Dong Eui Chang

Muhammad Usama, Dong Eui Chang

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.

Dong Eui Chang, Fernando Jimenez, Matthew Perlmutter

A new method is proposed to numerically integrate a dynamical system on a manifold such that the trajectory stably remains on the manifold and preserves first integrals of the system. The idea is that given an initial point in the manifold we extend the dynamics from the manifold to its ambient Euclidean space and then modify the dynamics outside the intersection of the manifold and the level sets of the first integrals containing the initial point such that the intersection becomes a unique local attractor of the resultant dynamics. While the modified dynamics theoretically produces the same trajectory as the original dynamics, it yields a numerical trajectory that stably remains on the manifold and preserves the first integrals. The big merit of our method is that the modified dynamics can be integrated with any ordinary numerical integrator such as Euler or Runge-Kutta. We illustrate this method by applying it to three famous problems: the free rigid body, the Kepler problem and a perturbed Kepler problem with rotational symmetry. We also carry out simulation studies to demonstrate the excellence of our method and make comparisons with the standard projection method, a splitting method and Störmer-Verlet schemes.

Dong Eui Chang, Matthew Perlmutter

The theory of feedback integrators is extended to handle mechanical systems with nonholonomic constraints with or without symmetry, so as to produce numerical integrators that preserve the nonholonomic constraints as well as other conserved quantities. To extend the feedback integrators, we develop a suitable extension theory for nonholonomic systems, and also a corresponding reduction theory for systems with symmetry. It is then applied to various nonholonomic systems such as the Suslov problem on SO(3), the knife edge, the Chaplygin sleigh, the vertical rolling disk, the roller racer, the Heisenberg system, and the nonholonomic oscillator.

Juho Bae, Dong Eui Chang

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.

Dong Eui Chang

We show that any continuously differentiable force is decomposed into the sum of a Rayleigh force and a gyroscopic force. We also extend this result to piecewise continuously differentiable forces. Our result improves the result on the decomposition of forces in a book by David Merkin and further extends it to piecewise continuously differentiable forces.

Dong Eui Chang, Taeyoung Lee

We propose a 12-dimensional, global, continuous, and exponentially convergent observer for gyro bias and attitude of a rigid body. Any attitude observer developed on the special orthogonal group suffers from the topological restriction that prohibits global attractivity in continuous flow. In this paper, the observer is designed in the set of 3 by 3 real matrices, thus making the topological obstruction on the special orthogonal group irrelevant. The efficacy of the proposed approach against other attitude observers is illustrated by an indoor experiment utilizing visual landmarks.

Fanchen Bu, Dong Eui Chang

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.

Muhammad Usama, Hee-Deok Jang, Soham Shanbhag et al.

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.

Muhammad Usama, Dong Eui Chang

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}.

Dong Eui Chang

A method of designing observers and observer-based tracking controllers is proposed for nonlinear systems on manifolds via embedding into Euclidean space and transversal stabilization. Given a system on a manifold, we first embed the manifold and the system into Euclidean space and extend the system dynamics to the ambient Euclidean space in such a way that the manifold becomes an invariant attractor of the extended system, thus securing the transversal stability of the manifold in the extended dynamics. After the embedding, we design state observers and observer-based controllers for the extended system in one single global coordinate system in the ambient Euclidean space, and then restrict them to the original state-space manifold to produce observers and observer-based controllers for the original system on the manifold. This procedure has the merit that any existing control method that has been developed in Euclidean space can be applied globally to systems defined on nonlinear manifolds, thus making nonlinear controller design on manifolds easier. The detail of the method is demonstrated on the fully actuated rigid body system.

Dong Eui Chang

Given a control system on a manifold that is embedded in Euclidean space, it is sometimes convenient to use a single global coordinate system in the ambient Euclidean space for controller design rather than to use multiple local charts on the manifold or coordinate-free tools from differential geometry. In this paper, we develop a theory about this and apply it to the fully actuated rigid body system for stabilization and tracking. A noteworthy point in this theory is that we legitimately modify the system dynamics outside its state-space manifold before controller design so as to add attractiveness to the manifold in the resulting dynamics.

Muhammad Usama, Dong Eui Chang

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.

Muhammad Usama, Dong Eui Chang

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.

Soham Shanbhag, Dong Eui Chang

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.

Tianqi Wang, Dong Eui Chang

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.

Xiaowei Xing, Dong Eui Chang

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.

Fanchen Bu, Dong Eui Chang

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.

Xiaowei Xing, Dong Eui Chang

Deep reinforcement learning trains neural networks using experiences sampled from the replay buffer, which is commonly updated at each time step. In this paper, we propose a method to update the replay buffer adaptively and selectively to train a robot arm to accomplish a suction task in simulation. The response time of the agent is thoroughly taken into account. The state transitions that remain stuck at the boundary of constraint are not stored. The policy trained with our method works better than the one with the common replay buffer update method. The result is demonstrated both by simulation and by experiment with a real robot arm.

