arXiv subjects

Dong Eui Chang

Publications and source records attributed to Dong Eui Chang.

At least 19 recordsLinked to original sources

arXiv2026

Feedback Integrators: Non-Asymptotic Invariance for One-Step Methods and Gain Selection under Euler Discretization

For dynamical systems evolving on a manifold and admitting first integrals, standard one-step numerical methods generally cause the discrete trajectory to drift off the manifold and the numerical values of the first integrals to deviate from their prescribed values. Feedback integrators address this by extending the dynamics to an ambient Euclidean space and adding a feedback term that drives the numerical trajectory toward the set satisfying both the manifold constraint and the prescribed values of the first integrals. Existing theory, however, has two limitations: it remains asymptotic, guaranteeing only eventual entrance into an attractor containing the desired set, and it does not explain how the feedback gain should be chosen. In this paper, we first close the former gap for general one-step methods by proving positive invariance of arbitrarily small sublevel neighborhoods of the feedback Lyapunov function for sufficiently small step sizes. We then specialize to Euler discretization and analyze how the feedback gain enters the Taylor-based error bound. In this setting, we characterize a range of scaled gains that guarantee positive invariance for sufficiently small step sizes and identify the scaling that minimizes the Taylor-based upper bound. We further propose adaptive gain-selection rules under Euler discretization, including both stepwise and periodically updated variants, and establish corresponding boundedness guarantees for the resulting discrete trajectories. These results identify Euler discretization as the first setting in which gain selection for feedback integrators closes in explicit form, whereas extensions to general higher-order one-step methods remain genuinely method-dependent. Numerical experiments on free rigid body motion in $\operatorname{SO}(3)$, the Kepler problem, and a perturbed Kepler problem with rotational symmetry support the analysis.

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arXiv2026

Convergence Without Understanding: When Language Models Agree on Representations but Disagree on Reasoning

Large language models trained under diverse objectives and architectures have been shown to develop increasingly similar internal representations, an observation formalized as the Platonic Representation Hypothesis. Whether this representational convergence extends to the reasoning processes that operate over shared representations remains untested. We evaluate representational similarity across 16 language models from 8 families (1.5B to 72B parameters) on 800 reasoning problems spanning mathematics, science, commonsense, and truthfulness, stratifying by problem difficulty, computational stage, and causal relevance. Our analysis reveals three dissociations: a difficulty inversion, where models converge more on problems they collectively fail (Centered Kernel Alignment [CKA] = 0.897) than on those they solve (CKA = 0.830); a generation gap, where pre-decision representations align (CKA = 0.875) while post-decision representations diverge (CKA = 0.274); and epiphenomenal correctness, where shared information is decodable across models (66% transfer accuracy) but exerts minimal causal influence on predictions (1.5% to 5.5% flip rate across ablation protocols). These results indicate that representational convergence in language models reflects shared input processing constraints rather than shared reasoning strategies, with direct implications for ensemble design, interpretability transfer, and evaluations of model similarity. Code is available at https://github.com/Usama1002/convergence-without-understanding.

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arXiv2026

Distributional Reinforcement Learning with Information Bottleneck for Uncertainty-Aware DRAM Equalization

Equalizer parameter optimization is critical for signal integrity in high-speed memory systems operating at multi-gigabit data rates. However, existing methods suffer from computationally expensive eye diagram evaluation, optimization of expected rather than worst-case performance, and absence of uncertainty quantification for deployment decisions. In this paper, we propose a distributional risk-sensitive reinforcement learning framework integrating Information Bottleneck latent representations with Conditional Value-at-Risk optimization. We introduce rate-distortion optimal signal compression achieving 51 times speedup over eye diagrams while quantifying epistemic uncertainty through Monte Carlo dropout. Distributional reinforcement learning with quantile regression enables explicit worst-case optimization, while PAC-Bayesian regularization certifies generalization bounds. Experimental validation on 2.4 million waveforms from eight memory units demonstrated mean improvements of 37.1\% and 41.5\% for 4-tap and 8-tap equalizer configurations with worst-case guarantees of 33.8\% and 38.2\%, representing 80.7\% and 89.1\% improvements over Q-learning baselines. The framework achieved 62.5\% high-reliability classification eliminating manual validation for most configurations. These results suggest the proposed framework provides a practical solution for production-scale equalizer optimization with certified worst-case guarantees.

