Field-programmable gate array (FPGA) is a preferred solution for a CMOS image sensor (CIS) automatic test equipment (ATE) because it provides fast upgradability for the timely testing of CIS products using a new interface protocol. However, implementing a Mobile Industry Processor Interface (MIPI) C-PHY receiver to receive images from the CIS in an FPGA can be challenging due to the use of three wires, three distinct voltage levels, and the requirements of fast clock data recovery (CDR) lock time and wide CDR tracking bandwidth. To overcome these challenges, we have developed an FPGA-only MIPI C-PHY receiver that utilizes a blind oversampling CDR technique, which offers fast CDR lock time and wide CDR bandwidth. We used an Altera Stratix 10 GX FPGA as an oversampling device by operating its transceiver in a lock-to-reference-clock mode. We developed a parallel gate-based clock recovery algorithm and a fork and join-based data decision algorithm. As a result, we were able to test CIS wafers at symbol rates of up to 3.5 Giga-symbols per second, achieving performance comparable to that of sophisticated ASIC-based CIS ATEs.

Optimal Transport (OT) theory investigates the cost-minimizing transport map that moves a source distribution to a target distribution. Recently, several approaches have emerged for learning the optimal transport map for a given cost function using neural networks. We refer to these approaches as the OT Map. OT Map provides a powerful tool for diverse machine learning tasks, such as generative modeling and unpaired image-to-image translation. However, existing methods that utilize max-min optimization often experience training instability and sensitivity to hyperparameters. In this paper, we propose a novel method to improve stability and achieve a better approximation of the OT Map by exploiting displacement interpolation, dubbed Displacement Interpolation Optimal Transport Model (DIOTM). We derive the dual formulation of displacement interpolation at specific time $t$ and prove how these dual problems are related across time. This result allows us to utilize the entire trajectory of displacement interpolation in learning the OT Map. Our method improves the training stability and achieves superior results in estimating optimal transport maps. We demonstrate that DIOTM outperforms existing OT-based models on image-to-image translation tasks.

Aggregating data from multiple sources can be formalized as an *Optimal Transport* (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, in real-world scenarios, the presence of outliers and noise in the data measures can significantly hinder the performance of traditional statistical methods for estimating OT barycenters. To address this issue, we propose a novel scalable approach for estimating the *robust* continuous barycenter, leveraging the dual formulation of the *(semi-)unbalanced* OT problem. To the best of our knowledge, this paper is the first attempt to develop an algorithm for robust barycenters under the continuous distribution setup. Our method is framed as a $\min$-$\max$ optimization problem and is adaptable to *general* cost functions. We rigorously establish the theoretical underpinnings of the proposed method and demonstrate its robustness to outliers and class imbalance through a number of illustrative experiments. Our source code is publicly available at https://github.com/milenagazdieva/U-NOTBarycenters.

We address the convergence problem in learning the Optimal Transport (OT) map, where the OT Map refers to a map from one distribution to another while minimizing the transport cost. Semi-dual Neural OT, a widely used approach for learning OT Maps with neural networks, often generates spurious solutions that fail to transfer one distribution to another accurately. We identify a sufficient condition under which the max-min solution of Semi-dual Neural OT recovers the true OT Map. Moreover, to address cases when this sufficient condition is not satisfied, we propose a novel method, OTP, which learns both the OT Map and the Optimal Transport Plan, representing the optimal coupling between two distributions. Under sharp assumptions on the distributions, we prove that our model eliminates the spurious solution issue and correctly solves the OT problem. Our experiments show that the OTP model recovers the optimal transport map where existing methods fail and outperforms current OT-based models in image-to-image translation tasks. Notably, the OTP model can learn stochastic transport maps when deterministic OT Maps do not exist, such as one-to-many tasks like colorization.

Unpaired point cloud completion is crucial for real-world applications, where ground-truth data for complete point clouds are often unavailable. By learning a completion map from unpaired incomplete and complete point cloud data, this task avoids the reliance on paired datasets. In this paper, we propose the \textit{Unbalanced Optimal Transport Map for Unpaired Point Cloud Completion (\textbf{UOT-UPC})} model, which formulates the unpaired completion task as the (Unbalanced) Optimal Transport (OT) problem. Our method employs a Neural OT model learning the UOT map using neural networks. Our model is the first attempt to leverage UOT for unpaired point cloud completion, achieving competitive or superior performance on both single-category and multi-category benchmarks. In particular, our approach is especially robust under the class imbalance problem, which is frequently encountered in real-world unpaired point cloud completion scenarios.

Evaluating the clock quality of a device's phase-locked loop (PLL) using automatic test equipment (ATE) at an affordable cost is challenging due to the large number of channels and long test times required. This study proposes a new low-cost method for testing the clock jitter of the device using PLL, delay, gate, etc. in the FPGA. Using this circuit, the total jitter analysis function of an expensive, heavy, and slow oscilloscope can be performed simultaneously with tens of CH of clocks within 1us time on a smart phone size board with only tens of dollars of FPGA.

