arXiv subjects

Soohyun Park

Publications and source records attributed to Soohyun Park.

At least 19 recordsLinked to original sources

arXiv2026

Fourier-Geometric Circuit Design for Gate and Entanglement Placement in Quantum Neural Networks

The output of a parameterized quantum circuit (PQC) can be expressed as a finite Fourier series whose accessible frequencies are fixed by the data-encoding gates. While the encoder determines which frequencies can appear, the corresponding Fourier coefficients depend on how the trainable and entangling gates are arranged. Although existing studies provide metrics for characterizing how gate structure affects Fourier coefficients, they do not translate these analyses into an explicit design criterion specifying how gates should be arranged to make a target coefficient reachable. In this paper, we provide such a criterion. Using the adjoint action of the encoding generator, we decompose operator space into two-dimensional invariant planes indexed by frequency and show that each Fourier coefficient is exactly a sum of bilinear projections of the effective state and observable onto the planes at that frequency. Because, for Pauli encodings, high-frequency planes are spanned by mixed multi-qubit Pauli strings, a target coefficient can contribute to the output only when local rotations and entangling layers are arranged so that both the effective state and observable acquire support on one of its planes. For Pauli readouts and commuting two-qubit entanglers, this yields a circuit design rule that specifies, for a given interaction graph, a placement of local rotations and entangling layers that makes a target Fourier coefficient reachable. Using a single encoding layer, we validate the proposed design through a placement ablation, regression tasks from PDEBench and physics-informed Maxwell field modeling, and further demonstrate its robustness to moderate simulated gate noise and damping.

quant-ph↗

arXiv2026

QuPID: Quantum Parameter-Efficient Input-Dependent Retrieval Adaptation for Medical RAG

Fidelity-based quantum retrieval ranks candidates by the fidelity between query and archive states. Applying a shared input-independent unitary after fixed state encoding leaves that fidelity unchanged, so training the circuit cannot alter the ranking. Quantum parameter-efficient input-dependent retrieval adaptation (QuPID) repairs this by making the circuit input-dependent through data re-uploading and by comparing measurement readouts, vectors of local Pauli expectations, rather than states. The result is a small readout for adapting frozen image features to a local archive with limited data: training simulates the circuit classically, and inference runs on a GPU with fixed learned parameters. We characterize the class as a structured factorization of input-modulated quadratic feature maps, bound the frequency support of its re-uploading channel, and give a parameter-count generalization bound that motivates its small budget. Under a shared frozen backbone and a label-free protocol, QuPID's 60 parameters give higher precision-at-5 (P@5) on ChestX-ray14 and MURA than frozen medical encoders, and than adapters and low-rank adaptation (LoRA) with up to 5.25 million trainable parameters. On ChestX-ray14, the P@5 gain over the frozen encoder is +0.116, the lead over retuned adapters is widest at 512 adaptation examples (+0.040), and the full-budget margin over an equally compact classical rotation-plane head is +0.023 with a 95% interval excluding zero. Medical imaging is the primary testbed; the pattern recurs on two non-medical benchmarks, in report generation, and under simulated gate noise and finite-shot readout.

cs.AI↗

arXiv2026

IL-ACT: Imitation Learning with Adaptive Cartesian Tracking Control for a 30-ton Excavator

Autonomous excavator control is challenged by coupled kinematics, actuation lag, and uncertainty. We propose imitation learning and adaptive Cartesian tracking (IL-ACT), a novel motion control framework for a 30-ton-class excavator. An anchored, 14-input imitation policy pretrained on operator demonstrations generates nominal joint rates; adaptive Cartesian feedback and gated gain/bias estimation correct these commands before a stopping-distance governor constrains joint-reference generation. Simscape evaluation covers 100 sequential goals and spiral, figure-eight, and rounded-raster tracking, including 88 additional runs across three training seeds, two initializations, and speeds, under hydraulic response and sensing conditions. Compared with Teacher+ACT, IL-ACT completes all goals with shorter duration and lower terminal errors under both response conditions. Telemetry-initialized IL-ACT lowers RMSE in all 24 figure-eight and rounded-raster seed comparisons and lowers additional-load spiral mean RMSE by approximately 29%. Original spiral RMSE also improves over IL-only and PID. Under a shared sensor-noise realization, telemetry-initialized IL-ACT achieves 27.67% lower mean RMSE than Teacher+ACT; enabling estimation reduces mean RMSE by $22.44\%$ relative to the frozen estimator. Pretrained-weight effects remain mixed, and the original teacher comparison exhibits a spiral RMSE--maximum-error tradeoff. Analysis establishes bounded adaptive states and Cartesian feedback, with reference admissibility conditional on governor feasibility.