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arXiv2025

Deep Reinforcement Learning-Based DRAM Equalizer Parameter Optimization Using Latent Representations

Equalizer parameter optimization for signal integrity in high-speed Dynamic Random Access Memory systems is crucial but often computationally demanding or model-reliant. This paper introduces a data-driven framework employing learned latent signal representations for efficient signal integrity evaluation, coupled with a model-free Advantage Actor-Critic reinforcement learning agent for parameter optimization. The latent representation captures vital signal integrity features, offering a fast alternative to direct eye diagram analysis during optimization, while the reinforcement learning agent derives optimal equalizer settings without explicit system models. Applied to industry-standard Dynamic Random Access Memory waveforms, the method achieved significant eye-opening window area improvements: 42.7\% for cascaded Continuous-Time Linear Equalizer and Decision Feedback Equalizer structures, and 36.8\% for Decision Feedback Equalizer-only configurations. These results demonstrate superior performance, computational efficiency, and robust generalization across diverse Dynamic Random Access Memory units compared to existing techniques. Core contributions include an efficient latent signal integrity metric for optimization, a robust model-free reinforcement learning strategy, and validated superior performance for complex equalizer architectures.

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arXiv2025

Learning High-Quality Latent Representations for Anomaly Detection and Signal Integrity Enhancement in High-Speed Signals

This paper addresses the dual challenge of improving anomaly detection and signal integrity in high-speed dynamic random access memory signals. To achieve this, we propose a joint training framework that integrates an autoencoder with a classifier to learn more distinctive latent representations by focusing on valid data features. Our approach is evaluated across three anomaly detection algorithms and consistently outperforms two baseline methods. Detailed ablation studies further support these findings. Furthermore, we introduce a signal integrity enhancement algorithm that improves signal integrity by an average of 11.3%. The source code and data used in this study are available at https://github.com/Usama1002/learning-latent-representations.

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arXiv2024

Globally exponentially convergent observer for systems evolving on matrix Lie groups

We propose a globally exponentially convergent observer for the dynamical system evolving on matrix Lie groups with bounded velocity with unknown bound. We design the observer in the ambient Euclidean space and show exponential convergence of the observer to the state of the system. We show the convergence with an example of a rigid body rotation and translation system on the special Euclidean group. We compare the proposed observer with an observer present in the literature.

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arXiv2024

Angular velocity and linear acceleration measurement bias estimators for the rigid body system with global exponential convergence

Rigid body systems usually consider measurements of the pose of the body using onboard cameras/LiDAR systems, that of linear acceleration using an accelerometer and of angular velocity using an IMU. However, the measurements of the linear acceleration and angular velocity are usually biased with an unknown constant or slowly varying bias. We propose a measurement bias estimator for such systems under assumption of boundedness of angular velocity. We also provide continuous estimates to the state of the system, i.e. the pose, linear velocity, and position of the body. These estimates are globally exponentially convergent to the state of the rigid body system. We propose two bias estimators designed with the estimate of the pose in the ambient Euclidean space of the Special Euclidean group and show global exponential convergence of the proposed observers to the state of the system. The first observer assumes knowledge of bounds of the angular velocity, while the second observer uses a Riccati observer to overcome this limitation. We show the convergence with an example of a rigid body rotation and translation system on the special Euclidean group. We show that the observer is able to estimate the bias using data collected from an Intel Realsense camera.

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arXiv2024

Machine learning based state observer for discrete time systems evolving on Lie groups

In this paper, a machine learning based observer for systems evolving on manifolds is designed such that the state of the observer is restricted to the Lie group on which the system evolves. Conventional techniques involving machine learning based observers on systems evolving on Lie groups involve designing charts for the Lie group, training a machine learning based observer for each chart, and switching between the trained models based on the state of the system. We propose a novel deep learning based technique whose predictions are restricted to a measure 0 subset of Euclidean space without using charts. Using this network, we design an observer ensuring that the state of the observer is restricted to the Lie group, and predicting the state using only one trained algorithm. The deep learning network predicts an ``error term'' on the Lie algebra of the Lie group, uses the map from the Lie algebra to the group, and uses the group action and the present state to estimate the state at the next epoch. This model being purely data driven does not require the model of the system. The proposed algorithm provides a novel framework for constraining the output of machine learning networks to a measure 0 subset of a Euclidean space without chart specific training and without requiring switching. We show the validity of this method using Monte Carlo simulations performed of the rigid body rotation and translation system.

