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Optimization · Everything Else

Yuhang Liu, Tao Li, Zhehao Huang, Zuopeng Yang, Xiaolin Huang

Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large pre-trained models. Yet LoRA can face generalization challenges. One promising way to improve the generalization is Sharpness-Aware Minimization (SAM), which has proven effective for small-scale training scenarios. In this paper, we propose **Bi**-directional **Lo**w-**R**ank **A**daptation (Bi-LoRA), which introduces an auxiliary adversarial LoRA module. This design explicitly decouples sharpness optimization, handled by the auxiliary module, from task adaptation, performed by the primary module. Such a separation yields two key benefits. First, it transforms the sequential computation of primary LoRA update and adversarial perturbation into a parallel form, which roughly halves the time and conquers the main obstacle of applying SAM in LoRA. Second, it provides perturbations from the auxiliary module that do not collapse into the restricted optimization subspace of the primary module, enabling broader sharpness exploration and flatter minima. Bi-LoRA simultaneously achieves both efficiency and effectiveness within a single framework, as verified by extensive experiments across diverse architectures and tasks.

Deep Learning · Everything Else

Alan Sun, Mariya Toneva

Mechanistic interpretability (MI) is an emerging framework for interpreting neural networks. Given a task and model, MI aims to discover a succinct algorithmic process, an interpretation, that explains the model's decision process on that task. However, MI is difficult to scale and generalize. This stems in part from two key challenges: there is no precise notion of a valid interpretation; and, generating interpretations is often an ad hoc process. In this paper, we address these challenges by defining and studying the problem of interpretive equivalence: determining whether two different models share a common interpretation, without requiring an explicit description of what that interpretation is. At the core of our approach, we propose and formalize the principle that two interpretations of a model are equivalent if all of their possible implementations are also equivalent. We develop an algorithm to estimate interpretive equivalence and case study its use on Transformer-based models. To analyze our algorithm, we introduce necessary and sufficient conditions for interpretive equivalence based on models' representation similarity. We provide guarantees that simultaneously relate a model's algorithmic interpretations, circuits, and representations. Our framework lays a foundation for the development of more rigorous evaluation methods of MI and automated, generalizable interpretation discovery methods.

Reinforcement Learning · Everything Else

Aladin Djuhera, Farhan Ahmed, Swanand Kadhe, Syed Zawad, Heiko Ludwig, Holger Boche

Aligning large language models (LLMs) is a central objective of post-training, often achieved through reward modeling and reinforcement learning methods. Among these, direct preference optimization (DPO) has emerged as a widely adopted technique that fine-tunes LLMs on preferred completions over less favorable ones. While most frontier LLMs do not disclose their curated preference pairs, the broader LLM community has released several open-source DPO datasets, including TuluDPO, ORPO, UltraFeedback, HelpSteer, and Code-Preference-Pairs. However, systematic comparisons remain scarce, largely due to the high computational cost and the lack of rich quality annotations, making it difficult to understand how preferences were selected, which task types they span, and how well they reflect human judgment on a per-sample level. In this work, we present the first comprehensive, data-centric analysis of popular open-source DPO corpora. We leverage the Magpie framework to annotate each sample for task category, input quality, and preference reward, a reward-model-based signal that validates the preference order without relying on human annotations. This enables a scalable, fine-grained inspection of preference quality across datasets, revealing structural and qualitative discrepancies in reward margins. Building on these insights, we systematically curate a new DPO mixture, **UltraMix**, that draws selectively from all five corpora while removing noisy or redundant samples. UltraMix is 30\% smaller than the best-performing individual dataset yet exceeds its performance across key benchmarks. We publicly release all annotations, metadata, and our curated mixture to facilitate future research in data-centric preference optimization.

General Machine Learning · Everything Else

Nicolas Salvy, Hugues Talbot, Bertrand Thirion

Although generative models have made remarkable progress in recent years, their use in critical applications has been hindered by an inability to reliably evaluate the quality of their generated samples. Quality refers to at least two complementary concepts: fidelity and coverage. Current quality metrics often lack reliable, interpretable values due to an absence of calibration or insufficient robustness to outliers. To address these shortcomings, we introduce two novel metrics: $\textit{Clipped Density}$ and $\textit{Clipped Coverage}$. By clipping individual sample contributions, as well as the radii of nearest neighbor balls for fidelity, our metrics prevent out-of-distribution samples from biasing the aggregated values. Through analytical and empirical calibration, these metrics demonstrate linear score degradation as the proportion of bad samples increases. Thus, they can be straightforwardly interpreted as equivalent proportions of good samples. Extensive experiments on synthetic and real-world datasets demonstrate that $\textit{Clipped Density}$ and $\textit{Clipped Coverage}$ outperform existing methods in terms of robustness, sensitivity, and interpretability when evaluating generative models.

