ICML 2024 论文列表

International Conference on Machine Learning

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2,610篇论文

按官方录用论文列表统计,可能与会议公布的数字略有出入。

  • Oral
    1445.5%
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    1917.3%
  • Poster
    2,27587.2%

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State-Constrained Zero-Sum Differential Games with One-Sided Information

Mukesh Ghimire, Lei Zhang, Zhe Xu, Yi Ren

展开摘要

We study zero-sum differential games with state constraints and one-sided information, where the informed player (Player 1) has a categorical payoff type unknown to the uninformed player (Player 2). The goal of Player 1 is to minimize his payoff without violating the constraints, while that of Player 2 is to violate the state constraints if possible, or to maximize the payoff otherwise. One example of the game is a man-to-man matchup in football. Without state constraints, Cardaliaguet (2007) showed that the value of such a game exists and is convex to the common belief of players. Our theoretical contribution is an extension of this result to games with state constraints and the derivation of the primal and dual subdynamic principles necessary for computing behavioral strategies. Different from existing works that are concerned about the scalability of no-regret learning in games with discrete dynamics, our study reveals the underlying structure of strategies for belief manipulation resulting from information asymmetry and state constraints. This structure will be necessary for scalable learning on games with continuous actions and long time windows. We use a simplified football game to demonstrate the utility of this work, where we reveal player positions and belief states in which the attacker should (or should not) play specific random deceptive moves to take advantage of information asymmetry, and compute how the defender should respond.

Poster
On the Recoverability of Causal Relations from Temporally Aggregated I.I.D. Data

Shunxing Fan, Mingming Gong, Kun Zhang

展开摘要

We consider the effect of temporal aggregation on instantaneous (non-temporal) causal discovery in general setting. This is motivated by the observation that the true causal time lag is often considerably shorter than the observational interval. This discrepancy leads to high aggregation, causing time-delay causality to vanish and instantaneous dependence to manifest. Although we expect such instantaneous dependence has consistency with the true causal relation in certain sense to make the discovery results meaningful, it remains unclear what type of consistency we need and when will such consistency be satisfied. We proposed functional consistency and conditional independence consistency in formal way correspond functional causal model-based methods and conditional independence-based methods respectively and provide the conditions under which these consistencies will hold. We show theoretically and experimentally that causal discovery results may be seriously distorted by aggregation especially in complete nonlinear case and we also find causal relationship still recoverable from aggregated data if we have partial linearity or appropriate prior. Our findings suggest community should take a cautious and meticulous approach when interpreting causal discovery results from such data and show why and when aggregation will distort the performance of causal discovery methods.

Poster
Split-and-Denoise: Protect large language model inference with local differential privacy

Peihua Mai, Ran Yan, Zhe Huang, Youjia Yang, Yan Pang

展开摘要

Large Language Models (LLMs) excel in natural language understanding by capturing hidden semantics in vector space. This process enriches the value of text embeddings for various downstream tasks, thereby fostering the Embedding-as-a-Service (EaaS) business model. However, the risk of privacy leakage due to direct text transmission to servers remains a critical concern. To address this, we introduce Split-N-Denoise (SnD), an private inference framework that splits the model to execute the token embedding layer on the client side at minimal computational cost. This allows the client to introduce noise prior to transmitting the embeddings to the server, and subsequently receive and denoise the perturbed output embeddings for downstream tasks. Our approach is designed for the inference stage of LLMs and requires no modifications to the model parameters. Extensive experiments demonstrate SnD’s effectiveness in optimizing the privacy-utility tradeoff across various LLM architectures and diverse downstream tasks. The results reveal an improvement in performance under the same privacy budget compared to the baselines by over 10% on average, offering clients a privacy-preserving solution for local privacy protection.

Poster
Timer: Generative Pre-trained Transformers Are Large Time Series Models

Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long

展开摘要

Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world data-scarce scenarios, which can be concealed due to the performance saturation with small models on current benchmarks. Meanwhile, large models have demonstrated great powers in these scenarios through large-scale pre-training. Continuous progress has been achieved with the emergence of large language models, exhibiting unprecedented abilities such as few-shot generalization, scalability, and task generality, which are however absent in small deep models. To change the status quo of training scenario-specific small models from scratch, this paper aims at the early development of large time series models (LTSM). During pre-training, we curate large-scale datasets with up to 1 billion time points, unify heterogeneous time series into single-series sequence (S3) format, and develop the GPT-style architecture toward LTSMs. To meet diverse application needs, we convert forecasting, imputation, and anomaly detection of time series into a unified generative task. The outcome of this study is a Time Series Transformer (Timer), which is generative pre-trained by next token prediction and adapted to various downstream tasks with promising capabilities as an LTSM. Code and datasets are available at: https://github.com/thuml/Large-Time-Series-Model.

