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Jie Gao

Publications and source records attributed to Jie Gao.

At least 19 recordsLinked to original sources
arXiv2026

Optimal Non-Adaptive Vantage Point Selection

We study the \emph{vantage point selection} problem, introduced by Ashvinkumar, Chowdhury, Gao, Goswami, Mitchell, and Polishchuk [WADS'25] to model the problem of estimating bottleneck capacities on the Internet. The input is a weighted undirected graph with unique shortest paths where every edge has a distinct unknown \emph{capacity}. When the algorithm \emph{queries} a vertex $v$, it reveals the minimum-capacity edge on the shortest path from $v$ to every other vertex reachable from $v$. The goal is to maximize the total number of revealed edges. The quality of an algorithm is measured by its competitive ratio against an optimal algorithm that knows all edge capacities a priori. We first consider the foundational single-query setting, where both the algorithm and the optimal algorithm are restricted to a single query. There is a trivial upper bound of $O(n)$ on the competitive ratio and the best known lower bound was $\tildeΩ(\sqrt{n})$. We provide an algorithm and matching lower bound (up to polylogarithmic factors) showing that the best possible competitive ratio is $\tildeΘ(n^{2/3})$. Furthermore, we extend our results to the general setting where the optimal algorithm is allowed $k$ queries and our algorithm is allowed $αk$ queries for $α\geq 1$. We present a randomized non-adaptive algorithm and matching lower bound (up to polylogarithmic factors) showing that the best possible expected competitive ratio for non-adaptive algorithms is the following surprisingly complex bound: $$ \tildeΘ\left( \min\left\{ \frac{n}{αk}, \max\left( \sqrt{\frac{n}α}, \frac{n^{2/3}}{αk^{1/3}} \right) \right\} \right). $$

cs.DS↗
arXiv2026

ResLearn-XR: Residual Learning for Network Traffic and Quality-of-Experience-Aware Modeling in Extended Reality

We present ResLearn-XR, a residual learning framework for predicting eXtended Reality (XR) network traffic and estimating Quality-of-Experience (QoE) risk. ResLearn-XR adopts a two-stage temporal learning structure comprising a base sequence prediction model augmented with task-specific residual learning components to improve adaptability to bursty, non-stationary XR traffic dynamics. The residual learning stages operate in the value space for continuous XR traffic forecasting and in the logit space for probabilistic QoE risk estimation. \rev{For the QoE-risk branch, we introduce a Data Descriptor Algorithm (DDA), a causal feature-construction module that converts packet-level application-layer observables into frame-timing-aware descriptors suitable for encrypted traffic analysis. We also construct an XR Traffic-QoE dataset that pairs continuous XR traffic traces with session-level user-reported QoE labels. ResLearn-XR reduces SMAPE by up to 17.84% across frame-count, frame-size, and inter-arrival-time prediction, while reducing QoE-risk estimation SMAPE by up to 87.8% over single-stage baselines.

cs.AI↗
arXiv2026

Agent-as-Peer-Debriefer: A Multi-Agent Framework with Perspective-Based Refinement for Qualitative Analysis

Large language models (LLMs) are increasingly used for qualitative data analysis (QDA), yet their outputs often miss the depth and nuance of human analysis. We argue this gap reflects a missing credibility practice from human QDA: peer debriefing, in which an analyst seeks feedback from a disinterested peer and uses it to refine their coding. To bring this practice into LLM-assisted QDA, we propose Agent-as-Peer-Debriefer, a multi-agent QDA framework that builds peer debriefing into key coding steps. In our framework, a Hierarchical Coding Agent follows the standard QDA process to generate codes, sub-themes, and themes, along with self-explanations and reflection memos. It then shares these outputs with three Peer-Debriefing Agents, each applying a distinct analytical perspective (Theory-Driven, Data-Driven, or Applied) and refining the codes by keeping, renaming, reassigning, merging, or splitting them. These perspectives are drawn from established human QDA practices that generalize across domains and datasets. To evaluate the framework, we test it on three datasets across two domains with three LLMs, measuring semantic similarity to human-annotated codes. Across all settings, perspective-based, peer-debriefing refinement aligns more closely with human codes than a single-LLM baseline, and an ablation further shows the gain is not merely from additional refinement. The three perspectives also produce distinct trade-offs, showing that the choice of perspective is a meaningful and controllable design decision. More broadly, these findings suggest that simulating peer debriefing with explicit perspectives is a promising route to more credible LLM-assisted QDA.