General Machine Learning · Everything Else

Qingyang Hao, Wenbo Liao, Bingyi Jing, Hongxin Wei

Selecting high-quality candidates from large-scale datasets is critically important in resource-constrained applications such as drug discovery, precision medicine, and the alignment of large language models. While conformal selection methods offer a rigorous solution with False Discovery Rate (FDR) control, their applicability is confined to single-threshold scenarios (i.e., y > c) and overlooks practical needs for multi-condition selection, such as conjunctive or disjunctive conditions. In this work, we propose the Multi-Condition Conformal Selection (MCCS) algorithm, which extends conformal selection to scenarios with multiple conditions. In particular, we introduce a novel nonconformity score with regional monotonicity for conjunctive conditions and a global Benjamini–Hochberg (BH) procedure for disjunctive conditions, thereby establishing finite-sample FDR control with theoretical guarantees. The integration of these components enables the proposed method to achieve rigorous FDR-controlled selection in various multi-condition environments. Extensive experiments validate the superiority of MCCS over baselines, its generalizability across diverse condition combinations, different real-world modalities, and multi-task scalability.

Deep Learning · Everything Else

Daniel Israel, Tian Jin, Ellie Cheng, Guy Van den Broeck, Aditya Grover, Suvinay Subramanian, Michael Carbin

Most existing large language models are autoregressive: they generate text one token at a time, and cannot decode any new tokens until they have decoded every token before it. Discrete diffusion language models offer a promising alternative by generating multiple tokens in parallel, but sampling from them requires a _denoising order_, the strategy for deciding which tokens to decode at each step. Determining the right denoising order is difficult, and existing approaches use heuristics that create a steep trade-off between quality and latency. We propose _planned diffusion_, a system that trains the model to determine its own denoising order. Planned diffusion uses a single model that transitions between autoregressive and diffusion-based generation: first, the model autoregressively generates a plan that partitions the response into semantically independent chunks, defining a denoising order that parallelizes sampling across chunks; second, the model executes this plan via diffusion denoising. On AlpacaEval, a suite of 805 instruction-following prompts, planned diffusion achieves Pareto-optimal trade-off between quality and latency, achieving 1.27x to 1.81x speedup over autoregressive generation with only 0.87\% to 5.4\% drop in win rate. Our empirical results show that planned diffusion exhibits superior performance scaling on downstream tasks compared to autoregressive baselines while offering the runtime flexibility to precisely navigate the quality-latency trade-off.

Deep Learning · Everything Else

Jiayu Zhang, Chuangxin Zhao, Canran Xiao, Ruibo Duan, Wenyi Mo, Haoyu Gao, Wenshuo Wang

When deployed on non-stationary data streams, foundation vision-language models require continual updates without access to past data. However, naive fine-tuning undermines their zero-shot recognition capabilities and prompt robustness. We seek a replay-free principle that preserves pre-trained cross-modal generalization under domain/prompt shifts. We introduce Prompt-Invariant CCA Certificates (Pi-CCA), a geometry-first approach that summarizes image--text alignment with a compact certificate capturing the top-k canonical spectrum and subspace. During adaptation, we match this summary using only mini-batch statistics and induce prompt robustness via averaging over perturbations. Across MTIL, X-TAIL, VLCL, and ConStruct-VL, Pi-CCA achieves state-of-the-art performance among replay-free methods. By optimizing alignment invariants rather than proxy signals, Pi-CCA provides a simple, generator-free, constant-memory path to continual adaptation with strong zero-shot retention and resilience to prompt/style shifts.