Recently, there has been significant progress in learning-based diffusion samplers, which aim to sample from a given unnormalized density. Many of these approaches formulate the sampling task as a stochastic optimal control (SOC) problem using a canonical uninformative reference process, which limits their ability to efficiently guide trajectories toward the target distribution. In this work, we propose the **Non-Equilibrium Annealed Adjoint Sampler (NAAS)**, a novel SOC-based diffusion framework that employs annealed reference dynamics as a non-stationary base SDE. This annealing structure provides a natural progression toward the target distribution and generates informative reference trajectories, thereby enhancing the stability and efficiency of learning the control. Owing to our SOC formulation, our framework can incorporate a variety of SOC solvers, thereby offering high flexibility in algorithmic design. As one instantiation, we employ a lean adjoint system inspired by adjoint matching, enabling efficient and scalable training. We demonstrate the effectiveness of NAAS across a range of tasks, including sampling from classical energy landscapes and molecular Boltzmann distributions.

Computational methods for learning to sample from the Boltzmann distribution—where the target distribution is known only up to an unnormalized energy function—have advanced significantly recently. Due to the lack of explicit target samples, however, prior diffusion-based methods, known as _diffusion samplers_, often require importance-weighted estimation or complicated learning processes. Both trade off scalability with extensive evaluations of the energy and model, thereby limiting their practical usage. In this work, we propose **Adjoint Schrödinger Bridge Sampler (ASBS)**, a new diffusion sampler that employs simple and scalable matching-based objectives yet without the need to estimate target samples during training. ASBS is grounded on a mathematical model—the Schrödinger Bridge—which enhances sampling efficiency via kinetic-optimal transportation. Through a new lens of stochastic optimal control theory, we demonstrate how SB-based diffusion samplers can be learned at scale via Adjoint Matching and prove convergence to the global solution. Notably, ASBS generalizes the recent Adjoint Sampling (Havens et al., 2025) to arbitrary source distributions by relaxing the so-called memoryless condition that largely restricts the design space. Through extensive experiments, we demonstrate the effectiveness of ASBS on sampling from classical energy functions, amortized conformer generation, and molecular Boltzmann distributions. Codes are available at https://github.com/facebookresearch/adjoint_samplers

We study the problem of learning a neural sampler to generate samples from discrete state spaces where the target probability mass function $\pi\propto\mathrm{e}^{-U}$ is known up to a normalizing constant, which is an important task in fields such as statistical physics, machine learning, combinatorial optimization, etc. To better address this challenging task when the state space has a large cardinality and the distribution is multi-modal, we propose **M**asked **D**iffusion **N**eural **S**ampler (**MDNS**), a novel framework for training discrete neural samplers by aligning two path measures through a family of learning objectives, theoretically grounded in the stochastic optimal control of the continuous-time Markov chains. We validate the efficiency and scalability of MDNS through extensive experiments on various distributions with distinct statistical properties, where MDNS learns to accurately sample from the target distributions despite the extremely high problem dimensions and outperforms other learning-based baselines by a large margin. A comprehensive study of ablations and extensions is also provided to demonstrate the efficacy and potential of the proposed framework. Our code is available at https://github.com/yuchen-zhu-zyc/MDNS.

Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a measure for assessing the distance between data and generated distributions. Recently, OT transport map between data and prior distributions has been utilized as a generative model. These OT-based generative models share a similar adversarial training objective. In this paper, we begin by unifying these OT-based adversarial methods within a single framework. Then, we elucidate the role of each component in training dynamics through a comprehensive analysis of this unified framework. Moreover, we suggest a simple but novel method that improves the previously best-performing OT-based model. Intuitively, our approach conducts a gradual refinement of the generated distribution, progressively aligning it with the data distribution. Our approach achieves a FID score of 2.51 on CIFAR-10 and 5.99 on CelebA-HQ-256, outperforming unified OT-based adversarial approaches.

Wasserstein gradient flow (WGF) describes the gradient dynamics of probability density within the Wasserstein space. WGF provides a promising approach for conducting optimization over the probability distributions. Numerically approximating the continuous WGF requires the time discretization method. The most well-known method for this is the JKO scheme. In this regard, previous WGF models employ the JKO scheme and parametrized transport map for each JKO step. However, this approach results in quadratic training complexity $O(K^2)$ with the number of JKO step $K$. This severely limits the scalability of WGF models. In this paper, we introduce a scalable WGF-based generative model, called Semi-dual JKO (S-JKO). Our model is based on the semi-dual form of the JKO step, derived from the equivalence between the JKO step and the Unbalanced Optimal Transport. Our approach reduces the training complexity to $O(K)$. We demonstrate that our model significantly outperforms existing WGF-based generative models, achieving FID scores of 2.62 on CIFAR-10 and 6.42 on CelebA-HQ-256, which are comparable to state-of-the-art image generative models.

