can inform the development of varied and complex Lifelong Learning systems. We highlight how the proposed suite of metrics quantifies performance trade-offs present during Lifelong Learning system development - both the widely discussed Stability-Plasticity dilemma and the newly proposed relationship between Sample Efficient and Robust Learning. Further, we make recommendations for the formulation and use of metrics to guide the continuing development of Lifelong Learning systems and assess their progress in the future.

Yuzhe Lu, Zhenlin Wang, Runtian Zhai et al.

Out-of-distribution (OOD) data poses serious challenges in deployed machine learning models as even subtle changes could incur significant performance drops. Being able to estimate a model's performance on test data is important in practice as it indicates when to trust to model's decisions. We present a simple yet effective method to predict a model's performance on an unknown distribution without any addition annotation. Our approach is rooted in the Optimal Transport theory, viewing test samples' output softmax scores from deep neural networks as empirical samples from an unknown distribution. We show that our method, Confidence Optimal Transport (COT), provides robust estimates of a model's performance on a target domain. Despite its simplicity, our method achieves state-of-the-art results on three benchmark datasets and outperforms existing methods by a large margin.

Parsa Nooralinejad, Ali Abbasi, Soroush Abbasi Koohpayegani et al.

We demonstrate that a deep model can be reparametrized as a linear combination of several randomly initialized and frozen deep models in the weight space. During training, we seek local minima that reside within the subspace spanned by these random models (i.e., `basis' networks). Our framework, PRANC, enables significant compaction of a deep model. The model can be reconstructed using a single scalar `seed,' employed to generate the pseudo-random `basis' networks, together with the learned linear mixture coefficients. In practical applications, PRANC addresses the challenge of efficiently storing and communicating deep models, a common bottleneck in several scenarios, including multi-agent learning, continual learners, federated systems, and edge devices, among others. In this study, we employ PRANC to condense image classification models and compress images by compacting their associated implicit neural networks. PRANC outperforms baselines with a large margin on image classification when compressing a deep model almost $100$ times. Moreover, we show that PRANC enables memory-efficient inference by generating layer-wise weights on the fly. The source code of PRANC is here: \url{https://github.com/UCDvision/PRANC}

Farbod Davoodi, Seyed Reza Tavakoli Shiyadeh, Pooria Safaei et al.

Text-to-Image (TTI) systems are now everyday infrastructure for journalism, education, advertising, and public communication, and the demographic and cultural stereotypes they inherit from training data (rendering women, people of colour, older adults, and non-Western cultures as under-represented or caricatured) become a population-level harm at deployment scale. Existing mitigations either require costly retraining, infeasible for the closed-source backbones that dominate consumer products, or rely on fixed demographic templates that ignore cultural context. We present KG-FairDiff, a model-agnostic, inference-time framework that formalises fairness-aware prompt refinement as a constrained optimisation problem and operationalises it as a closed-loop pipeline: a knowledge graph of ~1,200 culture- and bias-related triples retrieves structured context, an LLM rewriter proposes refinements, and a validator accepts only prompts that reduce a divergence-based fairness loss while preserving semantic fidelity to the user's original intent. We prove a finite-termination bound for the refinement loop, contribute a mathematically consistent evaluation suite linking Bias-P/Bias-W to divergence from target distributions and ENS to KL divergence, and audit eight widely-deployed backbone generators. KG-FairDiff substantially reduces gender, race, age, and intersectional disparities while preserving prompt semantics, offering a practical, deployment-ready route to more equitable generative AI.

Xinran Liu, Yikun Bai, Yuzhe Lu et al.

Measuring similarities between different tasks is critical in a broad spectrum of machine learning problems, including transfer, multi-task, continual, and meta-learning. Most current approaches to measuring task similarities are architecture-dependent: 1) relying on pre-trained models, or 2) training networks on tasks and using forward transfer as a proxy for task similarity. In this paper, we leverage the optimal transport theory and define a novel task embedding for supervised classification that is model-agnostic, training-free, and capable of handling (partially) disjoint label sets. In short, given a dataset with ground-truth labels, we perform a label embedding through multi-dimensional scaling and concatenate dataset samples with their corresponding label embeddings. Then, we define the distance between two datasets as the 2-Wasserstein distance between their updated samples. Lastly, we leverage the 2-Wasserstein embedding framework to embed tasks into a vector space in which the Euclidean distance between the embedded points approximates the proposed 2-Wasserstein distance between tasks. We show that the proposed embedding leads to a significantly faster comparison of tasks compared to related approaches like the Optimal Transport Dataset Distance (OTDD). Furthermore, we demonstrate the effectiveness of our proposed embedding through various numerical experiments and show statistically significant correlations between our proposed distance and the forward and backward transfer between tasks.

Ali Abbasi, Parsa Nooralinejad, Vladimir Braverman et al.

Continual/lifelong learning from a non-stationary input data stream is a cornerstone of intelligence. Despite their phenomenal performance in a wide variety of applications, deep neural networks are prone to forgetting their previously learned information upon learning new ones. This phenomenon is called "catastrophic forgetting" and is deeply rooted in the stability-plasticity dilemma. Overcoming catastrophic forgetting in deep neural networks has become an active field of research in recent years. In particular, gradient projection-based methods have recently shown exceptional performance at overcoming catastrophic forgetting. This paper proposes two biologically-inspired mechanisms based on sparsity and heterogeneous dropout that significantly increase a continual learner's performance over a long sequence of tasks. Our proposed approach builds on the Gradient Projection Memory (GPM) framework. We leverage k-winner activations in each layer of a neural network to enforce layer-wise sparse activations for each task, together with a between-task heterogeneous dropout that encourages the network to use non-overlapping activation patterns between different tasks. In addition, we introduce two new benchmarks for continual learning under distributional shift, namely Continual Swiss Roll and ImageNet SuperDog-40. Lastly, we provide an in-depth analysis of our proposed method and demonstrate a significant performance boost on various benchmark continual learning problems.

Eseoghene Ben-Iwhiwhu, Saptarshi Nath, Praveen K. Pilly et al.