cs.AI↗
arXiv2026

Using Grounded Theory for Agent Behavior Analysis at Scale

Understanding agent behavior requires methods that scale to thousands of trajectories and surface new patterns in long, often unfamiliar tasks where pre-built classifiers fall short. We propose to bring grounded theory into agent trajectory analysis: a six-decade-old qualitative method from the social sciences, with a principled saturation criterion and an auditable trail from data to theory. We propose AutoTraceGT (Automated Trace analysis through Grounded Theory), the first multi-agent pipeline that automates grounded theory on agent trajectories. It iteratively performs open, axial, and theoretical coding until saturation, producing a behavioral taxonomy tailored to each task. Across six trajectory corpora, AutoTraceGT produces codebooks that recover 73-91 percent of the failure modes in human-annotated taxonomies and surface additional patterns that those taxonomies miss. The emergent theoretical narrative aligns with prior expert accounts. Used as a deductive feature space, the codebook outperforms zero-shot and few-shot LLM baselines on downstream failure prediction. These results suggest Grounded Theory offers a scalable analytic tool for ML researchers and agent developers studying what agents actually do.

cs.CL↗
arXiv2026

ButterMamba: Butterworth-Enhanced Spatial-Temporal Mamba for Efficient Traffic Flow Prediction

Accurate traffic flow prediction is fundamental to intelligent transportation systems, playing a pivotal role in urban mobility optimization and smart city development. While Graph Neural Networks (GNNs) integrated with time series forecasting have emerged as promising solutions, two critical limitations persist: (1) the quadratic complexity of attention-based architectures hinders real-time deployment in large-scale networks, and (2) high-frequency noise in sensor data significantly degrades prediction reliability. These challenges are particularly acute in metropolitan scenarios where both computational efficiency and noise robustness are paramount. To address these limitations, we introduce \textbf{ButterMamba}, a novel and efficient framework based on State Space Models (SSMs). ButterMamba consists of two key components: (1) a Butterworth Spectral Filtering module that preprocesses the data by removing high-frequency noise, allowing the model to focus on significant underlying trends, and (2) a Spatial-Temporal State Mixer that uses a parallel Mamba architecture to efficiently capture both long-range temporal dependencies and complex spatial correlations across the road network. By decoupling noise filtering from spatial-temporal modeling, ButterMamba achieves superior predictive accuracy with linear computational complexity. Extensive experiments on three public datasets demonstrate that ButterMamba not only outperforms existing state-of-the-art models in terms of prediction accuracy but also considerably reduces training time and memory usage.

physics.soc-ph↗
arXiv2026

The Discrepancy of Shortest Paths

The hereditary discrepancy of a set system is a certain quantitative measure of the pseudorandom properties of the system. Roughly, hereditary discrepancy measures how well one can $2$-color the elements of the system so that each set contains approximately the same number of elements of each color. Hereditary discrepancy has well-studied applications e.g. in communication complexity and derandomization. More recently, the hereditary discrepancy of set systems of shortest paths has found applications in differential privacy [Chen et al.~SODA 23]. The contribution of this paper is to improve the upper and lower bounds on the hereditary discrepancy of set systems of unique shortest paths in graphs. In particular, we show that any system of unique shortest paths in an undirected weighted graph has hereditary discrepancy $\widetilde{O}(n^{1/4})$, and we construct lower bound examples demonstrating that this bound is tight up to hidden $\text{polylog } n$ factors. Our lower bounds apply even in the planar and bipartite settings, and they improve on a previous lower bound of $Ω(n^{1/6})$ obtained by applying the trace bound of Chazelle and Lvov [SoCG'00] to a classical point-line system of Erdős. As applications, we improve the lower bound on the additive error for differentially-private all pairs shortest distances from $Ω(n^{1/6})$ [Chen et al.~SODA 23] to $Ω(n^{1/4})$, and we improve the lower bound on additive error for the differentially-private all sets range queries problem to $Ω(n^{1/4})$, which is tight up to hidden $\text{polylog } n$ factors [Deng et al.~WADS 23].