cs.RO↗

arXiv2026

Gamma positivity, PL homeomorphism types, and orthogonal polynomials

Using preservations of piecewise linear (PL) homeomorphism types under edge contractions (the link condition) as a topological proxy for flagness, we give a quantitative description of the effect flagness on on gamma positivity of simplicial spheres. In particular, we show that the link condition has a trivial effect on the $g$-vectors (and thus gamma vectors) of high-dimensional simplicial spheres with nonnegative gamma vectors in many cases. Note that this reflects a dichotomy between quantitative behavior arising from $g_1$ components (e.g. measuring ``net number of edge subdivisions'' from the boundary of a cross polytope) that are linear in the dimension and those that are superlinear in the dimension. When the link condition is nontrivial, we show that it gives a lower bound for growth rates of $g$-vector components. This lower bound increases as the number of edges and the distance of the $M$-vector condition on $g$-vectors of simplicial spheres from equality decrease. These lower bounds translate to ones on top gamma vector components and give lower bounds on gamma vector growth rates when the gamma vector components are dominant terms in the $g$-vector components with the same index (e.g. $g$-vectors with components increasing quickly compared to the dimension). Finally, we show that the same results apply to positivity properties generalizing gamma positivity arising from connections between orthogonal polynomials and lattice paths. In the course of doing this, we describe gamma vector components in terms of monomer/dimer covers and point out connections between repeated (stellar) edge subdivisions (Tchebyshev subdivisions) and dimer covers.

math.CO↗

arXiv2026

Convex unions and completions from simplicial pseudomanifolds

While intersections of convex sets are convex, their unions have rather complicated behavior. Some natural contexts where they appear include duality arguments involving boundaries of convex sets and valuations, which have an Euler characteristic-like structure. However, there are certain settings where the convexity property itself is important to consider. For example, this includes (preservation of) positivity properties of divisors on toric varieties under blowdowns. In the case of (restrictions of) conormal bundles, this can be interpreted in terms of interactions between local convexity data stored in rational equivalence relations. We consider generalizations to realizations of simplicial pseudomanifolds and replace rational equivalence with effects of PL homeomorphisms. Decomposing the PL homeomorphisms into edge subdivisions and contractions, we characterize the space of suitable contraction points compatible with local convexity properties in terms of convex unions and completions. This gives rise to certain external edge subdivisions that make this ``contraction space'' of the starting edge empty, which is unexpected given the expected ``increased convexity'' from edge subdivisions. We also obtain strong affine/linear restrictions on realizations of facets containing nearby edges preserving local convexity. This implies that contracting certain nearby edges results in a very large or very small contraction space of the starting edge. As for boundary behavior, there are parallels between effects of PL homeomorphisms on induced 4-cycles in the 1-skeleton. Finally, we find effects of PL homeomorphisms and suspensions on analogues of local convexity properties stored by linear systems of parameters. This indicates that simplicial spheres PL homeomorphic to the boundary of a cross polytope store record local convexity changes in the most natural way.

math.CO↗

arXiv2025

Gamma vectors as inverted Chebyshev expansions, type A to B transformations, and connections to algebraic structures

Given a reciprocal/palindromic polynomial of even degree, we show that the gamma vector is essentially given by an inverted Chebyshev polynomial basis expansion. As an immediate consequence, we characterize real-rootedness of a linear combination of Chebyshev polynomials in terms of real-rootedness of that of the reciprocal polynomial built out of an inverted scaled tuple of the coefficients with one fixed and the rest divided by 2. It can be taken as a counterpart for arbitrary dimensions of a recent result of Bel-Afia--Meroni--Telen on hyperbolicity of Chebyshev curves with respect to the origin. In general, Chebyshev varieties serve as a counterpart of toric varieties in sparse polynomial root finding. Apart from this, the inverted Chebyshev expansion also yields connections between intrinsic properties of the gamma vector construction and the geometric combinatorics of simplicial complexes and posets. We find this by applying work of Hetyei on Tchebyshev subdivisions and Tchebyshev posets. In particular, we find that the gamma vector transformation is closely related to $f$-vectors of simplicial complexes resulting from successive edge subdivisions that transform the type A Coxeter complex to the type B Coxeter complex. Lifting to this to a modification of $cd$-indices, we show that the gamma vector inverted Chebyshev polynomial expansion lifts to a sum of (subdivisions of) cross polytopes which can be computed using (topological) descent statistics. While there are many examples where gamma positivity involving descent statistics, it is interesting to note we only assume the input polynomial is reciprocal/palindromic. Finally, Chebyshev polynomials of the second kind from derivatives give connections to Hopf algebras and quasisymmetric functions along with Lefschetz-type maps induced by $\mathfrak{sl}_2(\mathbb{C})$-representations.