Poster
Monitoring AI-Modified Content at Scale: A Case Study on the Impact of ChatGPT on AI Conference Peer Reviews

Weixin Liang, Zachary Izzo, Yaohui Zhang, Haley Lepp, Hancheng Cao, Xuandong Zhao, Lingjiao Chen, Haotian Ye, Sheng Liu, Zhi Huang, Daniel McFarland, James Y. Zou

展开摘要

We present an approach for estimating the fraction of text in a large corpus which is likely to be substantially modified or produced by a large language model (LLM). Our maximum likelihood model leverages expert-written and AI-generated reference texts to accurately and efficiently examine real-world LLM-use at the corpus level. We apply this approach to a case study of scientific peer review in AI conferences that took place after the release of ChatGPT: *ICLR* 2024, *NeurIPS* 2023, *CoRL* 2023 and *EMNLP* 2023. Our results suggest that between 6.5% and 16.9% of text submitted as peer reviews to these conferences could have been substantially modified by LLMs, i.e. beyond spell-checking or minor writing updates. The circumstances in which generated text occurs offer insight into user behavior: the estimated fraction of LLM-generated text is higher in reviews which report lower confidence, were submitted close to the deadline, and from reviewers who are less likely to respond to author rebuttals. We also observe corpus-level trends in generated text which may be too subtle to detect at the individual level, and discuss the implications of such trends on peer review. We call for future interdisciplinary work to examine how LLM use is changing our information and knowledge practices.

Oral
Safety Fine-Tuning at (Almost) No Cost: A Baseline for Vision Large Language Models

Yongshuo Zong, Ondrej Bohdal, Tingyang Yu, Yongxin Yang, Timothy Hospedales

展开摘要

Current vision large language models (VLLMs) exhibit remarkable capabilities yet are prone to generate harmful content and are vulnerable to even the simplest jailbreaking attacks. Our initial analysis finds that this is due to the presence of harmful data during vision-language instruction fine-tuning, and that VLLM fine-tuning can cause forgetting of safety alignment previously learned by the underpinning LLM. To address this issue, we first curate a vision-language safe instruction-following dataset VLGuard covering various harmful categories. Our experiments demonstrate that integrating this dataset into standard vision-language fine-tuning or utilizing it for post-hoc fine-tuning effectively safety aligns VLLMs. This alignment is achieved with minimal impact on, or even enhancement of, the models' helpfulness. The versatility of our safety fine-tuning dataset makes it a valuable resource for safety-testing existing VLLMs, training new models or safeguarding pre-trained VLLMs. Empirical results demonstrate that fine-tuned VLLMs effectively reject unsafe instructions and substantially reduce the success rates of several black-box adversarial attacks, which approach zero in many cases. The code and dataset will be open-sourced.

Poster
Position: TrustLLM: Trustworthiness in Large Language Models

Yue Huang, Lichao Sun, Haoran Wang, Siyuan Wu, Qihui Zhang, Yuan Li, Chujie Gao, Yixin Huang, Wenhan Lyu, Yixuan Zhang, Xiner Li, Hanchi Sun, Zhengliang Liu, Yixin Liu, Yijue Wang, Zhikun Zhang, Bertie Vidgen, Bhavya Kailkhura, Caiming Xiong, Chaowei Xiao, Chunyuan Li, Eric P. Xing, Furong Huang, Hao Liu, Heng Ji, Hongyi Wang, Huan Zhang, Huaxiu Yao, Manolis Kellis, Marinka Zitnik, Meng Jiang, Mohit Bansal, James Zou, Jian Pei, Jian Liu, Jianfeng Gao, Jiawei Han, Jieyu Zhao, Jiliang Tang, Jindong Wang, Joaquin Vanschoren, John Mitchell, Kai Shu, Kaidi Xu, Kai-Wei Chang, Lifang He, Lifu Huang, Michael Backes, Neil Zhenqiang Gong, Philip S. Yu, Pin-Yu Chen, Quanquan Gu, Ran Xu, Rex Ying, Shuiwang Ji, Suman Jana, Tianlong Chen, Tianming Liu, Tianyi Zhou, William Yang Wang, Xiang Li, Xiangliang Zhang, Xiao Wang, Xing Xie, Xun Chen, Xuyu Wang, Yan Liu, Yanfang Ye, Yinzhi Cao, Yong Chen, Yue Zhao