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arXiv2024

Transversally exponentially stable Euclidean space extension technique for discrete time systems

We propose a modification technique for discrete time systems for exponentially fast convergence to compact sets. The extension technique allows us to use tools defined on Euclidean spaces to systems evolving on manifolds by modifying the dynamics of the system such that the manifold is an attractor set. We show the stability properties of this technique using the simulation of the rigid body rotation system on the unit sphere $S^3$. We also show the improvement afforded due to this technique on a Luenberger like observer designed for the rigid body rotation system on $S^3$.

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arXiv2022

Unscented Kalman filter with stable embedding for simple, accurate and computationally efficient state estimation of systems on manifolds in Euclidean space

This paper proposes a simple, accurate and computationally efficient method to apply the ordinary unscented Kalman filter developed in Euclidean space to systems whose dynamics evolve on manifolds.We use the mathematical theory called stable embedding to make a variant of unscented Kalman filter that keeps state estimates in closeproximity to the manifold while exhibiting excellent estimation performance. We confirm the performance of our devised filter by applying it to the satellite system model and comparing the performance with other unscented Kalman filters devised specifically for systems on manifolds. Our devised filter has a low estimation error, keeps the state estimates in close proximity to the manifold as expected, and consumes a minor amount of computation time. Also our devised filter is simple and easy to use because our filter directly employs the off-the-shelf standard unscented Kalman filter devised in Euclidean space without any particular manifold-structure-preserving discretization method or coordinate transformation.

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arXiv2022

Feedback Gradient Descent: Efficient and Stable Optimization with Orthogonality for DNNs

The optimization with orthogonality has been shown useful in training deep neural networks (DNNs). To impose orthogonality on DNNs, both computational efficiency and stability are important. However, existing methods utilizing Riemannian optimization or hard constraints can only ensure stability while those using soft constraints can only improve efficiency. In this paper, we propose a novel method, named Feedback Gradient Descent (FGD), to our knowledge, the first work showing high efficiency and stability simultaneously. FGD induces orthogonality based on the simple yet indispensable Euler discretization of a continuous-time dynamical system on the tangent bundle of the Stiefel manifold. In particular, inspired by a numerical integration method on manifolds called Feedback Integrators, we propose to instantiate it on the tangent bundle of the Stiefel manifold for the first time. In the extensive image classification experiments, FGD comprehensively outperforms the existing state-of-the-art methods in terms of accuracy, efficiency, and stability.

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arXiv2021

Robust Navigation for Racing Drones based on Imitation Learning and Modularization

This paper presents a vision-based modularized drone racing navigation system that uses a customized convolutional neural network (CNN) for the perception module to produce high-level navigation commands and then leverages a state-of-the-art planner and controller to generate low-level control commands, thus exploiting the advantages of both data-based and model-based approaches. Unlike the state-of-the-art method which only takes the current camera image as the CNN input, we further add the latest three drone states as part of the inputs. Our method outperforms the state-of-the-art method in various track layouts and offers two switchable navigation behaviors with a single trained network. The CNN-based perception module is trained to imitate an expert policy that automatically generates ground truth navigation commands based on the pre-computed global trajectories. Owing to the extensive randomization and our modified dataset aggregation (DAgger) policy during data collection, our navigation system, which is purely trained in simulation with synthetic textures, successfully operates in environments with randomly-chosen photorealistic textures without further fine-tuning.

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arXiv2021

Interaction-aware Kalman Neural Networks for Trajectory Prediction

Forecasting the motion of surrounding obstacles (vehicles, bicycles, pedestrians and etc.) benefits the on-road motion planning for intelligent and autonomous vehicles. Complex scenes always yield great challenges in modeling the patterns of surrounding traffic. For example, one main challenge comes from the intractable interaction effects in a complex traffic system. In this paper, we propose a multi-layer architecture Interaction-aware Kalman Neural Networks (IaKNN) which involves an interaction layer for resolving high-dimensional traffic environmental observations as interaction-aware accelerations, a motion layer for transforming the accelerations to interaction aware trajectories, and a filter layer for estimating future trajectories with a Kalman filter network. Attributed to the multiple traffic data sources, our end-to-end trainable approach technically fuses dynamic and interaction-aware trajectories boosting the prediction performance. Experiments on the NGSIM dataset demonstrate that IaKNN outperforms the state-of-the-art methods in terms of effectiveness for traffic trajectory prediction.