math.CO↗

arXiv2025

Flag complex face structures and decompositions

One of the most common and effective methods of obtaining structural information on simplicial complexes is to use tools from algebraic geometry/commutative algebra (often motivated by properties of toric varieties). However, there is no general algebro-geometric description of components of the gamma vector holding for arbitary flag simplicial spheres. This invariant occurs in many different contexts including permutation statistics, signatures of toric varieties, and Euler characteristics of nonpositively curved piecewise Euclidean manifolds. Combinatorial methods resulting from an explicit inverted Chebyshev expansion give rise to new positivity properties and cell complex structures that are of interest in their own right. Note that the focus is on the $f$-vector rather than the $h$-vector in ``algebraic'' settings. For flag simplicial spheres $Δ$, the fact that $h(Δ) = f(Γ)$ and compatibility between Chebyshev expansions and a modification of the $f$-polynomial by work of Hetyei are the key inputs. In the main formula implying new positivity results, local structures of $CAT(0)$ complexes and cubical analogues of barycentric subdivisions give deeper connections with cubical complex structures complementing earlier work related to the top gamma vector component. Afterwards, we return to the motivating example of barycentric subdivisions and consider how $f$-vectors of Cohen--Macaulay and vertex decomposable flag complexes in geometric settings decompose and interact with geometric transformations. This includes subdivisions of simplicial complexes and recursive properties they share with vertex decomposable flag complexes.

math.CO↗

arXiv2025

Signature 0 toric varieties, wall crossings, and cross polytope-like structures

We describe the structure of simplicial locally convex fans associated to even-dimensional complete toric varieties with signature 0. They belong to the set of such toric varieties whose even degree Betti numbers yield a top gamma vector component equal to 0. The gamma vector is an invariant of palindromic polynomials whose nonnegativity lies between unimodality and real-rootedness. It is known (and expected more generally) that the cases where this top component is 0 are among the "building blocks" of those where it is nonnegative. This means minimality with respect to a certain restricted class of blowups. However, this equality to 0 case is currently poorly understood. In the course of addressing this situation, we find that this interpretation encodes *intrinsic* combinatorial information on the fan in addition to earlier compatibility with existing natural combinatorial examples. Our main method uses wall crossings. The links of the fan come from a repeated suspension of the maximal linear subspace in its realization in the ambient space of the fan. Conversely, the centers of these links containing any particular line form a cone or a repeated suspension of one. The intersection patterns between these "anchoring" linear subspaces come from how far certain submodularity inequalities are from equality and parity conditions on their dimensions. This involves linear dependence and containment relations between them which are connected to optimization. We obtain these relations by viewing the vanishing of certain mixed volumes from the perspective of the exponents. Finally, these wall crossings yield a simple method of generating induced 4-cycles covering the minimal objects described above. We intersect rational equivalence relations with 2-dimensional orbit closures instead of 1-dimensional ones as in most combinatorial applications.

math.AG↗

arXiv2025

How Can Quantum Deep Learning Improve Large Language Models?

The rapid progress of large language models (LLMs) has transformed natural language processing, yet the challenge of efficient adaptation remains unresolved. Full fine-tuning achieves strong performance but imposes prohibitive computational and memory costs. Parameter-efficient fine-tuning (PEFT) strategies, such as low-rank adaptation (LoRA), Prefix tuning, and sparse low-rank adaptation (SoRA), address this issue by reducing trainable parameters while maintaining competitive accuracy. However, these methods often encounter limitations in scalability, stability, and generalization across diverse tasks. Recent advances in quantum deep learning introduce novel opportunities through quantum-inspired encoding and parameterized quantum circuits (PQCs). In particular, the quantum-amplitude embedded adaptation (QAA) framework demonstrates expressive model updates with minimal overhead. This paper presents a systematic survey and comparative analysis of conventional PEFT methods and QAA. The analysis demonstrates trade-offs in convergence, efficiency, and representational capacity, while providing insight into the potential of quantum approaches for future LLM adaptation.

quant-ph↗

arXiv2025

Hallucination-Aware Generative Pretrained Transformer for Cooperative Aerial Mobility Control