Lifelong learning aims to create AI systems that continuously and incrementally learn during a lifetime, similar to biological learning. Attempts so far have met problems, including catastrophic forgetting, interference among tasks, and the inability to exploit previous knowledge. While considerable research has focused on learning multiple supervised classification tasks that involve changes in the input distribution, lifelong reinforcement learning (LRL) must deal with variations in the state and transition distributions, and in the reward functions. Modulating masks with a fixed backbone network, recently developed for classification, are particularly suitable to deal with such a large spectrum of task variations. In this paper, we adapted modulating masks to work with deep LRL, specifically PPO and IMPALA agents. The comparison with LRL baselines in both discrete and continuous RL tasks shows superior performance. We further investigated the use of a linear combination of previously learned masks to exploit previous knowledge when learning new tasks: not only is learning faster, the algorithm solves tasks that we could not otherwise solve from scratch due to extremely sparse rewards. The results suggest that RL with modulating masks is a promising approach to lifelong learning, to the composition of knowledge to learn increasingly complex tasks, and to knowledge reuse for efficient and faster learning.

Yikun Bai, Berhnard Schmitzer, Mathew Thorpe et al.

Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its application. Optimal Partial Transport (OPT) is a recently proposed solution to this limitation. Similar to the OT problem, the computation of OPT relies on solving a linear programming problem (often in high dimensions), which can become computationally prohibitive. In this paper, we propose an efficient algorithm for calculating the OPT problem between two non-negative measures in one dimension. Next, following the idea of sliced OT distances, we utilize slicing to define the sliced OPT distance. Finally, we demonstrate the computational and accuracy benefits of the sliced OPT-based method in various numerical experiments. In particular, we show an application of our proposed Sliced-OPT in noisy point cloud registration.

Zihao Wu, Huy Tran, Hamed Pirsiavash et al.

Continual and multi-task learning are common machine learning approaches to learning from multiple tasks. The existing works in the literature often assume multi-task learning as a sensible performance upper bound for various continual learning algorithms. While this assumption is empirically verified for different continual learning benchmarks, it is not rigorously justified. Moreover, it is imaginable that when learning from multiple tasks, a small subset of these tasks could behave as adversarial tasks reducing the overall learning performance in a multi-task setting. In contrast, continual learning approaches can avoid the performance drop caused by such adversarial tasks to preserve their performance on the rest of the tasks, leading to better performance than a multi-task learner. This paper proposes a novel continual self-supervised learning setting, where each task corresponds to learning an invariant representation for a specific class of data augmentations. In this setting, we show that continual learning often beats multi-task learning on various benchmark datasets, including MNIST, CIFAR-10, and CIFAR-100.

Yikun Bai, Ivan Medri, Rocio Diaz Martin et al.

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed. In this paper, we propose the Linear optimal partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem. The proposed embedding allows for faster computation of OPT distance between pairs of positive measures. Besides our theoretical contributions, we demonstrate the LOPT embedding technique in point-cloud interpolation and PCA analysis.

Ali Abbasi, Parsa Nooralinejad, Hamed Pirsiavash et al.

Continual learning has gained substantial attention within the deep learning community, offering promising solutions to the challenging problem of sequential learning. Yet, a largely unexplored facet of this paradigm is its susceptibility to adversarial attacks, especially with the aim of inducing forgetting. In this paper, we introduce "BrainWash," a novel data poisoning method tailored to impose forgetting on a continual learner. By adding the BrainWash noise to a variety of baselines, we demonstrate how a trained continual learner can be induced to forget its previously learned tasks catastrophically, even when using these continual learning baselines. An important feature of our approach is that the attacker requires no access to previous tasks' data and is armed merely with the model's current parameters and the data belonging to the most recent task. Our extensive experiments highlight the efficacy of BrainWash, showcasing degradation in performance across various regularization-based continual learning methods.

Ali Abbasi, Chayne Thrash, Elaheh Akbari et al.

The rapid progress of AI, combined with its unprecedented public adoption and the propensity of large neural networks to memorize training data, has given rise to significant data privacy concerns. To address these concerns, machine unlearning has emerged as an essential technique to selectively remove the influence of specific training data points on trained models. In this paper, we approach the machine unlearning problem through the lens of continual learning. Given a trained model and a subset of training data designated to be forgotten (i.e., the "forget set"), we introduce a three-step process, named CovarNav, to facilitate this forgetting. Firstly, we derive a proxy for the model's training data using a model inversion attack. Secondly, we mislabel the forget set by selecting the most probable class that deviates from the actual ground truth. Lastly, we deploy a gradient projection method to minimize the cross-entropy loss on the modified forget set (i.e., learn incorrect labels for this set) while preventing forgetting of the inverted samples. We rigorously evaluate CovarNav on the CIFAR-10 and Vggface2 datasets, comparing our results with recent benchmarks in the field and demonstrating the efficacy of our proposed approach.

Ali Abbasi, Chayne Thrash, Haoran Qin et al.

Large language models deliver strong performance across language and reasoning tasks, but their storage and compute costs remain major barriers to deployment in resource-constrained and latency-sensitive settings. SVD-based post-training compression offers a hardware-agnostic way to reduce model size and improve inference efficiency through low-rank factorization. However, existing methods often rely on input-only whitening spaces, homogeneous rank allocation, or loss-agnostic allocation heuristics, limiting their ability to preserve model quality under aggressive compression. We propose Input-Output Whitened SVD (IO-SVD), a post-training compression method that forms a KL-aware double-sided whitening space for model weights. Using a second-order expansion of the KL loss over the top-K token probabilities, IO-SVD constructs an output-side metric that captures predictive sensitivity, while input whitening captures activation statistics. We further introduce an efficient heterogeneous rank-allocation strategy that scores whitened singular components using first-order calibration loss estimates and prunes the least sensitive components under a global budget. Inspired by prior work that combines SVD truncation with quantization, we improve hybrid SVD-quantization compression through loss-aware remapping, which selects low-rank factor rows for 8-bit quantization based on the predicted loss change incurred by quantizing them. Extensive experiments across diverse LLM and VLM families, and inference-time analysis shows that IO-SVD compresses LLMs with minimal performance degradation while delivering practical inference speedups. Code is available at https://github.com/mint-vu/IO-SVD.git

Yikun Bai, Huy Tran, Steven B. Damelin et al.

Point cloud registration plays a crucial role in various fields, including robotics, computer graphics, and medical imaging. This process involves determining spatial relationships between different sets of points, typically within a 3D space. In real-world scenarios, complexities arise from non-rigid movements and partial visibility, such as occlusions or sensor noise, making non-rigid registration a challenging problem. Classic non-rigid registration methods are often computationally demanding, suffer from unstable performance, and, importantly, have limited theoretical guarantees. The optimal transport problem and its unbalanced variations (e.g., the optimal partial transport problem) have emerged as powerful tools for point-cloud registration, establishing a strong benchmark in this field. These methods view point clouds as empirical measures and provide a mathematically rigorous way to quantify the `correspondence' between (the transformed) source and target points. In this paper, we approach the point-cloud registration problem through the lens of optimal transport theory and first propose a comprehensive set of non-rigid registration methods based on the optimal partial transportation problem. Subsequently, leveraging the emerging work on efficient solutions to the one-dimensional optimal partial transport problem, we extend our proposed algorithms via slicing to gain significant computational efficiency, resulting in fast and robust non-rigid registration algorithms. We demonstrate the effectiveness of our proposed methods and compare them against baselines on various 3D and 2D non-rigid registration problems where the source and target point clouds are corrupted by random noise.