展开摘要

Large language models (LLMs) have gained considerable attention for their excellent natural language processing capabilities. Nonetheless, these LLMs present many challenges, particularly in the realm of trustworthiness. This paper introduces TrustLLM, a comprehensive study of trustworthiness in LLMs, including principles for different dimensions of trustworthiness, established benchmark, evaluation, and analysis of trustworthiness for mainstream LLMs, and discussion of open challenges and future directions. Specifically, we first propose a set of principles for trustworthy LLMs that span eight different dimensions. Based on these principles, we further establish a benchmark across six dimensions including truthfulness, safety, fairness, robustness, privacy, and machine ethics. We then present a study evaluating 16 mainstream LLMs in TrustLLM, consisting of over 30 datasets. Our findings firstly show that in general trustworthiness and capability (i.e., functional effectiveness) are positively related. Secondly, our observations reveal that proprietary LLMs generally outperform most open-source counterparts in terms of trustworthiness, raising concerns about the potential risks of widely accessible open-source LLMs. However, a few open-source LLMs come very close to proprietary ones, suggesting that open-source models can achieve high levels of trustworthiness without additional mechanisms like *moderator*, offering valuable insights for developers in this field. Thirdly, it is important to note that some LLMs may be overly calibrated towards exhibiting trustworthiness, to the extent that they compromise their utility by mistakenly treating benign prompts as harmful and consequently not responding. Besides these observations, we've uncovered key insights into the multifaceted trustworthiness in LLMs. We emphasize the importance of ensuring transparency not only in the models themselves but also in the technologies that underpin trustworthiness. We advocate that the establishment of an AI alliance between industry, academia, the open-source community to foster collaboration is imperative to advance the trustworthiness of LLMs.

Poster
Preference Fine-Tuning of LLMs Should Leverage Suboptimal, On-Policy Data

Fahim Tajwar, Anikait Singh, Archit Sharma, Rafael Rafailov, Jeff Schneider, Tengyang Xie, Stefano Ermon, Chelsea Finn, Aviral Kumar

展开摘要

Learning from preference labels plays a crucial role in fine-tuning large language models --- this is done via supervised learning, on-policy reinforcement learning (RL), or contrastive learning. Different methods come with different implementation tradeoffs, and existing empirical findings present different conclusions, for instance, some results show that online RL is quite important to attain good fine-tuning results, while others find offline methods sufficient. This raises a question: **what kind of approaches are important for fine-tuning with preference data and why?** In this paper, we answer this question by performing a rigorous analysis of a number of fine-tuning techniques on didactic and full-scale LLM problems. Our main finding is that approaches that use on-policy sampling and attempt to push down the likelihood on certain responses (i.e., employ a ''negative gradient'') outperform offline and maximum likelihood objectives. We conceptualize our insights and unify methods that use on-policy sampling or negative gradient under a notion of mode-seeking objectives for categorical distributions. Mode-seeking objectives are able to alter probability mass on specific bins of a categorical distribution at a fast rate compared to maximum likelihood, allowing them to relocate masses across bins more effectively. Our analysis prescribes actionable insights for preference fine-tuning of LLMs and informs how data should be collected for maximal improvement.

