arXiv subjects

Taekyun Lee

Publications and source records attributed to Taekyun Lee.

11 recordsLinked to original sources

arXiv2026

The Exact Online Threshold for the Asymmetric Binary Perceptron

Let $G\in\mathbb{R}^{M\times N}$ have independent standard Gaussian entries. For a fixed margin $κ\in\mathbb{R}$, the asymmetric binary perceptron asks for $σ\in\{\pm1\}^N$ such that $Gσ/\sqrt{N}\geκ\mathbf{1}_M$. We study the online version of this problem, in which the columns of $G$ arrive sequentially and each sign must be chosen irrevocably before future columns are revealed. We determine the exact threshold $α_{\mathrm{on}}(κ)$ for every fixed $κ$: for $M/N\toα$ with $α<α_{\mathrm{on}}(κ)$, there is a deterministic online algorithm, using $O(MN)$ arithmetic operations and polynomial bit complexity, that succeeds with high probability, while for $α>α_{\mathrm{on}}(κ)$, no online algorithm succeeds with high probability. The threshold is characterized by a one-dimensional stochastic control problem for Brownian motion. The main difficulty is to upgrade a single-coordinate Brownian limit to simultaneous feasibility of all $M=Θ(N)$ constraints, which we do with half-line monotonicity and a short final correction block. At zero margin, we give a computer-assisted proof that $0.32747<α_{\mathrm{on}}(0)<0.36664$. In particular, every density below $0.32747$ is achievable online by such an algorithm, more than tripling the best density previously proved attainable by any polynomial-time algorithm, online or offline (the previous bound was $α\le0.1$, due to Li, Schramm, and Zhou). As $κ\to+\infty$, the online threshold agrees to first order with the offline storage capacity. As $κ\to-\infty$, it has the same asymptotic scale as the best known offline polynomial-time guarantee, while the storage capacity is larger by a factor of order $κ^2$.

cs.DS↗

arXiv2026

From Interface to Inference: Eliciting Any-Order Inference from Any-Order Models

Many discrete reasoning tasks, such as code generation, are inherently non-causal: programmers move between high-level structure and local details, a process we call any-order inference. For autoregressive language models, which lack a native any-order interface, non-causal abilities such as infilling and next-edit prediction require hand-designed mechanisms. Can we instead design models that natively support any-order inference? Masked diffusion models have recently emerged as compelling candidates, as their any-order training objective naturally offers an any-order prediction interface. This interface, however, does not automatically yield any-order inference. We demonstrate that this interface-inference gap stems from positional uncertainty: fixed-canvas, token-level models may know what semantic component should appear without knowing where to place it. In light of this, we propose two complementary approaches: (1) Insertion-based masked diffusion, building on FlexMDM (Kim et al, 2025), relaxes fixed-position commitments via insertions, enabling generation across non-contiguous regions. (2) Latent-space masked diffusion shifts prediction to coarser semantic segments, enabling search over latent generation orders. Empirically, we train a 7B FlexMDM for Python coding and a 125M LatentMDM for GSM8K and show that both approaches induce distinct any-order inference behaviors and improve downstream performance. We release our codebase at https://github.com/SeunggeunKimkr/genuine-any-order.

cs.LG↗

arXiv2026

Efficient Weighted Sampling via Score-based Generative Models

Weighted sampling -- sampling from a probability density function (PDF) proportional to the product of a base PDF and a weight function -- is a fundamental technique with wide-ranging applications in variance reduction, biased sampling, data augmentation, and more. Leveraging the increasing availability of pretrained score-based generative models (SGMs), we propose a training-free weighted sampling framework that approximates the backward diffusion process of the target distribution by augmenting the pretrained base score function with an auxiliary guidance term, in a principled and computationally efficient manner. Our approach builds on two key components: a lightweight approximation of the guidance that avoids costly higher-order derivatives of both the score and weight functions, and an uncertainty-aware scheduler that dynamically adjusts the guidance strength based on a temporal analysis of approximation error. Together, these components enable accurate and stable sampling without relying on particle-based resampling or Hessian evaluations commonly required by existing methods. We validate the effectiveness of our method from synthetic to large-scale settings such as Stable Diffusion XL, where our framework achieves $1.2\times$ to $4.7\times$ speedups while consistently matching or outperforming state-of-the-art baselines in task performance. These results position our method as a scalable and inference-efficient solution for task-adaptive, time-sensitive sampling in generative applications.