cs.DS↗
arXiv2026

PromptKWS: A Novel Prompt-Guided Open-Vocabulary Keyword Spotting Framework

In this paper, we present PromptKWS, a novel Prompt-guided keyword spotting (KWS) framework to improve the accuracy of open vocabulary KWS systems. In specific terms, we introduce the Prompt Phrases Prediction Network (PPN), an encoder-decoder architecture designed to effectively extract keyword prompts embeddings. we employ the PPN encoder to encode the keyword prompts and infuse the prompt embedding into the Prompt-guided KWS encoder by utilizing a Prompt-acoustic Multi-head Cross-attention (MHCA). Experiments show that PromptKWS improves the wakeup rate by over 10% compared to baseline system. Notably, another strength of PromptKWS is its ability to effectively leverage keyword prompts for adapting to complex real-world environments involving noise and pronunciation variations. In comparison to purely acoustic models, which often struggle in such situations, PromptKWS demonstrates remarkable performance, with an average accuracy improvement of over 15% in test sets.

cs.CL↗
arXiv2026

Language-Specialized Multi-Teacher On-Policy Distillation for Multilingual LLM-Based ASR

Modern LLM-based ASR systems have established multilingual capability as a standard feature, leveraging large-scale multilingual corpora and LLMs' cross-lingual knowledge to achieve competitive performance across multilingual benchmarks. However, jointly modeling languages with heterogeneous acoustic, phonological, and lexical characteristics inevitably introduces optimization conflicts, undermining language-wise specialization. To address this challenge, we propose Language-Specialized Multi-Teacher On-Policy Distillation (LS-MOPD), which decouples language-specific knowledge acquisition from multilingual capability integration: language-specialized teachers are independently optimized via reinforcement learning (RL), with their expertise then integrated into a generalist multilingual student through language routing and token-level multi-teacher distillation, thereby reducing direct cross-lingual optimization conflicts. We further explore static and dynamic acoustic-prefix configurations to examine how teacher-student prefix consistency influences the efficacy of on-policy distillation. Experiments on benchmarks covering Mandarin, Mandarin subdialects, Cantonese, and English demonstrate that LS-MOPD substantially outperforms RL baselines and surpasses the empirical performance envelope defined by the best-performing RL teachers on nearly all benchmarks, revealing its potential to generalize beyond all teachers in multilingual ASR.

cs.CL↗
arXiv2026

Beyond Borrowed Histories: Person-Aligned User Simulation for Interactive Role-Playing Evaluation

Role-playing agents (RPAs) have become one of the most important consumer applications of large language models. Users engage in multi-turn conversations with RPAs for experiences such as emotional comfort, making reliable evaluation essential for measuring capability, comparing systems, and guiding further improvement. Existing benchmarks, however, typically require an RPA to continue a fixed dialogue history and then evaluate the continuation using a fixed rubric detached from the user. We identify and empirically demonstrate two limitations of this design. First, an RPA's output is shaped by the preceding dialogue history, preventing a scientifically grounded assessment of its role-playing ability in real multi-turn settings. Second, user experience varies substantially across individuals, and conventional fixed rubrics need not align with user satisfaction. We therefore introduce PALATE (Person-Aligned LLM-Simulated-User Assessment with Tailored Evaluation), a scalable RPA benchmark built on user simulators. PALATE is accompanied by a pool of 300 character profiles. Its main evaluation trains five per-user simulators and lets them engage candidate RPAs in free-form, multi-turn conversations over a pre-frozen panel of character profiles. Alongside a general quality rubric, we construct personalized rubrics to measure user satisfaction; on held-out annotated data, the personalized rubrics show higher agreement with human judgments than the general rubric. In the main evaluation of 16 candidates, PALATE separately characterizes generic turn quality, long-horizon session capability, and per-user experience on multi-turn trajectories co-constructed by each candidate. It thereby produces interpretable evaluations of specific user-RPA pairs rather than compressing systems into a single user-independent ranking.