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arXiv2020

The Adaptive Dynamic Programming Toolbox

The paper develops the Adaptive Dynamic Programming Toolbox (ADPT), which solves optimal control problems for continuous-time nonlinear systems. Based on the adaptive dynamic programming technique, the ADPT computes optimal feedback controls from the system dynamics in the model-based working mode, or from measurements of trajectories of the system in the model-free working mode without the requirement of knowledge of the system model. Multiple options are provided such that the ADPT can accommodate various customized circumstances. Compared to other popular software toolboxes for optimal control, the ADPT enjoys its computational precision and speed, which is illustrated with its applications to a satellite attitude control problem.

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arXiv2020

Learning-Driven Exploration for Reinforcement Learning

Effective and intelligent exploration has been an unresolved problem for reinforcement learning. Most contemporary reinforcement learning relies on simple heuristic strategies such as $ε$-greedy exploration or adding Gaussian noise to actions. These heuristics, however, are unable to intelligently distinguish the well explored and the unexplored regions of state space, which can lead to inefficient use of training time. We introduce entropy-based exploration (EBE) that enables an agent to explore efficiently the unexplored regions of state space. EBE quantifies the agent's learning in a state using merely state-dependent action values and adaptively explores the state space, i.e. more exploration for the unexplored region of the state space. We perform experiments on a diverse set of environments and demonstrate that EBE enables efficient exploration that ultimately results in faster learning without having to tune any hyperparameter. The code to reproduce the experiments is given at \url{https://github.com/Usama1002/EBE-Exploration} and the supplementary video is given at \url{https://youtu.be/nJggIjjzKic}.

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arXiv2020

Tracking Controller Design for Satellite Attitude Under Unknown Constant Disturbance Using Stable Embedding

We propose a tracking control law for the fully actuated rigid body system in the presence of any unknown constant disturbance by employing quaternions with the stable embedding technique and Lyapunov stability theory. The stable embedding technique extends the attitude dynamics from the set of unit quaternions to the set of quaternions, which is a Euclidean space, such that the set of unit quaternions is an invariant set of the extended dynamics. Such a stable extension of the system dynamics to a Euclidean space allows us to employ well studied Lyapunov techniques in Euclidean spaces such as LaSalle-Yoshizawa's theorem. A robust tracking control law is proposed for the attitude dynamics subject to unknown constant disturbance and the convergence properties of the tracking control law is rigorously proven. It is demonstrated with the help of numerical simulations that the proposed control law has a remarkable performance even in some challenging situations.

math.OC↗

arXiv2020

Double Prioritized State Recycled Experience Replay

Experience replay enables online reinforcement learning agents to store and reuse the previous experiences of interacting with the environment. In the original method, the experiences are sampled and replayed uniformly at random. A prior work called prioritized experience replay was developed where experiences are prioritized, so as to replay experiences seeming to be more important more frequently. In this paper, we develop a method called double-prioritized state-recycled (DPSR) experience replay, prioritizing the experiences in both training stage and storing stage, as well as replacing the experiences in the memory with state recycling to make the best of experiences that seem to have low priorities temporarily. We used this method in Deep Q-Networks (DQN), and achieved a state-of-the-art result, outperforming the original method and prioritized experience replay on many Atari games.

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arXiv2019

Noise Removal of FTIR Hyperspectral Images via MMSE

Fourier transform infrared (FTIR) hyperspectral imaging systems are deployed in various fields where spectral information is exploited. Chemical warfare agent (CWA) detection is one of such fields and it requires a fast and accurate process from the measurement to the visualization of detection results, including noise removal. A general concern of existing noise removal algorithms is a trade-off between time and performance. This paper suggests a minimum mean square error (MMSE) approach as an efficient noise removal algorithm for FTIR hyperspectral images. The experimental result shows that the MMSE estimator spends less time to achieve comparable performance to the existing algorithms.

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