Derya Cansever

Bo Jiang, Hamid Krim, Tianfu Wu et al.

The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability distributions by some optimal metric, has been creatively exploited and shown to hold promise for many real-world data challenges. In a related theme in the present work, we posit that domain adaptation robustness is rooted in the intrinsic (latent) representations of the respective data, which are inherently lying in a non-linear submanifold embedded in a higher dimensional Euclidean space. We account for the geometric properties by refining the $l^2$ Euclidean metric to better reflect the geodesic distance between two distinct representations. We integrate a metric correction term as well as a prior cluster structure in the source data of the OT-driven adaptation. We show that this is tantamount to an implicit Bayesian framework, which we demonstrate to be viable for a more robust and better-performing approach to domain adaptation. Substantiating experiments are also included for validation purposes.

Qian Zhang, Sadie Zhao, Lucy Diao et al.

Coincident Peak (CP) pricing is widely used in U.S. electricity markets to allocate capacity and transmission costs. This paper develops a behavioral game-theoretic framework for CP-driven load shifting that couples a nonlinear cost-allocation model with day-ahead (one-shot) and real-time (sequential-learning) decision processes. We examine two update rules, namely best-response dynamics (BRD) and fictitious-play dynamics (FPD), across continuous and finite action spaces to quantify how flexibility, action resolution, and participation influence peak outcomes. Using ERCOT peak-day data, we find that FPD reliably reduces system peaks, whereas BRD is more variable and can increase peaks under tight-capacity conditions. Finer action resolution improves peak shaving, while the number of participants is largely neutral when aggregate flexibility is fixed. Meanwhile, information-provider signals can induce herding, whereas response-aware or diverse signals improve peak shaving. These results highlight both the potential and limits of CP pricing: smoothing information and enabling granular control are as important as the amount of available flexibility. The framework offers practical guidance for system operators and consumers: For ISOs, broadcasting smoothed CP signals and setting minimum controllable-capacity thresholds enhance coordination. For consumers, greater flexibility and finer control resolution improve both cost savings and peak-shaving performance.

Yuyang Zhang, Derya Cansever, Na Li

This paper focuses on learning efficient sensor allocations that ensure observability of unknown high-dimensional linear systems using only a small number of sensors. Existing methods either require an impractically large number of sensors or assume access to an observable allocation in advance. We propose a two-stage framework that overcomes these limitations: first, a novel system identification algorithm integrates information from multiple trajectories, each observing different subsets of state coordinates; then, a classic sensor allocation method is adapted to operate on the learned system parameters. Our non-asymptotic guarantees show that the proposed approach learns a sensor allocation with a near-optimal number of sensors when sensors can be allocated on any state coordinate. We further extend the results to settings with inaccessible state coordinates that are unavailable for sensor allocation.

Vahid Jebraeeli, Bo Jiang, Derya Cansever et al.

In the era of big data, the sheer volume and complexity of datasets pose significant challenges in machine learning, particularly in image processing tasks. This paper introduces an innovative Autoencoder-based Dataset Condensation Model backed by Koopman operator theory that effectively packs large datasets into compact, information-rich representations. Inspired by the predictive coding mechanisms of the human brain, our model leverages a novel approach to encode and reconstruct data, maintaining essential features and label distributions. The condensation process utilizes an autoencoder neural network architecture, coupled with Optimal Transport theory and Wasserstein distance, to minimize the distributional discrepancies between the original and synthesized datasets. We present a two-stage implementation strategy: first, condensing the large dataset into a smaller synthesized subset; second, evaluating the synthesized data by training a classifier and comparing its performance with a classifier trained on an equivalent subset of the original data. Our experimental results demonstrate that the classifiers trained on condensed data exhibit comparable performance to those trained on the original datasets, thus affirming the efficacy of our condensation model. This work not only contributes to the reduction of computational resources but also paves the way for efficient data handling in constrained environments, marking a significant step forward in data-efficient machine learning.

Vahid Jebraeeli, Hamid Krim, Derya Cansever

Vision Transformer (ViT) based autoencoders often underutilize the global Class token and employ static attention mechanisms, limiting both generative control and optimization efficiency. This paper introduces ViTCAE, a framework that addresses these issues by re-purposing the Class token into a generative linchpin. In our architecture, the encoder maps the Class token to a global latent variable that dictates the prior distribution for local, patch-level latent variables, establishing a robust dependency where global semantics directly inform the synthesis of local details. Drawing inspiration from opinion dynamics, we treat each attention head as a dynamical system of interacting tokens seeking consensus. This perspective motivates a convergence-aware temperature scheduler that adaptively anneals each head's influence function based on its distributional stability. This process enables a principled head-freezing mechanism, guided by theoretically-grounded diagnostics like an attention evolution distance and a consensus/cluster functional. This technique prunes converged heads during training to significantly improve computational efficiency without sacrificing fidelity. By unifying a generative Class token with an adaptive attention mechanism rooted in multi-agent consensus theory, ViTCAE offers a more efficient and controllable approach to transformer-based generation.

Vahid Jebraeeli, Bo Jiang, Hamid Krim et al.

Limited data availability in machine learning significantly impacts performance and generalization. Traditional augmentation methods enhance moderately sufficient datasets. GANs struggle with convergence when generating diverse samples. Diffusion models, while effective, have high computational costs. We introduce an Expansive Synthesis model generating large-scale, information-rich datasets from minimal samples. It uses expander graph mappings and feature interpolation to preserve data distribution and feature relationships. The model leverages neural networks' non-linear latent space, captured by a Koopman operator, to create a linear feature space for dataset expansion. An autoencoder with self-attention layers and optimal transport refines distributional consistency. We validate by comparing classifiers trained on generated data to those trained on original datasets. Results show comparable performance, demonstrating the model's potential to augment training data effectively. This work advances data generation, addressing scarcity in machine learning applications.

Bo Jiang, Hamid Krim, Tianfu Wu et al.

We introduce in this paper a new statistical perspective, exploiting the Jaccard similarity metric, as a measure-based metric to effectively invoke non-linear features in the loss of self-supervised contrastive learning. Specifically, our proposed metric may be interpreted as a dependence measure between two adapted projections learned from the so-called latent representations. This is in contrast to the cosine similarity measure in the conventional contrastive learning model, which accounts for correlation information. To the best of our knowledge, this effectively non-linearly fused information embedded in the Jaccard similarity, is novel to self-supervision learning with promising results. The proposed approach is compared to two state-of-the-art self-supervised contrastive learning methods on three image datasets. We not only demonstrate its amenable applicability in current ML problems, but also its improved performance and training efficiency.