Deep Learning · Everything Else

Anik Pramanik, Murat Kantarcioglu, Vincent Oria, Shantanu Sharma

Federated Learning (FL) enables a group of clients to collaboratively train a model without sharing individual data, but its performance drops when client data are heterogeneous. Clustered FL tackles this by grouping similar clients. However, existing clustered FL approaches rely solely on either data similarity or gradient similarity; however, this results in an incomplete assessment of client similarities. Prior clustered FL approaches also restrict knowledge and representation sharing to clients within the same cluster. This prevents cluster models from benefiting from the diverse client population across clusters. To address these limitations, FEDDAG introduces a clustered FL framework, FEDDAG, that employs a weighted, class-wise similarity metric that integrates both data and gradient information, providing a more holistic measure of similarity during clustering. In addition, FEDDAG adopts a dual-encoder architecture for cluster models, comprising a primary encoder trained on its own clients' data and a secondary encoder refined using gradients from complementary clusters. This enables cross-cluster feature transfer while preserving cluster-specific specialization. Experiments on diverse benchmarks and data heterogeneity settings show that FEDDAG consistently outperforms state-of-the-art clustered FL baselines in accuracy.

Applications · Everything Else

JUNYONG AHN, Hyeongrok Han, Bong Gyun Kang, Jisoo Mok, Byunghan Lee, Sungroh Yoon

Developing a mobile system capable of generating responses based on stored user data is a crucial challenge. Since user data is stored in the form of Knowledge Graphs, the field of knowledge graph question answering (KGQA) presents a promising avenue towards addressing this problem. However, existing KGQA systems face two critical limitations that preclude their on-device deployment: resource constraints and the inability to handle data accumulation. Therefore, we propose MobileKGQA, the first on-device KGQA system capable of adapting to evolving databases with minimal resource demands. MobileKGQA significantly reduces computational overhead through embedding hashing. Moreover, it successfully adapts to evolving databases under resource constraints through a novel annotation generation method. Its mobile applicability is validated on the NVIDIA Jetson Orin Nano edge-device platform, achieving 20.3% higher performance while using only 30.4% of the energy consumed by the SOTA (state-of-the-art). On standard KGQA benchmarks, using just 7.2% of the computation and 9% of the parameters, MobileKGQA demonstrates performance that is empirically indistinguishable from the SOTA and outperforms baselines under distribution shift scenarios.

Reinforcement Learning · Everything Else

Haoming Meng, Kexin Huang, Shaohang Wei, Chiyu Ma, Shuo Yang, xue wang, Guoyin Wang, Bolin Ding, Jingren Zhou

Reinforcement learning with verifiable rewards (RLVR) has significantly improved reasoning in large language models (LLMs), yet the token-level mechanisms underlying these improvements remain unclear. We present a systematic empirical study of RLVR’s distributional effects organized around three main analyses: (1) token-level characterization of distributional shifts between base and RL models, (2) the impact of token-level distributional shifts on reasoning performance through cross-sampling interventions, and (3) fine-grained mechanics of these shifts at the token level. We find that RL fine-tuning induces highly sparse and targeted changes, with only a small fraction of token distributions exhibiting meaningful divergence. We further characterize the structure of these shifts through analyses of token entropy, positional concentration, and reallocation of probability mass. To assess the functional importance of these sparse changes, we conduct cross-sampling experiments that selectively swap token choices between the base and RL models. Inserting only a small fraction of RL-sampled tokens into base generations progressively recovers RL performance gains, while injecting a similarly small number of base token choices into RL-generated responses collapses performance to base levels, isolating a sparse set of token-level decisions directly responsible for RLVR’s improvements. Finally, we explore divergence-weighted variants of the advantage signal as a diagnostic intervention, finding that they can yield improvements over baselines. Together, our results shed light on the distributional changes induced by RLVR and provide a fine-grained, token-level lens for understanding RLVR as a targeted refinement process.

Applications · Everything Else

Moises Andrade, Joonhyuk Cha, Brandon Ho, Vriksha Srihari, Karmesh Yadav, Zsolt Kira