Tianqi Wang, Dong Eui Chang

We present a training pipeline for the autonomous driving task given the current camera image and vehicle speed as the input to produce the throttle, brake, and steering control output. The simulator Airsim's convenient weather and lighting API provides a sufficient diversity during training which can be very helpful to increase the trained policy's robustness. In order to not limit the possible policy's performance, we use a continuous and deterministic control policy setting. We utilize ResNet-34 as our actor and critic networks with some slight changes in the fully connected layers. Considering human's mastery of this task and the high-complexity nature of this task, we first use imitation learning to mimic the given human policy and leverage the trained policy and its weights to the reinforcement learning phase for which we use DDPG. This combination shows a considerable performance boost comparing to both pure imitation learning and pure DDPG for the autonomous driving task.

Wonshick Ko, Dong Eui Chang

In this paper, we propose a dual memory structure for reinforcement learning algorithms with replay memory. The dual memory consists of a main memory that stores various data and a cache memory that manages the data and trains the reinforcement learning agent efficiently. Experimental results show that the dual memory structure achieves higher training and test scores than the conventional single memory structure in three selected environments of OpenAI Gym. This implies that the dual memory structure enables better and more efficient training than the single memory structure.

Muhammad Usama, Dong Eui Chang

Robotic navigation concerns the task in which a robot should be able to find a safe and feasible path and traverse between two points in a complex environment. We approach the problem of robotic navigation using reinforcement learning and use deep $Q$-networks to train agents to solve the task of robotic navigation. We compare the Entropy-Based Exploration (EBE) with the widely used $ε$-greedy exploration strategy by training agents using both of them in simulation. The trained agents are then tested on different versions of the environment to test the generalization ability of the learned policies. We also implement the learned policies on a real robot in complex real environment without any fine tuning and compare the effectiveness of the above-mentioned exploration strategies in the real world setting. Video showing experiments on TurtleBot3 platform is available at \url{https://youtu.be/NHT-EiN_4n8}.

Chang Sik Lee, Dong Eui Chang

An energy based approach for stabilizing a mechanical system has offered a simple yet powerful control scheme. However, since it does not impose such strong constraints on parameter space of the controller, finding appropriate parameter values for an optimal controller is known to be hard. This paper intends to generate an optimal energy-based controller for swinging up a rotary inverted pendulum, also known as the Furuta pendulum, by applying the Bayesian optimization called Entropy Search. Simulations and experiments show that the optimal controller has an improved performance compared to a nominal controller for various initial conditions.

Ce Ju, Zheng Wang, Cheng Long et al.

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.

Muhammad Usama, Dong Eui Chang

Deep neural networks have shown remarkable performance across a wide range of vision-based tasks, particularly due to the availability of large-scale datasets for training and better architectures. However, data seen in the real world are often affected by distortions that not accounted for by the training datasets. In this paper, we address the challenge of robustness and stability of neural networks and propose a general training method that can be used to make the existing neural network architectures more robust and stable to input visual perturbations while using only available datasets for training. Proposed training method is convenient to use as it does not require data augmentation or changes in the network architecture. We provide theoretical proof as well as empirical evidence for the efficiency of the proposed training method by performing experiments with existing neural network architectures and demonstrate that same architecture when trained with the proposed training method perform better than when trained with conventional training approach in the presence of noisy datasets.

Dong Eui Chang

A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state-space manifold $M$ of a given control system into some Euclidean space $\mathbb R^n$, extend the system from $M$ to the ambient space $\mathbb R^n$, and modify it outside $M$ to add transversal stability to $M$ in the final dynamics in $\mathbb R^n$. Controllers are designed for the final system in the ambient space $\mathbb R^n$. Then, their restriction to $M$ produces controllers for the original system on $M$. This method has the merit that only one single global Cartesian coordinate system in the ambient space $\mathbb R^n$ is used for controller synthesis, and any controller design method in $\mathbb R^n$, such as the linearization method, can be globally applied for the controller synthesis. The proposed method is successfully applied to the tracking problem for the following two benchmark systems: the fully actuated rigid body system and the quadcopter drone system.

Anthony Caterini, Dong Eui Chang

Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However, the representation is non-standardized, and the gradient calculation methods are often performed using component-based approaches that break parameters down into scalar units, instead of considering the parameters as whole entities. In this work, these problems are addressed. Standard notation is used to represent DNNs in a compact framework. Gradients of DNN loss functions are calculated directly over the inner product space on which the parameters are defined. This framework is general and is applied to two common network types: the Multilayer Perceptron and the Deep Autoencoder.

Anthony L. Caterini, Dong Eui Chang

In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free manner. Convolutional neural networks are described in this framework in a compact form, with the gradients of standard --- and higher-order --- loss functions calculated for each layer of the network. This approach can be applied to other network structures and provides a basis on which to create new networks.