cs.LG↗

arXiv2026

Structured Masked Diffusion for Joint Multiuser Decoding

In joint multiuser decoding, a receiver recovers a set of messages from a single noisy aggregate of many simultaneous transmissions. Classical decoders rely on rule-based mechanisms such as successive interference cancellation, joint belief propagation, or list recovery, all of which become brittle or expensive as ambiguity increases. We propose CIDER, a learned multiuser decoder with masked-diffusion refinement steps. CIDER uses demixing to prevent duplicate-row collapse and uses parity-aware propagation to provide soft guidance from the code constraints. In higher-load regimes, we further improve reliability via a lightweight quality-guided remasking step that selectively re-decodes low-confidence sequences. On commonly used error-correcting codes, CIDER matches or improves on FFT-accelerated joint belief propagation-style decoding in symbol error rate while running more than $6\times$ to over $100\times$ faster, with the speedup widening as the blocklength grows. Code is available at https://github.com/jiyunyoung/CIDER.

cs.IT↗

arXiv2026

Fine-Tuning Masked Diffusion for Provable Self-Correction

A natural desideratum for generative models is self-correction--detecting and revising low-quality tokens at inference. While Masked Diffusion Models (MDMs) have emerged as a promising approach for generative modeling in discrete spaces, their capacity for self-correction remains poorly understood. Prior attempts to incorporate self-correction into MDMs either require overhauling MDM architectures/training or rely on imprecise proxies for token quality, limiting their applicability. Motivated by this, we introduce PRISM--Plug-in Remasking for Inference-time Self-correction of Masked Diffusions--a lightweight, model-agnostic approach that applies to any pretrained MDM. Theoretically, PRISM defines a self-correction loss that provably learns per-token quality scores, without RL or a verifier. These quality scores are computed in the same forward pass with MDM and used to detect low-quality tokens. Empirically, PRISM advances MDM inference across domains and scales: Sudoku; unconditional text (170M); and code with LLaDA (8B).

cs.LG↗

arXiv2026

Channel Geometry Preserving Generative Models for CSI Feedback in MU-MIMO

Under limited feedback, channel state information (CSI) reconstruction for multiuser multiple-input multiple-output (MU-MIMO) precoding is challenging, since the precoder should provide not only beamforming gain, but also robust suppression of inter-user interference. This paper revisits this classic problem by developing powerful decompression techniques at the base station (BS) that harness modern deep generative models. We propose two novel BS-side flow-matching generative CSI decoders that progressively transform either a simple prior or an initial CSI estimate into a reconstruction consistent with the feedback-conditioned channel distribution. We further show theoretically that conventional minimum mean-squared-error (MMSE)-based reconstructions of CSI often result in centroid-like compromises that fail to preserve the posterior geometry needed for inter-user interference suppression. In other words, MU-MIMO precoding based on MSE-oriented CSI reconstructions can be suboptimal, since such reconstructions frequently fail to maintain user orthogonality. Numerical results in FR3 spectrum show that the proposed flow-based methods consistently outperform MSE-based baselines in downlink sum-rate, with the advantage especially pronounced in interference-limited and spatially dense regimes. These results suggest that posterior-guided flow reconstruction is better aligned with MU-MIMO precoding than traditional MMSE-oriented CSI feedback, since it better preserves the channel geometry needed for user separation.

eess.SP↗

arXiv2025

Generating High Dimensional User-Specific Wireless Channels using Diffusion Models

Deep neural network (DNN)-based algorithms are emerging as an important tool for many physical and MAC layer functions in future wireless communication systems, including for large multi-antenna channels. However, training such models typically requires a large dataset of high-dimensional channel measurements, which are very difficult and expensive to obtain. This paper introduces a novel method for generating synthetic wireless channel data using diffusion-based models to produce user-specific channels that accurately reflect real-world wireless environments. Our approach employs a conditional denoising diffusion implicit model (cDDIM) framework, effectively capturing the relationship between user location and multi-antenna channel characteristics. We generate synthetic high fidelity channel samples using user positions as conditional inputs, creating larger augmented datasets to overcome measurement scarcity. The utility of this method is demonstrated through its efficacy in training various downstream tasks such as channel compression and beam alignment. Our diffusion-based augmentation approach achieves over a 1-2 dB gain in NMSE for channel compression, and an 11dB SNR boost in beamforming compared to prior methods, such as noise addition or the use of generative adversarial networks (GANs).