Verifiers—functions assigning rewards to agent behavior—have been key to AI progress in domains such as math, code, and games. However, extending these gains to domains without clear-cut success criteria (e.g., computer use) remains a challenge: while humans can recognize desired outcomes, translating this intuition into scalable rules is nontrivial. Multimodal LLMs (MLLMs) emerge as a promising solution, given vast world knowledge, human-preference alignment, and reasoning capabilities. We evaluate MLLMs as verifiers across web navigation, computer use, and robotics, spanning 13+ model families, 28+ evaluation templates, curated trajectories from diverse agents and of varying lengths, and distinct verifier applications. We identify a critical limitation: a strong tendency for MLLMs to over-validate agent behavior—a phenomenon we term agreement bias. This bias is pervasive across models, resilient to test-time scaling, and can harm methods relying on MLLM evaluations, such as filtered behavior cloning and self-improvement. We provide guidance on the design and evaluation of MLLM verifiers, and introduce Self-Grounded Verification (SGV), a lightweight method that harnesses MLLMs' own sampling mechanisms by modulating (un)conditional generation to better leverage their knowledge, alignment, and reasoning. SGV operates in two steps: first, the MLLM is elicited to generate broad priors about desired behavior, independent of the data under evaluation. Then, conditioned on self-generated priors, it reasons over and evaluates a candidate trajectory. Our methods yield gains across models and environments, improving failure detection by up to 25pp and accuracy by 14pp, with benefits extending to downstream applications. In self-improvement and online supervision, SGV boosts task completion of a GUI specialist in OSWorld, a diffusion policy in robomimic, and a ReAct agent in VisualWebArena—setting a new state of the art, surpassing the previous best by 20pp. Finally, we release an updated version of VisualWebArena featuring strong agent baselines, more human-aligned evaluators, high-fidelity environment parallelism, runtime speedups exceeding 10x, and VisualWebArena-Lite, a 1/3-scale subset with comparable evaluation fidelity. Our code, models, and data are publicly available at [our project page](https://mshalimay.github.io/agreement-bias-sgv/).

General Machine Learning · Everything Else

Zihuan Qiu, Lei Wang, Yang Cao, Runtong ZHANG, Bing Su, Yi Xu, Fanman Meng, Linfeng Xu, Qingbo Wu, Hongliang Li

Data-free continual model merging (DFCMM) aims to fuse independently fine-tuned models into a single backbone that evolves with incoming tasks without accessing task data. This paper revisits two fundamental desiderata for DFCMM: stability, avoiding interference with earlier tasks, and plasticity, adapting faithfully to each new task. This poses a challenge that existing approaches fail to address: how to bridge data-level desiderata with parameter-space optimization to ensure stability and plasticity in the absence of task data. To this end, we propose NUFILT(NUll-space FILTering) a data-free framework that directly links these desiderata into parameter-space optimization. Our key observation is that task vectors approximately align with representation subspaces, providing structural surrogates for enforcing stability and plasticity. Accordingly, we design a null-space projector that preserves prior responses by filtering overlapping components of new task vectors, ensuring stability. We further introduce a lightweight LoRA adapter that injects complementary task-specific signals to enable plasticity. The adapter is trained with a projection-based surrogate loss that preserves consistency with prior knowledge while introducing novel directions. This joint filtering–adaptation process enables the backbone to absorb new knowledge while retaining existing behaviors, with updates fused back in a layer-wise linear fashion without extra parameters or inference cost. Theoretically, we establish approximate subspace alignment guarantees that justify null-space filtering. Empirically, NUFILT achieves state-of-the-art performance with minimal forgetting on both vision and NLP benchmarks, improving average accuracy by 4–7% over OPCM and WUDI-Merging, while narrowing the gap to fine-tuning and reducing computation overhead. The code is available at: https://github.com/zihuanqiu/NUFILT

Deep Learning · Everything Else

Shihao Zhang, Haoyu Zhang, Ian Colbert, Rayan Saab

We introduce Qronos---a new post-training quantization algorithm that not only explicitly corrects errors due to both weight and activation quantization, but also corrects errors accumulated from previously quantized layers. Our iterative algorithm is based on an interpretable and disciplined optimization framework that surpasses existing data-driven approaches. At each step, Qronos alternates between error correction and diffusion via optimal update rules. Importantly, we prove that Qronos admits an equivalent formulation that significantly improves algorithmic efficiency; we use our discovery to reduce peak memory usage by 18\times on Llama3 8B, and our scaling analysis shows a speedup of up to 13.8\times for a single-layer microbenchmark. We demonstrate compatibility with existing transformation techniques such as Hadamard-based incoherence processing and weight-activation scaling equalization, among others. We evaluate Qronos using recent language models in the Llama3 and Qwen3 families; Qronos consistently outperforms previous state-of-the-art adaptive rounding methods when quantizing the weights, activations, and/or KV caches to 4 bits or fewer.