During wafer testing with probe cards in Automatic Test Equipment (ATE), it is challenging to maintain a stable VDD-GND voltage supplied to the Device Under Test (DUT) due to fluctuations in GND voltage caused by the return current from the DUT. Typically, due to a lack of channels, the test equipment reads and corrects the VDD voltage based on the representative GND voltage at an intermediate point where power is supplied, rather than the ground of each DUT. As a result, if there is a change in the GND voltage of each DUT, the test equipment is unable to detect and adjust for it. To overcome these limitations, this study proposes a method of configuring a circuit within the probe card that allows for the use of existing equipment functions such as current measurement and open-short testing while correcting changes in the individual DUT GND voltage of sensitive power sources. This approach aims to minimize wrong defect determination caused by changes in GND voltage during wafer testing.

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In this paper, we establish the interpretation of DDMs in terms of image restoration (IR). Integrating IR literature allows us to use an alternative objective and diverse forward processes, not confining to the diffusion process. By imposing prior knowledge on the loss function grounded on MAP-based estimation, we eliminate the need for the expensive sampling of DDMs. Also, we propose a multi-scale training, which improves the performance compared to the diffusion process, by taking advantage of the flexibility of the forward process. Experimental results demonstrate that our model improves the quality and efficiency of both training and inference. Furthermore, we show the applicability of our model to inverse problems. We believe that our framework paves the way for designing a new type of flexible general generative model.

When measuring the DC drive capability of the DUT's output pin in ATE, the DUT's output voltage is often measured with a termination resistor such as 100 ohms for a differential signal or 50 ohms for a single-ended signal. In this case, as the tester must always be accurate, it is important to create an accurate termination resistance condition. In addition, in some cases, it is desirable to measure the output voltage of the signal pin under different termination conditions. This paper presents a method of correcting an inaccurate termination resistance value or changing a termination resistance value to another value by using the current output function of a parametric measurement unit (PMU) in a tester with only one representative load resistor. In this way, the termination resistance deviation between equipment and CH can be evenly calibrated, and if a test is required under new termination resistance conditions that are not mounted on the tester, the test can be performed only by modifying the software without modifying H/W.

If a transmission line carrying a high-speed signal is damaged, for example by poor contact, the transmitted signal will have a slight increase in jitter. Normally, an oscilloscope or a Vector network analyzer (VNA) is required to measure this jitter increase. In this study, we will show that it is possible to diagnose small losses in transmission lines using only an FPGA without instruments by transmitting a pulse signal through the CH to be diagnosed and then oversampling it in an FPGA to statistically accurately measure the width of the transmitted pulse and detect the small pulse width reduction that occurs when a loss occurs.

Optimal Transport (OT) problem investigates a transport map that bridges two distributions while minimizing a given cost function. In this regard, OT between tractable prior distribution and data has been utilized for generative modeling tasks. However, OT-based methods are susceptible to outliers and face optimization challenges during training. In this paper, we propose a novel generative model based on the semi-dual formulation of Unbalanced Optimal Transport (UOT). Unlike OT, UOT relaxes the hard constraint on distribution matching. This approach provides better robustness against outliers, stability during training, and faster convergence. We validate these properties empirically through experiments. Moreover, we study the theoretical upper-bound of divergence between distributions in UOT. Our model outperforms existing OT-based generative models, achieving FID scores of 2.97 on CIFAR-10 and 6.36 on CelebA-HQ-256. The code is available at \url{https://github.com/Jae-Moo/UOTM}.

As signal transmission loss in automatic test equipment (ATE) is large, receiving a signal without an equalizer is difficult. This study designs a 4.5 Gsps mobile industry processor interface (MIPI) D-PHY analog front-end receiver circuit for ATE. The D-PHY signal uses a DC-coupled low-voltage signal, making the use of commercially available continuous time linear equalizer (CTLE)-included redrivers difficult. We propose a receiving circuit with an equalizer as an off-the-shelf device that can receive D-PHY signals from long distances. The developed receiving circuit achieved optimal signal restoration performance by tuning for the fixed loss characteristics. Additionally, using this receiving circuit, we verified the complete output-signal conversion into an image in a wafer mass production environment.

This paper presents a 3.5Gsps MIPI C-PHY analog front-end receiver circuit for Automatic Test Equipment. This circuit has two features. First, it is made entirely of off-the-shelf components. Second, it has powerful CTLE to compensate for transmission line loss. Since it does not use ASIC, it is possible to add functions at a low cost and in a short time. In the wafer test environment, the loss between the wafer and the receiving circuit is large. This CTLE can be fine-tuned and effectively compensate for the transmission line loss of the developed equipment.