This paper proposes SafeGPT, a two-tiered framework that integrates generative pretrained transformers (GPTs) with reinforcement learning (RL) for efficient and reliable unmanned aerial vehicle (UAV) last-mile deliveries. In the proposed design, a Global GPT module assigns high-level tasks such as sector allocation, while an On-Device GPT manages real-time local route planning. An RL-based safety filter monitors each GPT decision and overrides unsafe actions that could lead to battery depletion or duplicate visits, effectively mitigating hallucinations. Furthermore, a dual replay buffer mechanism helps both the GPT modules and the RL agent refine their strategies over time. Simulation results demonstrate that SafeGPT achieves higher delivery success rates compared to a GPT-only baseline, while substantially reducing battery consumption and travel distance. These findings validate the efficacy of combining GPT-based semantic reasoning with formal safety guarantees, contributing a viable solution for robust and energy-efficient UAV logistics.

cs.AI↗

arXiv2024

Repeated Lefschetz-like decompositions for flag doubly Cohen--Macaulay simplicial complexes and gamma vectors of flag spheres

We find decompositions of $h$-polynomials of flag doubly Cohen-Macaulay simplicial complex that yield a direct connection between gamma vectors of flag spheres and constructions used to build them geometrically. More specifically, they are determined by iterated double suspensions and a "net nonnegative set of edge subdivisions" taking it to the given flag doubly Cohen-Macaulay simplicial complex. By a "net nonnegative set of edge subdivision", we mean a collection of edge subdivisions and contractions where there are at least as many edge subdivisions as contractions. Returning to the flag spheres, these repeated decompositions involve links over collections of disjoint edges and give an analogue of a Lefschetz map that applies to each step of the decomposition. The constructions used also give a direct interpretation of the Boolean decompositions coming from links and those of the entire simplicial complex. Roughly speaking, the Boolean vs. non-Boolean distinction is used to measure how far a flag sphere is from being the boundary of a cross polytope. An analogue of this statement for flag doubly Cohen-Macaulay simplicial complexes would replace boundaries of cross polytopes by repeated suspensions of links over edges of the given simplicial complex.

math.CO↗

arXiv2024

Recursive properties of Cohen--Macaulay flag simplicial complexes and Lefschetz decompositions from $f$-vectors

Most applications of the hard Lefschetz theorem related to combinatorial properties of simplicial complexes involve their $h$-vectors. In the context of positivity properties involving $h$-vectors of flag spheres, $f$-vectors with a Lefschetz-type ``Boolean'' decomposition have been studied. In this note, we explore families of flag simplicial complexes where we can see this Boolean decomposition explicitly in terms of transformations connecting different simplicial complexes in this family. Note that we will take complexes in a given dimension to be PL homeomorphic to each other. In particular, the existence of a Boolean decomposition patched from local parts can be phrased in terms of a certain map formally satisfying an analogue of the hard Lefschetz theorem. The map is given by the composition of a double suspension with a ``net single edge subdivision''. Here, the former contributes to the Boolean part and the latter contributes to the disjoint non-Boolean part. The fact that the simplicial complex with the given $f$-vector can be taken to be balanced suggests algebraic versions of maps connected to these decompositions.

math.CO↗

arXiv2024

$f$-vectors of balanced simplicial complexes, flag spheres, and geometric Lefschetz decompositions

We show that there are $f$-vectors of balanced simplicial complexes giving a source of simplicial complexes exhibiting a Boolean decomposition similar to a geometric Lefschetz decomposition. The objects we are working with are $h$-vectors of flag spheres and balanced simplicial complexes whose $f$-vectors are equal to them. This builds on work of Nevo--Petersen--Tenner on a conjecture of Nevo--Petersen that the gamma vector of an odd-dimensional flag sphere is the $f$-vector of a balanced simplicial complex (which was shown for barycentric subdivisions by Nevo--Petersen--Tenner). We can connect our decomposition to positivity questions on reciprocal/palindromic polynomials associated to flag spheres and geometric questions motivating them. In addition, we note that the degrees in the Lefschetz-like decomposition are not halved unlike the usual $h$-vector setting.

math.CO↗

arXiv2024

Pointwise estimates of the Bergman kernel with an exponential weight on the unit ball

We consider the weighted Bergman space $A^2_ψ(\Bn)$ of all holomorphic functions on $\Bn$ square integrable with respect to a particular exponential weight measure $e^{-ψ} dV$ on $\Bn$, where \begin{align*} ψ(z):=\frac{1}{1-|z|^2}. \end{align*} We prove the following estimate for the Bergman kernel $K_ψ(z,w)$ of $A^2_ψ(\Bn)$: \begin{align*} |K_ψ(z,w)|^2\le C\frac{e^{ψ(z)+ψ(w)}}{{\rm Vol}(B_ψ(z,1)){\rm Vol}(B_ψ(w, 1))}e^{-\varepsilon d_ψ(z,w)}, \quad z, w\in\Bn, \end{align*} where $d_ψ$ is the Riemannian distance induced by the potential function $ψ$ and $B_ψ(z,1)$ is the $d_ψ$-ball of center $z$ and radius $1$. The result is motivated by Christ \cite{Chr}.