Reinforcement Learning · Everything Else

Bill Zheng, Vivek Myers, Benjamin Eysenbach, Sergey Levine

The problem of learning how to reach goals in an environment has been a long- standing challenge in for AI researchers. Effective goal-conditioned reinforcement learning (GCRL) methods promise to enable reaching distant goals without task- specific rewards by stitching together past experiences of different complexity. Mathematically, there is a duality between the notion of optimal goal-reaching value functions (the likelihood of success at reaching a goal) and temporal dis- tances (transit times states). Recent works have exploited this property by learning quasimetric distance representations that stitch long-horizon behaviors using the in- ductive bias of their architecture. These methods have shown promise in simulated benchmarks, reducing value learning to a shortest-path problem. But quasimet- ric, and more generally, goal-conditioned RL methods still struggle in complex environments with stochasticity and high-dimensional (visual) observations. There is a fundamental tension between the local dynamic programming (TD backups, temporal distances) that enables optimal shortest-path reasoning in theory and the statistical global MC updates (multistep returns, suboptimal in theory). We show how these approaches can be integrated into a practical GCRL method that fits a quasimetric distance using a multistep Monte-Carlo return. We show our method outperforms existing GCRL methods on long-horizon simulated tasks with up to 4000 steps, even with visual observations. We also demonstrate that our method can enable stitching in the real-world robotic manipulation domain (Bridge setup). Our approach is the first end-to-end GCRL method that enables multistep stitching in this real-world manipulation domain from an unlabeled offline dataset of visual observations.

General Machine Learning · Everything Else

Xingjian Hu, Ziqian Zhang, Yue Huang, Kai Zhang, Ruoxi Chen, Yixin Liu, Qingsong Wen, Kaidi Xu, Xiangliang Zhang, Neil Gong 等

Benchmarks establish a standardized evaluation framework to systematically assess the performance of large language models (LLMs), facilitating objective comparisons and driving advancements in the field. However, existing benchmarks fail to differentiate question difficulty, limiting their ability to effectively distinguish models' capabilities. To address this limitation, we propose Empirical Interaction Propagation (EIP), a novel framework designed to quantify both question difficulty and model competency. EIP introduces difficulty as the primary criterion for differentiation, enabling a more fine-grained evaluation of LLM capabilities. EIP's core mechanism facilitates bidirectional score propagation between models and questions. The core intuition of EIP is that a model earns a competency score when it correctly answers a question, while a question's difficulty score increases when it challenges a model. Using this framework, we evaluate 30 models on 35,550 questions across multiple domains. EIP achieves 90\% agreement with human judgments and consistently outperforms strong baselines such as IRT. It also exhibits strong stability, fast convergence, and high computational efficiency, making it a practical solution for large-scale, difficulty-aware LLM evaluation. Code is available at https://github.com/Leozz04/EIP.

Computer Vision · Everything Else

Gwangik Shin, Jaeha Song, Soonmin Hwang

Object detection in low-light environments is inherently challenging due to limited contrast and heavy noise, both of which significantly degrade feature representations. In this paper, we propose a novel self-guided low-light object detection framework that effectively addresses these issues without introducing additional parameters or increasing inference time. Our method incorporates a detachable auxiliary pipeline during training, consisting of an image enhancement module and a denoising module, followed by a Fourier-domain fusion block. This pipeline improves the feature representation of the detector's backbone, enhancing its robustness under low-light conditions. Importantly, at inference time, our method incurs no additional computational cost compared to the baseline detector while achieving substantial performance improvements. Extensive experiments on widely used low-light object detection benchmarks, such as DARK FACE and ExDark, demonstrate that our method achieves state-of-the-art performance. Notably, experiments on the nuImages dataset show that our approach can outperform domain adaptation methods—especially when a large domain gap between source and target domains is inevitable in the real-world applications—highlighting its practical effectiveness. Code is available at https://github.com/gw-shin/SGLDet.