Andrea Soltoggio, Eseoghene Ben-Iwhiwhu, Christos Peridis et al.

This paper introduces a set of formally defined and transparent problems for reinforcement learning algorithms with the following characteristics: (1) variable degrees of observability (non-Markov observations), (2) distal and sparse rewards, (3) variable and hierarchical reward structure, (4) multiple-task generation, (5) variable problem complexity. The environment provides 1D or 2D categorical observations, and takes actions as input. The core structure of the CT-graph is a multi-branch tree graph with arbitrary branching factor, depth, and observation sets that can be varied to increase the dimensions of the problem in a controllable and measurable way. Two main categories of states, decision states and wait states, are devised to create a hierarchy of importance among observations, typical of real-world problems. A large observation set can produce a vast set of histories that impairs memory-augmented agents. Variable reward functions allow for the easy creation of multiple tasks and the ability of an agent to efficiently adapt in dynamic scenarios where tasks with controllable degrees of similarities are presented. Challenging complexity levels can be easily achieved due to the exponential growth of the graph. The problem formulation and accompanying code provide a fast, transparent, and mathematically defined set of configurable tests to compare the performance of reinforcement learning algorithms, in particular in lifelong learning settings.

Xinran Liu, Yikun Bai, Huy Tran et al.

Optimal transport and its related problems, including optimal partial transport, have proven to be valuable tools in machine learning for computing meaningful distances between probability or positive measures. This success has led to a growing interest in defining transport-based distances that allow for comparing signed measures and, more generally, multi-channeled signals. Transport $\mathrm{L}^{p}$ distances are notable extensions of the optimal transport framework to signed and possibly multi-channeled signals. In this paper, we introduce partial transport $\mathrm{L}^{p}$ distances as a new family of metrics for comparing generic signals, benefiting from the robustness of partial transport distances. We provide theoretical background such as the existence of optimal plans and the behavior of the distance in various limits. Furthermore, we introduce the sliced variation of these distances, which allows for rapid comparison of generic signals. Finally, we demonstrate the application of the proposed distances in signal class separability and nearest neighbor classification.

Haoran Qin, Shansita Sharma, Ali Abbasi et al.

Low-rank approximation methods such as singular value decomposition (SVD) and its variants (e.g., Fisher-weighted SVD, Activation SVD) have recently emerged as effective tools for neural network compression. In this setting, decomposition acts as a "surgical" intervention, followed by fine-tuning that serves as "rehab" to recover accuracy. Inspired by prehabilitation in surgery, we introduce a pre-compression fine-tuning stage, Low-Rank Prehab, that explicitly encourages low-rank structure in weight matrices while preserving task performance. By conditioning the model before SVD, Prehab steers weights toward spectrally compact regions of the parameter space, enabling smoother low-rank approximation and improved recovery. Experiments on large language models (LLMs) and other Transformer-based architectures, including Vision Transformers (ViTs), show that Prehab substantially reduces the immediate accuracy drop after compression and consistently improves post-finetuning performance. Across a wide range of compression ratios, our method outperforms state-of-the-art SVD-based techniques such as SVD-LLM, highlighting the importance of preparing models for compression rather than only improving the compression and recovery stages. Source code is available at https://github.com/niqretnuh/PREHAB-SVD

Rocio Diaz Martin, Ivan Medri, Yikun Bai et al.

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e., probability measures supported on the unit circle, and introduce a new computationally efficient metric for these measures, denoted as Linear Circular Optimal Transport (LCOT). The proposed metric comes with an explicit linear embedding that allows one to apply Machine Learning (ML) algorithms to the embedded measures and seamlessly modify the underlying metric for the ML algorithm to LCOT. We show that the proposed metric is rooted in the Circular Optimal Transport (COT) and can be considered the linearization of the COT metric with respect to a fixed reference measure. We provide a theoretical analysis of the proposed metric and derive the computational complexities for pairwise comparison of circular probability measures. Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations of circular measures.

Ashkan Shahbazi, Ping He, Ali Abbasi et al.

Scaling attention faces a critical bottleneck: the $\mathcal{O}(n^2)$ quadratic computational cost of softmax attention, which limits its application in long-sequence domains. While linear attention mechanisms reduce this cost to $\mathcal{O}(n)$, they typically rely on fixed random feature maps, such as random Fourier features or hand-crafted functions. This reliance on static, data-agnostic kernels creates a fundamental trade-off, forcing practitioners to sacrifice significant model accuracy for computational efficiency. We introduce \textsc{LUNA}, a kernelized linear attention mechanism that eliminates this trade-off, retaining linear cost while matching and surpassing the accuracy of quadratic attention. \textsc{LUNA} is built on the key insight that the kernel feature map itself should be learned rather than fixed a priori. By parameterizing the kernel, \textsc{LUNA} learns a feature basis tailored to the specific data and task, overcoming the expressive limitations of fixed-feature methods. \textsc{Luna} implements this with a learnable feature map that induces a positive-definite kernel and admits a streaming form, yielding linear time and memory scaling in the sequence length. Empirical evaluations validate our approach across diverse settings. On the Long Range Arena (LRA), \textsc{Luna} achieves state-of-the-art average accuracy among efficient Transformers under compute parity, using the same parameter count, training steps, and approximate FLOPs. \textsc{Luna} also excels at post-hoc conversion: replacing softmax in fine-tuned BERT and ViT-B/16 checkpoints and briefly fine-tuning recovers most of the original performance, substantially outperforming fixed linearizations.

Huy Tran, Yikun Bai, Abihith Kothapalli et al.

Comparing spherical probability distributions is of great interest in various fields, including geology, medical domains, computer vision, and deep representation learning. The utility of optimal transport-based distances, such as the Wasserstein distance, for comparing probability measures has spurred active research in developing computationally efficient variations of these distances for spherical probability measures. This paper introduces a high-speed and highly parallelizable distance for comparing spherical measures using the stereographic projection and the generalized Radon transform, which we refer to as the Stereographic Spherical Sliced Wasserstein (S3W) distance. We carefully address the distance distortion caused by the stereographic projection and provide an extensive theoretical analysis of our proposed metric and its rotationally invariant variation. Finally, we evaluate the performance of the proposed metrics and compare them with recent baselines in terms of both speed and accuracy through a wide range of numerical studies, including gradient flows and self-supervised learning. Our code is available at https://github.com/mint-vu/s3wd.