cs.CL↗
arXiv2026

Capturing Token Tendencies for Training-Free Token Pruning in Multimodal Large Language Models

While visual token pruning is essential for efficient Multimodal Large Language Models (MLLMs), existing training-free methods suffer from a critical limitation: they rely on static, instantaneous heuristics to perform irreversible filtering. This approach ignores the hierarchical nature of MLLMs, where token importance often evolves dynamically rather than remaining fixed across layers. Consequently, tokens essential for deep-layer reasoning are often prematurely discarded by shallow-layer estimates. To address this, we propose Trend-aware Pruning, a novel framework that elevates pruning from a local snapshot decision to a temporal trajectory modeling problem. Instead of relying on isolated scores, our method captures the momentum of attention flow. This enables a dynamic rectification mechanism that selectively reactivates "late-blooming" tokens, those initially undervalued but exhibiting rising semantic importance, thereby preventing the loss of critical visual cues. Extensive experiments demonstrate that our approach achieves a superior efficiency-performance trade-off across diverse multimodal tasks. Notably, it reduces visual tokens by over 77.8%, retaining only approximately 23 tokens in the final layer while maintaining competitive performance, offering a robust and reversible solution for high-efficiency multimodal inference.

cs.CV↗
arXiv2026

Gravitational Wave Astronomy With TianQin

The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them.

astro-ph.GA↗
arXiv2026

Efficient Partitioning Method of Large-Scale Public Safety Spatio-Temporal Data based on Information Loss Constraints

The storage, management, and application of massive spatio-temporal data are widely used in practical scenarios, including public safety. However, due to the unique spatio-temporal distribution characteristics of real-world data, existing methods still face limitations in preserving spatio-temporal proximity and achieving load balancing in distributed storage. This paper proposes an efficient partitioning method for large-scale public safety spatio-temporal data based on information loss constraints, named IFL-LSTP. The model combines a spatio-temporal partitioning module (STPM) and a graph partitioning module (GPM). STPM reduces the scale of data under a predefined information-loss threshold, while GPM uses graph representation learning to obtain balanced graph partitions. Experiments on multiple real-world datasets show that IFL-LSTP can reduce data scale, shorten graph model training time, preserve spatio-temporal proximity, and improve load-balancing effectiveness.

cs.LG↗
arXiv2026

Behavior Foundations for Quadruped Robots: ABot-C0 Technical Report

The motion controller is one of the most fundamental modules in embodied intelligence systems. Driven by large-scale human motion-capture data and the motion-tracking paradigm, humanoid control has achieved remarkable progress in recent years. However, migrating this recipe to the quadrupedal setting is far less straightforward: animal motion data is scarcer and harder to capture at scale than human data, and cross-embodiment retargeting remains fragile. We present ABot-C0, a generalist motion-control system for quadruped robots that establishes three complementary behavior foundations: a scalable multi-source motion-data pipeline, robust policy learning across motion tracking, locomotion, and scene interaction, and a unified deployment stack for reliable real-world operation. Fundamentally, we construct a data pyramid through conditional video-generation synthesis, annotated motion capture, teleoperation, and human design, producing 16,074 physically feasible motion clips as the data foundation for diverse motion-learning demands. With large-scale motion data, a Flow-Matching generalist policy demonstrates, for the first time, a scaling law for quadruped motion tracking: performance improves consistently as training scales up, with zero-shot capability to track unseen motions. We then go a step further toward robust all-terrain locomotion by adopting a three-stage privileged-to-perceptive framework with temporal LiDAR memory and terrain-predictive supervision. Collectively, these components form a motion generalist that coordinates multi-policy execution, smooth behavior transitions, energy-efficient control, and safety mechanisms for real-world deployment. Extensive experiments on urban-terrain autonomous navigation and companion-style multimodal interaction demonstrate that quadruped robots can move beyond functional demos toward product-level behavioral intelligence.