Poster
Controlled Decoding from Language Models

Sidharth Mudgal, Jong Lee, Harish Ganapathy, Yaguang Li, Tao Wang, Yanping Huang, Zhifeng Chen, Heng-Tze Cheng, Michael Collins, Trevor Strohman, Jilin Chen, Alex Beutel, Ahmad Beirami

展开摘要

KL-regularized reinforcement learning (RL) is a popular alignment framework to control the language model responses towards high reward outcomes. We pose a tokenwise RL objective and propose a modular solver for it, called *controlled decoding (CD)*. CD exerts control through a separate *prefix scorer* module, which is trained to learn a value function for the reward. The prefix scorer is used at inference time to control the generation from a frozen base model, provably sampling from a solution to the RL objective. We empirically demonstrate that CD is effective as a control mechanism on popular benchmarks. We also show that prefix scorers for multiple rewards may be combined at inference time, effectively solving a multi-objective RL problem with no additional training. We show that the benefits of applying CD transfer to an unseen base model with no further tuning as well. Finally, we show that CD can be applied in a blockwise decoding fashion at inference-time, essentially bridging the gap between the popular best-of-$K$ strategy and tokenwise control through reinforcement learning. This makes CD a promising approach for alignment of language models.

Poster
Self-Infilling Code Generation

Lin Zheng, Jianbo Yuan, Zhi Zhang, Hongxia Yang, Lingpeng Kong

展开摘要

In this work, we introduce self-infilling code generation, a general framework that incorporates infilling operations into auto-regressive decoding. Our approach capitalizes on the observation that recent infilling-capable code language models can perform self-infilling: whereas conventional infilling is designed to fill in the middle based on a predefined prefix and suffix, self-infilling sequentially generates both such surrounding context and the infilled content. We utilize self-infilling to introduce novel interruption and looping mechanisms in conventional decoding, evolving it into a non-monotonic process. Interruptions allow for postponing the generation of specific code until a definitive suffix is established, enhancing control during decoding. Meanwhile, the looping mechanism, which leverages the complementary nature of self-infilling and left-to-right decoding, can iteratively update and synchronize each piece of generation cyclically. Extensive experiments across a variety of code generation benchmarks demonstrate that decoding with self-infilling not only improves the output quality but also regularizes the overall generation, which effectively mitigates potential degeneration and scaffolds code to be more consistent with intended functionality.

Poster
Differentiable Model Scaling using Differentiable Topk

Kai Liu, Ruohui Wang, Jianfei Gao, Kai Chen

展开摘要

Over the past few years, as large language models have ushered in an era of intelligence emergence, there has been an intensified focus on scaling networks. Although Neural Architecture Search (NAS) methods have been proposed to automate this process, they suffer from low search efficiency. This study introduces Differentiable Model Scaling (DMS), increasing the efficiency for searching optimal width and depth in networks. DMS can model both width and depth in a direct and fully differentiable way, making it easy to optimize. We have evaluated our DMS across diverse tasks, ranging from vision tasks to NLP tasks and various network architectures, including CNNs and Transformers. Results consistently indicate that our DMS can find improved structures and outperforms state-of-the-art NAS methods. Specifically, for image classification on ImageNet, our DMS improves the top-1 accuracy of EfficientNet-B0 and Deit-Tiny by 1.4% and 0.6%, respectively, and outperforms the state-of-the-art zero-shot NAS method, ZiCo, by 1.3% while requiring only 0.4 GPU days for searching. For object detection on COCO, DMS improves the mAP of Yolo-v8-n by 2.0%. For language modeling, our pruned Llama-7B outperforms the prior method with lower perplexity and higher zero-shot classification accuracy. Our code is available at https://github.com/LKJacky/Differentiable-Model-Scaling.

Poster
Graph-Triggered Rising Bandits

Gianmarco Genalti, Marco Mussi, Nicola Gatti, Marcello Restelli, Matteo Castiglioni, Alberto Maria Metelli

展开摘要

In this paper, we propose a novel generalization of rested and restless bandits where the evolution of the arms' expected rewards is governed by a graph defined over the arms. An edge connecting a pair of arms $(i,j)$ represents the fact that a pull of arm $i$ *triggers* the evolution of arm $j$, and vice versa. Interestingly, rested and restless bandits are both special cases of our model for some suitable (degenerate) graphs. Still, the model can represent way more general and interesting scenarios. We first tackle the problem of computing the optimal policy when no specific structure is assumed on the graph, showing that it is NP-hard. Then, we focus on a specific structure forcing the graph to be composed of a set of fully connected subgraphs (i.e., cliques), and we prove that the optimal policy can be easily computed in closed form. Then, we move to the learning problem presenting regret minimization algorithms for deterministic and stochastic cases. Our regret bounds highlight the complexity of the learning problem by incorporating instance-dependent terms that encode specific properties of the underlying graph structure. Moreover, we illustrate how the knowledge of the underlying graph is not necessary for achieving the no-regret property.