Optimization · Everything Else

Ali Saheb Pasand, Elvis Dohmatob

Grokking is the phenomenon whereby, unlike the training performance which peaks very early on during training, the test/generalization performance of a model stagnates over arbitrarily many epochs and then suddenly jumps to usually close to perfect levels. In practice, it is desirable to reduce the length of such plateaus, that is to make the learning process "grok" faster. In this work, we provide new insights into grokking. First, we show both empirically and theoretically that grokking can be induced by asymmetric speeds of (stochastic) gradient descent, along different principal (i.e singular directions) of the gradients. We then propose a simple modification that normalizes the gradients so that dynamics along all the principal directions evolves at exactly the same speed. Then, we establish that this modified method, which we call egalitarian gradient descent (EGD) and can be seen as a carefully modified form of natural gradient descent, groks much faster. In fact, in some cases the stagnation is completely removed. Finally, we empirically show that on classical arithmetic problems like modular addition and sparse parity problem which this stagnation has been widely observed and intensively studied, that our proposed method removes the plateaus.

Deep Learning · Everything Else

Monoshi Kumar Roy, Simin Chen, Benjamin Steenhoek, Jinjun Peng, Gail Kaiser, Baishakhi Ray, Wei Le

Understanding and reasoning about code semantics is essential for enhancing code LLMs' abilities to solve real-world software engineering (SE) tasks. Although several code reasoning benchmarks exist, most rely on synthetic datasets or educational coding problems and focus on coarse-grained reasoning tasks such as input/output prediction, limiting their effectiveness in evaluating LLMs in practical SE contexts. To bridge this gap, we propose CodeSense, the first benchmark that makes available a spectrum of fine-grained code reasoning tasks concerned with the software engineering of real-world code. We collected Python, C and Java software projects from real-world repositories. We executed tests from these repositories, collected their execution traces, and constructed a ground truth dataset for fine-grained semantic reasoning tasks. We then performed comprehensive evaluations on state-of-the-art LLMs. Our results show a clear performance gap for the models to handle fine-grained reasoning tasks. Although prompting techniques such as chain-of-thought and in-context learning helped, the lack of code semantics in LLMs fundamentally limit models' capabilities of code reasoning. Besides dataset, benchmark and evaluation, our work produced an execution tracing framework and tool set that make it easy to collect ground truth for fine-grained SE reasoning tasks, offering a strong basis for future benchmark construction and model post training. Our code and data are located at \url{https://codesense-bench.github.io/}.

Reinforcement Learning · Everything Else

Anthony GX-Chen, Jatin Prakash, Jeff Guo, Rob Fergus, Rajesh Ranganath

Classical intuitions cast minimizing reverse KL as "mode seeking" and forward KL as "mass covering". In KL-regularized reinforcement learning, however, the regularizer determines _both_ the target distribution's shape _and_ the divergence being implicitly minimized, making its role more nuanced than simply inducing generic mode-seeking or mass-covering behaviour. Specifically, the target distribution is defined jointly by the reward function, the reference model, the type of regularizer, and the regularization strength. We show that under common settings—such as low regularization strength and equal verifiable rewards—both forward and reverse KL regularization tend to specify target distributions whose mass concentrates on a single high-reward region. Thus, the objective itself _by construction_ induces diversity collapse, regardless of the policy optimization algorithm used. Building on this perspective, we introduce a simple and scalable modification that rescales rewards to induce target distributions assigning substantial probability across _all_ high-reward regions. This yields a principled objective that maintains high solution quality while achieving broad reward-mode coverage. Empirically, this approach improves post-training diversity and performance for Large Language Models and Chemical Language Models, and is effective with either forward or reverse KL regularization, while using either naively fails.

General Machine Learning · Everything Else

Kejing Lu, Chuan Xiao, Yoshiharu Ishikawa

In this paper, we study the angle testing problem in the context of similarity search in high-dimensional Euclidean spaces and propose two projection-based probabilistic kernel functions, one designed for angle comparison and the other for angle thresholding. Unlike existing approaches that rely on random projection vectors drawn from Gaussian distributions, our approach leverages reference angles and adopts a deterministic structure for the projection vectors. Notably, our kernel functions do not require asymptotic assumptions, such as the number of projection vectors tending to infinity, and can be theoretically and experimentally shown to outperform Gaussian-distribution-based kernel functions. We apply the proposed kernel function to Approximate Nearest Neighbor Search (ANNS) and demonstrate that our approach achieves a 2.5x--3x higher query-per-second (QPS) throughput compared to the widely-used graph-based search algorithm HNSW. Our code and data are available at https://github.com/KejingLu-810/KS.