cs.RO↗
arXiv2026

HiFA4: Training-Free 4-bit FlashAttention on Ascend HIF4 NPUs for LLM Inference

We present HiFA4, a post-training operator-level design that executes both QK^T and PV in FlashAttention as 4-bit HIF4 Cube GEMMs for LLM inference on Ascend NPUs, while maintaining the online softmax state in FP16. To our knowledge, HiFA4 is the first Ascend-HIF4-targeted design of this kind evaluated on standard NLP benchmarks. HiFA4 combines two mechanisms. Smooth-QK applies a calibration-static per-channel equivalent rescaling to Q and K after RoPE, transferring quantization difficulty from K to Q without per-tile online reduction at inference. P-Reordering accumulates the softmax normalizer from the same quantized attention weights P_hat used in the PV GEMM, rather than from a higher-precision reconstruction. We show that this inconsistent formulation introduces a coherent output-scaling error, and validate the effect on a Qwen3-8B Layer-0 MMLU trace, where all 3.6M measured attention tiles exhibit net probability-mass loss with median epsilon_bar = -0.064. P-Reordering also allows the normalizer to be fused into the PV Cube GEMM. Across five LLMs, HiFA4 reduces quantization-induced decision drift. On Qwen3-8B, it recovers 37.5% of the accuracy gap introduced by direct HIF4 quantization, narrows the sample-weighted accuracy loss from 1.12 pp to 0.70 pp, reduces BF16-inconsistent MMLU predictions from 16.3% to 8.2%, and cuts MMLU accuracy regressions by 57% (1071 to 465). On Gemma2-9B, mild smoothing keeps HiFA4 within 0.7 pp of BF16 while reducing MMLU regressions by 27%. On LLaMA3.1-8B, Mistral-7B, and Phi-4B, where Smooth-QK is disabled, P-Reordering with the adopted Q-Mean auxiliary still reduces full-set MMLU regressions by 41-52%. A preliminary instruction-scheduling analysis projects a 35.4% critical-path latency reduction relative to BF16 by fusing the softmax normalizer into the PV Cube GEMM; on-hardware validation is left to future work.

cs.LG↗
arXiv2026

One Reflection Is Not Enough: Self-Correcting Autonomous Research via Multi-Hypothesis Failure Attribution

Autonomous research agents can now draft hypotheses, write code, run experiments, and produce papers, but they remain brittle when experiments fail. Under the prevailing paradigm, failure recovery is usually delegated to a single free-form reflection: a rich trajectory of metrics, logs, and design choices is compressed into one verbal critique, which often leads either to localized trial-and-error or to hard pivots that discard useful context. We propose SAGE, a Self-correcting, Autonomous, Grounded Experimenter, to tackle this failure-recovery bottleneck. Its core mechanism, Multi-Hypothesis Failure Attribution (MHFA), treats recovery as a structured causal diagnosis. By analyzing dynamic trajectory features, MHFA systematically generates multiple evidence-grounded explanations for a failure, independently evaluates their severity, and deterministically routes the verified root cause to the correct intervention level (hypothesis, experimental design, or implementation). To guarantee scientific honesty, SAGE further employs a grounded reporting mechanism that explicitly constrains drafted results to actual measured values, redacting hallucinated numbers. On a 12-topic, 5-domain benchmark, SAGE increases metrics-bearing outputs from 42% to 92% over a reflection baseline, improves artifact quality from 5.00 to 6.75/10, and blindly outscores AI-Scientist-v2 (52.0 vs. 48.2), with gains concentrated in code development and execution. While fully autonomous scientific writing and generating conference-ready papers remain notoriously difficult open problems for the entire field, SAGE successfully produces significantly more reliable and higher-quality scientific artifacts. Ultimately, by coupling structured recovery with explicit grounding constraints, SAGE significantly outperforms monolithic reflection paradigms, establishing a highly trustworthy foundation for future autonomous research.