Navid NaderiAlizadeh, Darian Salehi, Xinran Liu et al.

Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions has proven challenging, often necessitating a large number of slices to achieve desirable performance and thereby increasing computational complexity. We introduce a constrained learning approach to optimize the slicing directions for SW distances. Specifically, we constrain the 1D transport plans to approximate the optimal plan in the original space, ensuring meaningful slicing directions. By leveraging continuous relaxations of these transport plans, we enable a gradient-based primal-dual approach to train the slicer parameters, alongside the remaining model parameters. We demonstrate how this constrained slicing approach can be applied to pool high-dimensional embeddings into fixed-length permutation-invariant representations. Numerical results on foundation models trained on images, point clouds, and protein sequences showcase the efficacy of the proposed constrained learning approach in learning more informative slicing directions. Our implementation code can be found at https://github.com/Stranja572/constrainedswe.

Ashkan Shahbazi, Elaheh Akbari, Darian Salehi et al.

While self-attention has been instrumental in the success of Transformers, it can lead to over-concentration on a few tokens during training, resulting in suboptimal information flow. Enforcing doubly-stochastic constraints in attention matrices has been shown to improve structure and balance in attention distributions. However, existing methods rely on iterative Sinkhorn normalization, which is computationally costly. In this paper, we introduce a novel, fully parallelizable doubly-stochastic attention mechanism based on sliced optimal transport, leveraging Expected Sliced Transport Plans (ESP). Unlike prior approaches, our method enforces doubly stochasticity without iterative Sinkhorn normalization, significantly enhancing efficiency. To ensure differentiability, we incorporate a temperature-based soft sorting technique, enabling seamless integration into deep learning models. Experiments across multiple benchmark datasets, including image classification, point cloud classification, sentiment analysis, and neural machine translation, demonstrate that our enhanced attention regularization consistently improves performance across diverse applications. Our implementation code can be found at https://github.com/dariansal/ESPFormer.

Yikun Bai, Rocio Diaz Martin, Abihith Kothapalli et al.

The Gromov-Wasserstein (GW) distance has gained increasing interest in the machine learning community in recent years, as it allows for the comparison of measures in different metric spaces. To overcome the limitations imposed by the equal mass requirements of the classical GW problem, researchers have begun exploring its application in unbalanced settings. However, Unbalanced GW (UGW) can only be regarded as a discrepancy rather than a rigorous metric/distance between two metric measure spaces (mm-spaces). In this paper, we propose a particular case of the UGW problem, termed Partial Gromov-Wasserstein (PGW). We establish that PGW is a well-defined metric between mm-spaces and discuss its theoretical properties, including the existence of a minimizer for the PGW problem and the relationship between PGW and GW, among others. We then propose two variants of the Frank-Wolfe algorithm for solving the PGW problem and show that they are mathematically and computationally equivalent. Moreover, based on our PGW metric, we introduce the analogous concept of barycenters for mm-spaces. Finally, we validate the effectiveness of our PGW metric and related solvers in applications such as shape matching, shape retrieval, and shape interpolation, comparing them against existing baselines. Our code is available at https://github.com/mint-vu/PGW_Metric.

Ali Abbasi, Chayne Thrash, Haoran Qin et al.

Advances in large language models have driven strong performance across many tasks, but their memory and compute costs still hinder deployment. SVD-based compression reduces storage and can speed up inference via low-rank factors, yet performance depends on how rank is allocated under a global compression ratio. Prior methods often use homogeneous ranks for similarly sized matrices, despite large differences in loss sensitivity, or rely on expensive iterative pre-truncation optimization to determine per matrix ranks. We propose \textbf{Zero Sum SVD} (\textbf{ZS-SVD}), a post-training method that performs \emph{global} singular component selection using activation whitening and first-order calibration loss estimates in whitened coordinates. \textbf{ZS-SVD} prunes components across the whole model with a \textbf{zero sum} rule that keeps the cumulative predicted loss change near zero, automatically yielding heterogeneous ranks without solving a rank allocation optimization. Motivated by evidence that gradients near pretrained solutions exhibit low rank structure, we also introduce an optional lightweight correction that applies a \textbf{single} projected gradient update after truncation, followed by re-truncation. Extensive experiments across multiple LLM architectures show consistent gains across diverse benchmarks and compression ratios. Code is available at https://github.com/mint-vu/Zero-Sum-SVD

Ashkan Shahbazi, Xinran Liu, Ping He et al.

We propose min Generalized Sliced Gromov--Wasserstein (min-GSGW), a sliced formulation for the Gromov--Wasserstein (GW) problem using expressive generalized slicers. The key idea is to learn coupled nonlinear slicers that assign compatible push-forward values to both input measures, so that monotone coupling in the projected domain lifts to a transport plan evaluated against the GW objective in the original spaces. The resulting plan induces a GW objective value, and min-GSGW minimizes this cost directly in the original spaces. We further show that min-GSGW is rigid-motion invariant, a crucial property for geometric matching and shape analysis tasks. Our contributions are threefold: 1) we introduce generalized slicers into the sliced GW framework, 2) we construct a slicing-based efficient GW transport plan; and 3) we develop an amortized variant that replaces per-instance optimization with a learned slicer for unseen input pairs. We perform experiments on animal mesh matching, horse mesh interpolation, and ShapeNet part transfer. Results show that min-GSGW produces meaningful geometric correspondences and GW objective values at substantially lower computational cost than existing GW solvers.

Ali Abbasi, Ashkan Shahbazi, Hamed Pirsiavash et al.

Dataset distillation is an emerging technique for reducing the computational and storage costs of training machine learning models by synthesizing a small, informative subset of data that captures the essential characteristics of a much larger dataset. Recent methods pair synthetic samples and their augmentations with soft labels from a teacher model, enabling student models to generalize effectively despite the small size of the distilled dataset. While soft labels are critical for effective distillation, the storage and communication overhead they incur, especially when accounting for augmentations, is often overlooked. In practice, each distilled sample is associated with multiple soft labels, making them the dominant contributor to storage costs, particularly in large-class settings such as ImageNet-1K. In this paper, we present a rigorous analysis of bit requirements across dataset distillation frameworks, quantifying the storage demands of both distilled samples and their soft labels. To address the overhead, we introduce a vector-quantized autoencoder (VQAE) for compressing soft labels, achieving substantial compression while preserving the effectiveness of the distilled data. We validate our method on both vision and language distillation benchmarks. On ImageNet-1K, our proposed VQAE achieves 30--40x additional compression over RDED, LPLD, SRE2L, and CDA baselines while retaining over $90\%$ of their original performance.