Poster
Modular Learning of Deep Causal Generative Models for High-dimensional Causal Inference

Md Musfiqur Rahman, Murat Kocaoglu

展开摘要

Sound and complete algorithms have been proposed to compute identifiable causal queries using the causal structure and data. However, most of these algorithms assume accurate estimation of the data distribution, which is impractical for high-dimensional variables such as images. On the other hand, modern deep generative architectures can be trained to sample from high-dimensional distributions. However, training these networks are typically very costly. Thus, it is desirable to leverage pre-trained models to answer causal queries using such high-dimensional data. To address this, we propose modular training of deep causal generative models that not only makes learning more efficient, but also allows us to utilize large, pre-trained conditional generative models. To the best of our knowledge, our algorithm, Modular-DCM is the first algorithm that, given the causal structure, uses adversarial training to learn the network weights, and can make use of pre-trained models to provably sample from any identifiable causal query in the presence of latent confounders. With extensive experiments on the Colored-MNIST dataset, we demonstrate that our algorithm outperforms the baselines. We also show our algorithm's convergence on the COVIDx dataset and its utility with a causal invariant prediction problem on CelebA-HQ.

Poster
Robust Data-driven Prescriptiveness Optimization

Mehran Poursoltani, Erick Delage, Angelos Georghiou

展开摘要

The abundance of data has led to the emergence of a variety of optimization techniques that attempt to leverage available side information to provide more anticipative decisions. The wide range of methods and contexts of application have motivated the design of a universal unitless measure of performance known as the coefficient of prescriptiveness. This coefficient was designed to quantify both the quality of contextual decisions compared to a reference one and the prescriptive power of side information. To identify policies that maximize the former in a data-driven context, this paper introduces a distributionally robust contextual optimization model where the coefficient of prescriptiveness substitutes for the classical empirical risk minimization objective. We present a bisection algorithm to solve this model, which relies on solving a series of linear programs when the distributional ambiguity set has an appropriate nested form and polyhedral structure. Studying a contextual shortest path problem, we evaluate the robustness of the resulting policies against alternative methods when the out-of-sample dataset is subject to varying amounts of distribution shift.

Poster
Watermarks in the Sand: Impossibility of Strong Watermarking for Language Models

Hanlin Zhang, Benjamin L. Edelman, Danilo Francati, Daniele Venturi, Giuseppe Ateniese, Boaz Barak

展开摘要

Watermarking generative models consists of planting a statistical signal (watermark) in a model's output so that it can be later verified that the output was generated by the given model. A strong watermarking scheme satisfies the property that a computationally bounded attacker cannot erase the watermark without causing significant quality degradation. In this paper, we study the (im)possibility of strong watermarking schemes. We prove that, under well-specified and natural assumptions, strong watermarking is impossible to achieve. This holds even in the private detection algorithm setting, where the watermark insertion and detection algorithms share a secret key, unknown to the attacker. To prove this result, we introduce a generic efficient watermark attack; the attacker is not required to know the private key of the scheme or even which scheme is used. Our attack is based on two assumptions: (1) The attacker has access to a "quality oracle" that can evaluate whether a candidate output is a high-quality response to a prompt, and (2) The attacker has access to a "perturbation oracle" which can modify an output with a nontrivial probability of maintaining quality, and which induces an efficiently mixing random walk on high-quality outputs. We argue that both assumptions can be satisfied in practice by an attacker with weaker computational capabilities than the watermarked model itself, to which the attacker has only black-box access. Furthermore, our assumptions will likely only be easier to satisfy over time as models grow in capabilities and modalities. We demonstrate the feasibility of our attack by instantiating it to attack three existing watermarking schemes for large language models: Kirchenbauer et al. (2023), Kuditipudi et al. (2023), and Zhao et al. (2023), and include preliminary results on vision-language models. The same attack successfully removes the watermarks planted by all schemes, with only minor quality degradation.