cs.AI↗
arXiv2026

NIM4-ASR: Towards Efficient, Robust, and Customizable Real-Time LLM-Based ASR

Integrating large language models (LLMs) into automatic speech recognition (ASR) has become a mainstream paradigm in recent years. Although existing LLM-based ASR models demonstrate impressive performance on public benchmarks, their training remains predominantly data-driven, leaving key practical challenges insufficiently addressed -- particularly limited downward scalability in resource-constrained deployments and hallucinations under acoustically challenging conditions. To address these issues, we present NIM4-ASR, a production-oriented LLM-based ASR framework optimized for both efficiency and robustness. Grounded in a principled delineation of functional roles between the encoder and the LLM, we redesign the multi-stage training paradigm to align each module with its intended capability boundary. Specifically, we reformulate the pre-training architecture and objective to mitigate the modality gap and improve parameter efficiency; introduce an iterative asynchronous SFT stage to preserve acoustic fidelity and constrain representation drift; and design an ASR-specialized reinforcement learning stage to further enhance recognition quality and robustness. We additionally incorporate a suite of production-oriented optimizations, including robustness under noisy and silent conditions, real-time streaming inference, and hotword customization via retrieval-augmented generation (RAG). Experiments show that NIM4-ASR achieves state-of-the-art performance on multiple public benchmarks with merely 2.3B parameters, while substantially outperforming larger-scale competitors on internal benchmarks -- particularly in entity-intensive real-world scenarios. NIM4-ASR further supports million-scale hotword customization via RAG with sub-millisecond retrieval latency, enabling efficient adaptation to emerging entities and personalized user requirements.

eess.AS↗
arXiv2026

Multi-Modal Hyper-Graph Fusion for Low-Light Crowd Counting

Crowd counting is a fundamental task in computer vision. However, crowd counting in low-light environments remains largely underexplored, despite its practical importance in the real world. Existing methods mainly focus on well-lit scenes or rely on single-modality Red-Green-Blue (RGB) representations, which often become unreliable under extreme darkness and complex non-uniform illumination. To handle this problem, we construct three new low-light crowd counting benchmarks, which consist of two synthetic datasets, SHA\_Dark and SHB\_Dark, and a real-world benchmark LC-Crowd (Low-light Crowd Dataset). Inspired by Retinex-based physical modeling, we introduce depth and Canny edge cues as complementary geometric and structural priors to enhance the intrinsic reflectance representation under low-light conditions. We propose a Multi-Modal Hyper-Graph Fusion module, which formulates RGB appearance, depth geometry, and edge structure cues as nodes in a unified hyper-graph and explicitly captures their high-order complementary relationships via dynamic hyperedge construction and message passing. Furthermore, to adaptively allocate computation in dense prediction, we propose a Deformable Rectangular Sparse Attention (DRSA) module, which concentrates computation on informative regions through anchor-aware estimation and adaptive rectangular window modeling. Based on these designs, we develop a unified Low-Light Counting Network (LCNet) for robust low-light crowd counting. Extensive experiments on three benchmarks demonstrate that the proposed method achieves the best overall performance against existing state-of-the-art (SOTA) methods. The code is in the supplementary material. The datasets will be made public upon acceptance.

cs.CV↗
arXiv2026

RT-Counter: Real-Time Text-Guided Open-Vocabulary Object Counting

Text-guided open-vocabulary object counting (TOOC) aims to count objects belonging to the categories specified by natural language descriptions. Although vision-language pre-trained models have been successful applied to TOOC tasks, they still struggle with fine-grained spatial understanding and real-time inference requirements in counting scenarios. To address these limitations, this paper proposes a real-time TOOC framework, called the Real-Time Counter (RT-Counter), that achieves not only good counting accuracy but also high computational efficiency. RT-Counter designs a novel Visual Prototype Textualization (VPT) module that can project learned visual features into a text feature space and then generate features containing the abstract information that is hard to capture with visual prototypes and the detailed prototype information that is difficult to describe in text, enhancing the object-level visual-language model's counting capabilities. Additionally, RT-Counter incorporates our Weaving Transformer (Weaformer) layers, maintaining high descriptive power at a fraction of the computational cost. The Weaformer layer adopts a novel hybrid attention mechanism that can efficiently weave together local and global visual features. Extensive experiments on three public datasets show that RT-Counter successfully breaks the accuracy-speed trade-off in TOOC. While achieving a competitive MAE of 13.30 on FSC147, RT-Counter operates at 112.48 FPS, making it 7.4x faster and over 4$\times$ more parameter-efficient than the existing leading methods in TOOC. Our work aims at balancing high accuracy and real-time performance in TOOC. Code is available at: https://github.com/Jason-Mar1/RT-Counter.

cs.CV↗