Chayne Thrash, Ali Abbasi, Soheil Kolouri

Large language models (LLMs) are costly to deploy due to their large memory footprint and high inference cost. Weight-activation quantization can reduce these costs, but low-bit activation quantization remains difficult because activation outliers induce large quantization error. Recent rotation-based methods address this by applying orthogonal transformations that redistribute activation magnitude across dimensions, but existing approaches either require expensive end-to-end rotation training or rely on stored activation corpora, introducing significant compute or storage overhead. We propose a lightweight post-training rotation calibration method for LLM activation quantization. Our method learns orthogonal rotations that align normalized activations with the corners of an inscribed hypercube, encouraging activation energy to be distributed more evenly across dimensions. This objective admits an efficient closed-form update via the orthogonal Procrustes problem, avoiding gradient-based optimization over the orthogonal group. We further introduce an online calibration procedure that updates rotations as calibration samples are processed, eliminating the need to store activations on disk and allowing rotations to adapt to quantized activation distributions during calibration. Experiments on Llama-2 and Llama-3 models from 3B to 70B parameters show that our method achieves competitive or improved performance across perplexity benchmarks and common sense reasoning tasks while avoiding both costly end-to-end training and large offline activation storage.

Chayne Thrash, Ali Abbasi, Reed Andreas et al.

The outstanding performance of large foundational models across diverse tasks, from computer vision to speech and natural language processing, has significantly increased their demand. However, storing and transmitting these models poses significant challenges due to their massive size (e.g., 750GB for Llama 3.1 405B). Recent literature has focused on compressing the original weights or reducing the number of parameters required for fine-tuning these models. These compression methods generally constrain the parameter space, for example, through low-rank reparametrization (e.g., LoRA), pruning, or quantization (e.g., QLoRA) during or after the model training. In this paper, we present a novel model compression method, which we term Manifold-Constrained Neural Compression (MCNC). This method constrains the parameter space to low-dimensional pre-defined and frozen nonlinear manifolds, which effectively cover this space. Given the prevalence of good solutions in over-parameterized deep neural networks, we show that by constraining the parameter space to our proposed manifold, we can identify high-quality solutions while achieving unprecedented compression rates across a wide variety of tasks and architectures. Through extensive experiments in computer vision and natural language processing tasks, we demonstrate that our method significantly outperforms state-of-the-art baselines in terms of compression, accuracy, and/or model reconstruction time. Our code is publicly available at https://github.com/mint-vu/MCNC.

Yikun Bai, Abihith Kothapalli, Hengrong Du et al.

The Gromov-Wasserstein (GW) problem, a variant of the classical optimal transport (OT) problem, has attracted growing interest in the machine learning and data science communities due to its ability to quantify similarity between measures in different metric spaces. However, like the classical OT problem, GW imposes an equal mass constraint between measures, which restricts its application in many machine learning tasks. To address this limitation, the partial Gromov-Wasserstein (PGW) problem has been introduced. It relaxes the equal mass constraint, allowing the comparison of general positive Radon measures. Despite this, both GW and PGW face significant computational challenges due to their non-convex nature. To overcome these challenges, we propose the linear partial Gromov-Wasserstein (LPGW) embedding, a linearized embedding technique for the PGW problem. For $K$ different metric measure spaces, the pairwise computation of the PGW distance requires solving the PGW problem ${O}(K^2)$ times. In contrast, the proposed linearization technique reduces this to ${O}(K)$ times. Similar to the linearization technique for the classical OT problem, we prove that LPGW defines a valid metric for metric measure spaces. Finally, we demonstrate the effectiveness of LPGW in practical applications such as shape retrieval and learning with transport-based embeddings, showing that LPGW preserves the advantages of PGW in partial matching while significantly enhancing computational efficiency. The code is available at https://github.com/mint-vu/Linearized_Partial_Gromov_Wasserstein.

Yuzhe Lu, Xinran Liu, Andrea Soltoggio et al.

Learning from set-structured data is an essential problem with many applications in machine learning and computer vision. This paper focuses on non-parametric and data-independent learning from set-structured data using approximate nearest neighbor (ANN) solutions, particularly locality-sensitive hashing. We consider the problem of set retrieval from an input set query. Such retrieval problem requires: 1) an efficient mechanism to calculate the distances/dissimilarities between sets, and 2) an appropriate data structure for fast nearest neighbor search. To that end, we propose Sliced-Wasserstein set embedding as a computationally efficient "set-2-vector" mechanism that enables downstream ANN, with theoretical guarantees. The set elements are treated as samples from an unknown underlying distribution, and the Sliced-Wasserstein distance is used to compare sets. We demonstrate the effectiveness of our algorithm, denoted as Set-LOcality Sensitive Hashing (SLOSH), on various set retrieval datasets and compare our proposed embedding with standard set embedding approaches, including Generalized Mean (GeM) embedding/pooling, Featurewise Sort Pooling (FSPool), and Covariance Pooling and show consistent improvement in retrieval results. The code for replicating our results is available here: \href{https://github.com/mint-vu/SLOSH}{https://github.com/mint-vu/SLOSH}.

Soheil Kolouri, Navid Naderializadeh, Gustavo K. Rohde et al.

We present Wasserstein Embedding for Graph Learning (WEGL), a novel and fast framework for embedding entire graphs in a vector space, in which various machine learning models are applicable for graph-level prediction tasks. We leverage new insights on defining similarity between graphs as a function of the similarity between their node embedding distributions. Specifically, we use the Wasserstein distance to measure the dissimilarity between node embeddings of different graphs. Unlike prior work, we avoid pairwise calculation of distances between graphs and reduce the computational complexity from quadratic to linear in the number of graphs. WEGL calculates Monge maps from a reference distribution to each node embedding and, based on these maps, creates a fixed-sized vector representation of the graph. We evaluate our new graph embedding approach on various benchmark graph-property prediction tasks, showing state-of-the-art classification performance while having superior computational efficiency. The code is available at https://github.com/navid-naderi/WEGL.

Mohammad Shifat-E-Rabbi, Xuwang Yin, Abu Hasnat Mohammad Rubaiyat et al.