cs.IT↗

arXiv2025

DiffLoc: Diffusion Model-Based High-Precision Positioning for 6G Networks

This paper introduces a novel framework for high-accuracy outdoor user equipment (UE) positioning that applies a conditional generative diffusion model directly to high-dimensional massive MIMO channel state information (CSI). Traditional fingerprinting methods struggle to scale to large, dynamic outdoor environments and require dense, impractical data surveys. To overcome these limitations, our approach learns a direct mapping from raw uplink Sounding Reference Signal (SRS) fingerprints to continuous geographic coordinates. We demonstrate that our DiffLoc framework achieves unprecedented sub-centimeter precision, with our best model (DiffLoc-CT) delivering 0.5 cm fusion accuracy and 1-2 cm single base station (BS) accuracy in a realistic, ray-traced Tokyo urban macro-cell environment. This represents an order-of-magnitude improvement over existing methods, including supervised regression approaches (over 10 m error) and grid-based fusion (3 m error). Our consistency training approach reduces inference time from 200 steps to just 2 steps while maintaining exceptional accuracy even for high-speed users (15-25 m/s) and unseen user trajectories, demonstrating the practical feasibility of our framework for real-time 6G applications.

cs.NI↗

arXiv2025

DICE: Device-level Integrated Circuits Encoder with Graph Contrastive Pretraining

Pretraining models with unsupervised graph representation learning has led to significant advancements in domains such as social network analysis, molecular design, and electronic design automation (EDA). However, prior work in EDA has mainly focused on pretraining models for digital circuits, overlooking analog and mixed-signal circuits. To bridge this gap, we introduce DICE, a Device-level Integrated Circuits Encoder, which is the first graph neural network (GNN) pretrained via self-supervised learning specifically tailored for graph-level prediction tasks in both analog and digital circuits. DICE adopts a simulation-free pretraining approach based on graph contrastive learning, leveraging two novel graph augmentation techniques. Experimental results demonstrate substantial performance improvements across three downstream tasks, highlighting the effectiveness of DICE for both analog and digital circuits. The code is available at github.com/brianlsy98/DICE.

cs.LG↗

arXiv2025

Satellite Selection for In-Band Coexistence of Dense LEO Networks

We study spectrum sharing between two dense low-earth orbit (LEO) satellite constellations, an incumbent primary system and a secondary system that must respect interference protection constraints on the primary system. In particular, we propose a secondary satellite selection framework and algorithm that maximizes capacity while guaranteeing that the time-average interference and absolute interference inflicted upon each primary ground user never exceeds specified thresholds. We solve this NP-hard constrained, combinatorial satellite selection problem through Lagrangian relaxation to decompose it into simpler problems which can then be solved through subgradient methods. A high-fidelity simulation is developed based on public FCC filings and technical specifications of the Starlink and Kuiper systems. We use this case study to illustrate the effectiveness of our approach and that explicit protection is indeed necessary for healthy coexistence. We further demonstrate that deep learning models can be used to predict the primary satellite system associations, which helps the secondary system avoid inflicting excessive interference and maximize its own capacity.

eess.SP↗

arXiv2025

Generative Diffusion Model-based Compression of MIMO CSI

While neural lossy compression techniques have markedly advanced the efficiency of Channel State Information (CSI) compression and reconstruction for feedback in MIMO communications, efficient algorithms for more challenging and practical tasks-such as CSI compression for future channel prediction and reconstruction with relevant side information-remain underexplored, often resulting in suboptimal performance when existing methods are extended to these scenarios. To that end, we propose a novel framework for compression with side information, featuring an encoding process with fixed-rate compression using a trainable codebook for codeword quantization, and a decoding procedure modeled as a backward diffusion process conditioned on both the codeword and the side information. Experimental results show that our method significantly outperforms existing CSI compression algorithms, often yielding over twofold performance improvement by achieving comparable distortion at less than half the data rate of competing methods in certain scenarios. These findings underscore the potential of diffusion-based compression for practical deployment in communication systems.

cs.IT↗