arXiv subjects

Joseph Park

Publications and source records attributed to Joseph Park.

6 recordsLinked to original sources

arXiv2026

Group-Invariant Unsupervised Skill Discovery: Symmetry-aware Skill Representations for Generalizable Behavior

Unsupervised skill discovery aims to acquire behavior primitives that improve exploration and accelerate downstream task learning. However, existing approaches often ignore the geometric symmetries of physical environments, leading to redundant behaviors and sample inefficiency. To address this, we introduce Group-Invariant Skill Discovery (GISD), a framework that explicitly embeds group structure into the skill discovery objective. Our approach is grounded in a theoretical guarantee: we prove that in group-symmetric environments, the standard Wasserstein dependency measure admits a globally optimal solution comprised of an equivariant policy and a group-invariant scoring function. Motivated by this, we formulate the Group-Invariant Wasserstein dependency measure, which restricts the optimization to this symmetry-aware subspace without loss of optimality. Practically, we parameterize the scoring function using a group Fourier representation and define the intrinsic reward via the alignment of equivariant latent features, ensuring that the discovered skills generalize systematically under group transformations. Experiments on state-based and pixel-based locomotion benchmarks demonstrate that GISD achieves broader state-space coverage and improved efficiency in downstream task learning compared to a strong baseline.

cs.RO↗

arXiv2023

Control of complex systems with generalized embedding and empirical dynamic modeling

Effective control requires knowledge of the process dynamics to guide the system toward desired states. In many control applications this knowledge is expressed mathematically or through data-driven models, however, as complexity grows obtaining a satisfactory mathematical representation is increasingly difficult. Further, many data-driven approaches consist of abstract internal representations that may have no obvious connection to the underlying dynamics and control, or, require extensive model design and training. Here, we remove these constraints by demonstrating model predictive control from generalized state space embedding of the process dynamics providing a data-driven, explainable method for control of nonlinear, complex systems. Generalized embedding and model predictive control are demonstrated on nonlinear dynamics generated by an agent based model of 1200 interacting agents. The method is generally applicable to any type of controller and dynamic system representable in a state space.

eess.SY↗

arXiv2021

Experimentally testable whole brain manifolds that recapitulate behavior

We propose an algorithm grounded in dynamical systems theory that generalizes manifold learning from a global state representation, to a network of local interacting manifolds termed a Generative Manifold Network (GMN). Manifolds are discovered using the convergent cross mapping (CCM) causal inference algorithm which are then compressed into a reduced redundancy network. The representation is a network of manifolds embedded from observational data where each orthogonal axis of a local manifold is an embedding of a individually identifiable neuron or brain area that has exact correspondence in the real world. As such these can be experimentally manipulated to test hypotheses derived from theory and data analysis. Here we demonstrate that this representation preserves the essential features of the brain of flies,larval zebrafish and humans. In addition to accurate near-term prediction, the GMN model can be used to synthesize realistic time series of whole brain neuronal activity and locomotion viewed over the long term. Thus, as a final validation of how well GMN captures essential dynamic information, we show that the artificially generated time series can be used as a training set to predict out-of-sample observed fly locomotion, as well as brain activity in out of sample withheld data not used in model building. Remarkably, the artificially generated time series show realistic novel behaviors that do not exist in the training data, but that do exist in the out-of-sample observational data. This suggests that GMN captures inherently emergent properties of the network. We suggest our approach may be a generic recipe for mapping time series observations of any complex nonlinear network into a model that is able to generate naturalistic system behaviors that identifies variables that have real world correspondence and can be experimentally manipulated.

q-bio.NC↗

arXiv2021

kEDM: A Performance-portable Implementation of Empirical Dynamic Modeling using Kokkos

Empirical Dynamic Modeling (EDM) is a state-of-the-art non-linear time-series analysis framework. Despite its wide applicability, EDM was not scalable to large datasets due to its expensive computational cost. To overcome this obstacle, researchers have attempted and succeeded in accelerating EDM from both algorithmic and implementational aspects. In previous work, we developed a massively parallel implementation of EDM targeting HPC systems (mpEDM). However, mpEDM maintains different backends for different architectures. This design becomes a burden in the increasingly diversifying HPC systems, when porting to new hardware. In this paper, we design and develop a performance-portable implementation of EDM based on the Kokkos performance portability framework (kEDM), which runs on both CPUs and GPUs while based on a single codebase. Furthermore, we optimize individual kernels specifically for EDM computation, and use real-world datasets to demonstrate up to $5.5\times$ speedup compared to mpEDM in convergent cross mapping computation.

cs.DC↗

arXiv2021

Empirical Mode Modeling: A data-driven approach to recover and forecast nonlinear dynamics from noisy data

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated from available observations. Since observational data are frequently sampled with noise, it is possible that noise can corrupt the state-space representation degrading analytical performance. Here, we evaluate the synthesis of empirical mode decomposition with empirical dynamic modeling, which we term empirical mode modeling, to increase the information content of state-space representations in the presence of noise. Evaluation of a mathematical, and, an ecologically important geophysical application across three different state-space representations suggests that empirical mode modeling may be a useful technique for data-driven, model-free, state-space analysis in the presence of noise.

stat.ML↗

arXiv2020

Massively Parallel Causal Inference of Whole Brain Dynamics at Single Neuron Resolution

Empirical Dynamic Modeling (EDM) is a nonlinear time series causal inference framework. The latest implementation of EDM, cppEDM, has only been used for small datasets due to computational cost. With the growth of data collection capabilities, there is a great need to identify causal relationships in large datasets. We present mpEDM, a parallel distributed implementation of EDM optimized for modern GPU-centric supercomputers. We improve the original algorithm to reduce redundant computation and optimize the implementation to fully utilize hardware resources such as GPUs and SIMD units. As a use case, we run mpEDM on AI Bridging Cloud Infrastructure (ABCI) using datasets of an entire animal brain sampled at single neuron resolution to identify dynamical causation patterns across the brain. mpEDM is 1,530 X faster than cppEDM and a dataset containing 101,729 neuron was analyzed in 199 seconds on 512 nodes. This is the largest EDM causal inference achieved to date.

cs.DC↗