We present a new supervised image classification method applicable to a broad class of image deformation models. The method makes use of the previously described Radon Cumulative Distribution Transform (R-CDT) for image data, whose mathematical properties are exploited to express the image data in a form that is more suitable for machine learning. While certain operations such as translation, scaling, and higher-order transformations are challenging to model in native image space, we show the R-CDT can capture some of these variations and thus render the associated image classification problems easier to solve. The method -- utilizing a nearest-subspace algorithm in R-CDT space -- is simple to implement, non-iterative, has no hyper-parameters to tune, is computationally efficient, label efficient, and provides competitive accuracies to state-of-the-art neural networks for many types of classification problems. In addition to the test accuracy performances, we show improvements (with respect to neural network-based methods) in terms of computational efficiency (it can be implemented without the use of GPUs), number of training samples needed for training, as well as out-of-distribution generalization. The Python code for reproducing our results is available at https://github.com/rohdelab/rcdt_ns_classifier.

Ping He, Om Khangaonkar, Hamed Pirsiavash et al.

We establish a theoretical link between the recently proposed "drifting" generative dynamics and gradient flows induced by the Sinkhorn divergence. In a particle discretization, the drift field admits a cross-minus-self decomposition: an attractive term toward the target distribution and a repulsive/self-correction term toward the current model, both expressed via one-sided normalized Gibbs kernels. We show that Sinkhorn divergence yields an analogous cross-minus-self structure, but with each term defined by entropic optimal-transport couplings obtained through two-sided Sinkhorn scaling (i.e., enforcing both marginals). This provides a precise sense in which drifting acts as a surrogate for a Sinkhorn-divergence gradient flow, interpolating between one-sided normalization and full two-sided Sinkhorn scaling. Crucially, this connection resolves an identifiability gap in prior drifting formulations: leveraging the definiteness of the Sinkhorn divergence, we show that zero drift (equilibrium of the dynamics) implies that the model and target measures match. Experiments show that Sinkhorn drifting reduces sensitivity to kernel temperature and improves one-step generative quality, trading off additional training time for a more stable optimization, without altering the inference procedure used by drift methods. These theoretical gains translate to strong low-temperature improvements in practice: on FFHQ-ALAE at the lowest temperature setting we evaluate, Sinkhorn drifting reduces mean FID from 187.7 to 37.1 and mean latent EMD from 453.3 to 144.4, while on MNIST it preserves full class coverage across the temperature sweep. Project page: https://mint-vu.github.io/SinkhornDrifting/

Luyang Fang, Xiaowei Yu, Jiazhang Cai et al.

The exponential growth of Large Language Models (LLMs) continues to highlight the need for efficient strategies to meet ever-expanding computational and data demands. This survey provides a comprehensive analysis of two complementary paradigms: Knowledge Distillation (KD) and Dataset Distillation (DD), both aimed at compressing LLMs while preserving their advanced reasoning capabilities and linguistic diversity. We first examine key methodologies in KD, such as task-specific alignment, rationale-based training, and multi-teacher frameworks, alongside DD techniques that synthesize compact, high-impact datasets through optimization-based gradient matching, latent space regularization, and generative synthesis. Building on these foundations, we explore how integrating KD and DD can produce more effective and scalable compression strategies. Together, these approaches address persistent challenges in model scalability, architectural heterogeneity, and the preservation of emergent LLM abilities. We further highlight applications across domains such as healthcare and education, where distillation enables efficient deployment without sacrificing performance. Despite substantial progress, open challenges remain in preserving emergent reasoning and linguistic diversity, enabling efficient adaptation to continually evolving teacher models and datasets, and establishing comprehensive evaluation protocols. By synthesizing methodological innovations, theoretical foundations, and practical insights, our survey charts a path toward sustainable, resource-efficient LLMs through the tighter integration of KD and DD principles.

Xinran Liu, Rocío Díaz Martín, Yikun Bai et al.

The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between probability measures. To reduce the computational complexity of OT solvers, methods like entropic regularization and sliced optimal transport have been proposed. The sliced OT framework improves efficiency by comparing one-dimensional projections (slices) of high-dimensional distributions. However, despite their computational efficiency, sliced-Wasserstein approaches lack a transportation plan between the input measures, limiting their use in scenarios requiring explicit coupling. In this paper, we address two key questions: Can a transportation plan be constructed between two probability measures using the sliced transport framework? If so, can this plan be used to define a metric between the measures? We propose a "lifting" operation to extend one-dimensional optimal transport plans back to the original space of the measures. By computing the expectation of these lifted plans, we derive a new transportation plan, termed expected sliced transport (EST) plans. We prove that using the EST plan to weight the sum of the individual Euclidean costs for moving from one point to another results in a valid metric between the input discrete probability measures. We demonstrate the connection between our approach and the recently proposed min-SWGG, along with illustrative numerical examples that support our theoretical findings.

Ali Abbasi, Ashkan Shahbazi, Hamed Pirsiavash et al.

The extensive amounts of data required for training deep neural networks pose significant challenges on storage and transmission fronts. Dataset distillation has emerged as a promising technique to condense the information of massive datasets into a much smaller yet representative set of synthetic samples. However, traditional dataset distillation approaches often struggle to scale effectively with high-resolution images and more complex architectures due to the limitations in bi-level optimization. Recently, several works have proposed exploiting knowledge distillation with decoupled optimization schemes to scale up dataset distillation. Although these methods effectively address the scalability issue, they rely on extensive image augmentations requiring the storage of soft labels for augmented images. In this paper, we introduce Dataset Distillation using Diffusion Models (D3M) as a novel paradigm for dataset distillation, leveraging recent advancements in generative text-to-image foundation models. Our approach utilizes textual inversion, a technique for fine-tuning text-to-image generative models, to create concise and informative representations for large datasets. By employing these learned text prompts, we can efficiently store and infer new samples for introducing data variability within a fixed memory budget. We show the effectiveness of our method through extensive experiments across various computer vision benchmark datasets with different memory budgets.

Yikun Bai, Shuang Wang, Huy Tran et al.

Structured data, such as graphs, is vital in machine learning due to its capacity to capture complex relationships and interactions. In recent years, the Fused Gromov-Wasserstein (FGW) distance has attracted growing interest because it enables the comparison of structured data by jointly accounting for feature similarity and geometric structure. However, as a variant of optimal transport (OT), classical FGW assumes an equal mass constraint on the compared data. In this work, we relax this mass constraint and propose the Fused Partial Gromov-Wasserstein (FPGW) framework, which extends FGW to accommodate unbalanced data. Theoretically, we establish the relationship between FPGW and FGW and prove the metric properties of FPGW. Numerically, we introduce Frank-Wolfe solvers and Sinkhorn solvers for the proposed FPGW framework. Finally, we evaluate the FPGW distance through graph matching, graph classification and graph clustering experiments, demonstrating its robust performance.