math.CV↗

arXiv2024

Quantum Multi-Agent Reinforcement Learning for Cooperative Mobile Access in Space-Air-Ground Integrated Networks

Achieving global space-air-ground integrated network (SAGIN) access only with CubeSats presents significant challenges such as the access sustainability limitations in specific regions (e.g., polar regions) and the energy efficiency limitations in CubeSats. To tackle these problems, high-altitude long-endurance unmanned aerial vehicles (HALE-UAVs) can complement these CubeSat shortcomings for providing cooperatively global access sustainability and energy efficiency. However, as the number of CubeSats and HALE-UAVs, increases, the scheduling dimension of each ground station (GS) increases. As a result, each GS can fall into the curse of dimensionality, and this challenge becomes one major hurdle for efficient global access. Therefore, this paper provides a quantum multi-agent reinforcement Learning (QMARL)-based method for scheduling between GSs and CubeSats/HALE-UAVs in order to improve global access availability and energy efficiency. The main reason why the QMARL-based scheduler can be beneficial is that the algorithm facilitates a logarithmic-scale reduction in scheduling action dimensions, which is one critical feature as the number of CubeSats and HALE-UAVs expands. Additionally, individual GSs have different traffic demands depending on their locations and characteristics, thus it is essential to provide differentiated access services. The superiority of the proposed scheduler is validated through data-intensive experiments in realistic CubeSat/HALE-UAV settings.

eess.SP↗

arXiv2024

Explicit expressions for the gamma vector leading to connections to upper/lower bounds and structural properties

We find an explicit formula for the gamma vector in terms of the input polynomial in a way that extends it to arbitrary polynomials. More specifically, we find explicit linear combination in terms of coefficients of the input polynomial (using Catalan numbers and binomial coefficients) and an expression involving the derivative of the input polynomial. The first expression suggests connections to common Coxeter group/noncrossing partition structures in existing gamma positivity examples. In the case where the input is the $h$-polynomial of a simplicial complex, this gives an interpretation of the gamma vector as a measure of differences in local and global contributions. We also apply them to connect signs/inequalities of (shifts of) the gamma vector to upper/lower bound conditions on coefficients of the input polynomial. Finally, we make use of the shape of the sums used to make these estimates and connections with intersection numbers to relate these properties of the gamma vector to algebraic structures (e.g. characteristic classes involved in existing log concavity and Schur positivity properties).

math.CO↗

arXiv2024

Quantum Neural Network Software Testing, Analysis, and Code Optimization for Advanced IoT Systems: Design, Implementation, and Visualization

This paper introduces a novel run-time testing, analysis, and code optimization (TACO) method for quantum neural network (QNN) software in advanced Internet-of-Things (IoT) systems, which visually presents the learning performance that is called a barren plateau. The run-time visual presentation of barren plateau situations is helpful for real-time quantum-based advanced IoT software testing because the software engineers can easily be aware of the training performances of QNN. Moreover, this tool is obviously useful for software engineers because it can intuitively guide them in designing and implementing high-accurate QNN-based advanced IoT software even if they are not familiar with quantum mechanics and quantum computing. Lastly, the proposed TACO is also capable of visual feedback because software engineers visually identify the barren plateau situations using tensorboard. In turn, they are also able to modify QNN structures based on the information.

cs.SE↗

arXiv2023

Handover Protocol Learning for LEO Satellite Networks: Access Delay and Collision Minimization

This study presents a novel deep reinforcement learning (DRL)-based handover (HO) protocol, called DHO, specifically designed to address the persistent challenge of long propagation delays in low-Earth orbit (LEO) satellite networks' HO procedures. DHO skips the Measurement Report (MR) in the HO procedure by leveraging its predictive capabilities after being trained with a pre-determined LEO satellite orbital pattern. This simplification eliminates the propagation delay incurred during the MR phase, while still providing effective HO decisions. The proposed DHO outperforms the legacy HO protocol across diverse network conditions in terms of access delay, collision rate, and handover success rate, demonstrating the practical applicability of DHO in real-world networks. Furthermore, the study examines the trade-off between access delay and collision rate and also evaluates the training performance and convergence of DHO using various DRL algorithms.

cs.IT↗