Xinran Liu, Yikun Bai, Rocío Díaz Martín et al.

Efficient comparison of spherical probability distributions becomes important in fields such as computer vision, geosciences, and medicine. Sliced optimal transport distances, such as spherical and stereographic spherical sliced Wasserstein distances, have recently been developed to address this need. These methods reduce the computational burden of optimal transport by slicing hyperspheres into one-dimensional projections, i.e., lines or circles. Concurrently, linear optimal transport has been proposed to embed distributions into \( L^2 \) spaces, where the \( L^2 \) distance approximates the optimal transport distance, thereby simplifying comparisons across multiple distributions. In this work, we introduce the Linear Spherical Sliced Optimal Transport (LSSOT) framework, which utilizes slicing to embed spherical distributions into \( L^2 \) spaces while preserving their intrinsic geometry, offering a computationally efficient metric for spherical probability measures. We establish the metricity of LSSOT and demonstrate its superior computational efficiency in applications such as cortical surface registration, 3D point cloud interpolation via gradient flow, and shape embedding. Our results demonstrate the significant computational benefits and high accuracy of LSSOT in these applications.

Mingxing Rao, Yinhong Qin, Soheil Kolouri et al.

Purpose: In order to produce a surgical gesture recognition system that can support a wide variety of procedures, either a very large annotated dataset must be acquired, or fitted models must generalize to new labels (so called "zero-shot" capability). In this paper we investigate the feasibility of latter option. Methods: Leveraging the Bridge-Prompt framework, we prompt-tune a pre-trained vision-text model (CLIP) for gesture recognition in surgical videos. This can utilize extensive outside video data such as text, but also make use of label meta-data and weakly supervised contrastive losses. Results: Our experiments show that prompt-based video encoder outperforms standard encoders in surgical gesture recognition tasks. Notably, it displays strong performance in zero-shot scenarios, where gestures/tasks that were not provided during the encoder training phase are included in the prediction phase. Additionally, we measure the benefit of inclusion text descriptions in the feature extractor training schema. Conclusion Bridge-Prompt and similar pre-trained+prompt-tuned video encoder models present significant visual representation for surgical robotics, especially in gesture recognition tasks. Given the diverse range of surgical tasks (gestures), the ability of these models to zero-shot transfer without the need for any task (gesture) specific retraining makes them invaluable.

Ashkan Shahbazi, Chayne Thrash, Yikun Bai et al.

Transformers have proven highly effective across a wide range of modalities. However, the quadratic complexity of the standard softmax attention mechanism poses a fundamental barrier to scaling them to long context windows. A large body of work addresses this with linear attention, which reformulates attention as a kernel function and approximates it with finite feature maps to achieve linear-time computation. Orthogonal to computational scaling, most attention mechanisms -- both quadratic and linear -- produce row-normalized maps that can over-focus on a few tokens, degrading robustness and information flow. Enforcing doubly-stochastic attention alleviates this by balancing token participation across rows and columns, but existing doubly-stochastic attention mechanisms typically introduce substantial overhead, undermining scalability. We propose LOTFormer, a principled attention mechanism that is simultaneously linear-time and doubly-stochastic. Our approach exploits the connection between attention maps and transportation plans between query and key measures. The central idea is to constrain the transport plan to be low-rank by conditioning it on a learnable pivot measure with small support. Concretely, we solve two entropic optimal transport problems (queries $\to$ pivot and pivot $\to$ keys) and compose them into a conditional (glued) coupling. This yields an attention matrix that is provably doubly-stochastic, has rank at most $r \ll n$, and applies to values in $O(nr)$ time without forming the full $n \times n$ map. The pivot locations and masses are learned end-to-end. Empirically, LOTFormer achieves state-of-the-art results on the Long Range Arena benchmark, surpassing prior linear and transport-based attention methods in both accuracy and efficiency.

Ali Abbasi, Shima Imani, Chenyang An et al.

With the rapid scaling of neural networks, data storage and communication demands have intensified. Dataset distillation has emerged as a promising solution, condensing information from extensive datasets into a compact set of synthetic samples by solving a bilevel optimization problem. However, current methods face challenges in computational efficiency, particularly with high-resolution data and complex architectures. Recently, knowledge-distillation-based dataset condensation approaches have made this process more computationally feasible. Yet, with the recent developments of generative foundation models, there is now an opportunity to achieve even greater compression, enhance the quality of distilled data, and introduce valuable diversity into the data representation. In this work, we propose a two-stage solution. First, we compress the dataset by selecting only the most informative patches to form a coreset. Next, we leverage a generative foundation model to dynamically expand this compressed set in real-time, enhancing the resolution of these patches and introducing controlled variability to the coreset. Our extensive experiments demonstrate the robustness and efficiency of our approach across a range of dataset distillation benchmarks. We demonstrate a significant improvement of over 10% compared to the state-of-the-art on several large-scale dataset distillation benchmarks. The code will be released soon.

Huy Tran, Yikun Bai, Ashkan Shahbazi et al.

The practical applications of Wasserstein distances (WDs) are constrained by their sample and computational complexities. Sliced-Wasserstein distances (SWDs) provide a workaround by projecting distributions onto one-dimensional subspaces, leveraging the more efficient, closed-form WDs for one-dimensional distributions. However, in high dimensions, most random projections become uninformative due to the concentration of measure phenomenon. Although several SWD variants have been proposed to focus on \textit{informative} slices, they often introduce additional complexity, numerical instability, and compromise desirable theoretical (metric) properties of SWD. Amidst the growing literature that focuses on directly modifying the slicing distribution, which often face challenges, we revisit the classical Sliced-Wasserstein and propose instead to rescale the 1D Wasserstein to make all slices equally informative. Importantly, we show that with an appropriate data assumption and notion of \textit{slice informativeness}, rescaling for all individual slices simplifies to \textbf{a single global scaling factor} on the SWD. This, in turn, translates to the standard learning rate search for gradient-based learning in common machine learning workflows. We perform extensive experiments across various machine learning tasks showing that the classical SWD, when properly configured, can often match or surpass the performance of more complex variants. We then answer the following question: "Is Sliced-Wasserstein all you need for common learning tasks?"

Ashkan Shahbazi, Elaheh Akbari, Kyvia Pereira et al.

We introduce SurgFormer, a multiresolution gated transformer for data driven soft tissue simulation on volumetric meshes. High fidelity biomechanical solvers are often too costly for interactive use, so we train SurgFormer on solver generated data to predict nodewise displacement fields at near real time rates. SurgFormer builds a fixed mesh hierarchy and applies repeated multibranch blocks that combine local message passing, coarse global self attention, and pointwise feedforward updates, fused by learned per node, per channel gates to adaptively integrate local and long range information while remaining scalable on large meshes. For cut conditioned simulation, resection information is encoded as a learned cut embedding and provided as an additional input, enabling a unified model for both standard deformation prediction and topology altering cases. We also introduce two surgical simulation datasets generated under a unified protocol with XFEM based supervision: a cholecystectomy resection dataset and an appendectomy manipulation and resection dataset with cut and uncut cases. To our knowledge, this is the first learned volumetric surrogate setting to study XFEM supervised cut conditioned deformation within the same volumetric pipeline as standard deformation prediction. Across diverse baselines, SurgFormer achieves strong accuracy with favorable efficiency, making it a practical backbone for both tasks. {Code, data, and project page: \href{https://mint-vu.github.io/SurgFormer/}{available here}}

Xinran Liu, Elaheh Akbari, Rocio Diaz Martin et al.

Optimal Transport (OT) offers a powerful framework for finding correspondences between distributions and addressing matching and alignment problems in various areas of computer vision, including shape analysis, image generation, and multimodal tasks. The computation cost of OT, however, hinders its scalability. Slice-based transport plans have recently shown promise for reducing the computational cost by leveraging the closed-form solutions of 1D OT problems. These methods optimize a one-dimensional projection (slice) to obtain a conditional transport plan that minimizes the transport cost in the ambient space. While efficient, these methods leave open the question of whether learned optimal slicers can transfer to new distribution pairs under distributional shift. Understanding this transferability is crucial in settings with evolving data or repeated OT computations across closely related distributions. In this paper, we study the min-Sliced Transport Plan (min-STP) framework and investigate the transferability of optimized slicers: can a slicer trained on one distribution pair yield effective transport plans for new, unseen pairs? Theoretically, we show that optimized slicers remain close under slight perturbations of the data distributions, enabling efficient transfer across related tasks. To further improve scalability, we introduce a minibatch formulation of min-STP and provide statistical guarantees on its accuracy. Empirically, we demonstrate that the transferable min-STP achieves strong one-shot matching performance and facilitates amortized training for point cloud alignment and flow-based generative modeling.

Elaheh Akbari, Ping He, Ahmadreza Moradipari et al.

Flow-matching generative models have emerged as a powerful paradigm for continuous data generation, achieving state-of-the-art results across domains such as images, 3D shapes, and point clouds. Despite their success, these models suffer from slow inference due to the requirement of numerous sequential sampling steps. Recent work has sought to accelerate inference by reducing the number of sampling steps. In particular, Mean Flows offer a one-step generation approach that delivers substantial speedups while retaining strong generative performance. Yet, in many continuous domains, Mean Flows fail to faithfully approximate the behavior of the original multi-step flow-matching process. In this work, we address this limitation by incorporating optimal transport-based sampling strategies into the Mean Flow framework, enabling one-step generators that better preserve the fidelity and diversity of the original multi-step flow process. Experiments on controlled low-dimensional settings and on high-dimensional tasks such as image generation, image-to-image translation, and point cloud generation demonstrate that our approach achieves superior inference accuracy in one-step generative modeling.

Xinran Liu, Shansita D. Sharma, Soheil Kolouri

We introduce EMPEROR (Efficient Moment-Preserving Representation of Distributions), a mathematically rigorous and computationally efficient framework for representing high-dimensional probability measures arising in neural network representations. Unlike heuristic global pooling operations, EMPEROR encodes a feature distribution through its statistical moments. Our approach leverages the theory of sliced moments: features are projected onto multiple directions, lightweight univariate Gaussian mixture models (GMMs) are fit to each projection, and the resulting slice parameters are aggregated into a compact descriptor. We establish determinacy guarantees via Carleman's condition and the Cramér-Wold theorem, ensuring that the GMM is uniquely determined by its sliced moments, and we derive finite-sample error bounds that scale optimally with the number of slices and samples. Empirically, EMPEROR captures richer distributional information than common pooling schemes across various data modalities, while remaining computationally efficient and broadly applicable.

Saptarshi Nath, Christos Peridis, Eseoghene Benjamin et al.

Agentic AI aims to create systems that set their own goals, adapt proactively to change, and refine behavior through continuous experience. Recent advances suggest that, when facing multiple and unforeseen tasks, agents could benefit from sharing machine-learned knowledge and reusing policies that have already been fully or partially learned by other agents. However, how to query, select, and retrieve policies from a pool of agents, and how to integrate such policies remains a largely unexplored area. This study explores how an agent decides what knowledge to select, from whom, and when and how to integrate it in its own policy in order to accelerate its own learning. The proposed algorithm, \emph{Modular Sharing and Composition in Collective Learning} (MOSAIC), improves learning in agentic collectives by combining (1) knowledge selection using performance signals and cosine similarity on Wasserstein task embeddings, (2) modular and transferable neural representations via masks, and (3) policy integration, composition and fine-tuning. MOSAIC outperforms isolated learners and global sharing approaches in both learning speed and overall performance, and in some cases solves tasks that isolated agents cannot. The results also demonstrate that selective, goal-driven reuse leads to less susceptibility to task interference. We also observe the emergence of self-organization, where agents solving simpler tasks accelerate the learning of harder ones through shared knowledge.

Yuzhe Lu, Yilong Qin, Runtian Zhai et al.

Out-of-distribution (OOD) data poses serious challenges in deployed machine learning models, so methods of predicting a model's performance on OOD data without labels are important for machine learning safety. While a number of methods have been proposed by prior work, they often underestimate the actual error, sometimes by a large margin, which greatly impacts their applicability to real tasks. In this work, we identify pseudo-label shift, or the difference between the predicted and true OOD label distributions, as a key indicator to this underestimation. Based on this observation, we introduce a novel method for estimating model performance by leveraging optimal transport theory, Confidence Optimal Transport (COT), and show that it provably provides more robust error estimates in the presence of pseudo-label shift. Additionally, we introduce an empirically-motivated variant of COT, Confidence Optimal Transport with Thresholding (COTT), which applies thresholding to the individual transport costs and further improves the accuracy of COT's error estimates. We evaluate COT and COTT on a variety of standard benchmarks that induce various types of distribution shift -- synthetic, novel subpopulation, and natural -- and show that our approaches significantly outperform existing state-of-the-art methods with an up to 3x lower prediction error.