Poster
Genie: Generative Interactive Environments

Jake Bruce, Michael D Dennis, Ashley Edwards, Jack Parker-Holder, Yuge Shi, Edward Hughes, Matthew Lai, Aditi Mavalankar, Richie Steigerwald, Chris Apps, Yusuf Aytar, Sarah Maria Elisabeth Bechtle, Feryal Behbahani, Stephanie C.Y. Chan, Nicolas Heess, Lucy Gonzalez, Simon Osindero, Sherjil Ozair, Scott Reed, Jingwei Zhang, Konrad Zolna, Jeff Clune, Nando de Freitas, Satinder Singh, Tim Rocktäschel

展开摘要

We introduce Genie, the first *generative interactive environment* trained in an unsupervised manner from unlabelled Internet videos. The model can be prompted to generate an endless variety of action-controllable virtual worlds described through text, synthetic images, photographs, and even sketches. At 11B parameters, Genie can be considered a *foundation world model*. It is comprised of a spatiotemporal video tokenizer, an autoregressive dynamics model, and a simple and scalable latent action model. Genie enables users to act in the generated environments on a frame-by-frame basis *despite training without any ground-truth action labels* or other domain specific requirements typically found in the world model literature. Further the resulting learned latent action space facilitates training agents to imitate behaviors from unseen videos, opening the path for training generalist agents of the future.

Oral
Policy Evaluation for Variance in Average Reward Reinforcement Learning

Shubhada Agrawal, Prashanth L A, Siva Theja Maguluri

展开摘要

We consider an average reward reinforcement learning (RL) problem and work with asymptotic variance as a risk measure to model safety-critical applications. We design a temporal-difference (TD) type algorithm tailored for policy evaluation in this context. Our algorithm is based on linear stochastic approximation of an equivalent formulation of the asymptotic variance in terms of the solution of the Poisson equation. We consider both the tabular and linear function approximation settings, and establish $\tilde {O}(1/k)$ finite time convergence rate, where $k$ is the number of steps of the algorithm. Our work paves the way for developing actor-critic style algorithms for variance-constrained RL. To the best of our knowledge, our result provides the first sequential estimator for asymptotic variance of a Markov chain with provable finite sample guarantees, which is of independent interest.

Poster
High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

Yihang Chen, Fanghui Liu, Taiji Suzuki, Volkan Cevher

展开摘要

This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposition, we theoretically demonstrate that the re-weighting strategy allows for decreasing the variance. For bias, we analyze the regularization of the arbitrary or well-chosen scale, showing that the bias can behave very differently under different regularization scales. In our analysis, the bias and variance can be characterized by the spectral decay of a data-dependent regularized kernel: the original kernel matrix associated with an additional re-weighting matrix, and thus the re-weighting strategy can be regarded as a data-dependent regularization for better understanding. Besides, our analysis provides asymptotic expansion of kernel functions/vectors under covariate shift, which has its own interest.

Poster
Learning Solution-Aware Transformers for Efficiently Solving Quadratic Assignment Problem

Zhentao Tan, Yadong Mu

展开摘要

Recently various optimization problems, such as Mixed Integer Linear Programming Problems (MILPs), have undergone comprehensive investigation, leveraging the capabilities of machine learning. This work focuses on learning-based solutions for efficiently solving the Quadratic Assignment Problem (QAPs), which stands as a formidable challenge in combinatorial optimization. While many instances of simpler problems admit fully polynomial-time approximate solution (FPTAS), QAP is shown to be strongly NPhard. Even finding a FPTAS for QAP is difficult, in the sense that the existence of a FPTAS implies P = NP. Current research on QAPs suffer from limited scale and computational inefficiency. To attack the aforementioned issues, we here propose the first solution of its kind for QAP in the learn-to-improve category. This work encodes facility and location nodes separately, instead of forming computationally intensive association graphs prevalent in current approaches. This design choice enables scalability to larger problem sizes. Furthermore, a Solution AWare Transformer (SAWT) architecture integrates the incumbent solution matrix with the attention score to effectively capture higher-order information of the QAPs. Our model’s effectiveness is validated through extensive experiments on self-generated QAP instances of varying sizes and the QAPLIB benchmark.

Poster
Analyzing $D^\alpha$ seeding for $k$-means

Etienne Bamas, Sai Ganesh Nagarajan, Ola Svensson

展开摘要

One of the most popular clustering algorithms is the celebrated $D^\alpha$ seeding algorithm (also know as $k$-means++ when $\alpha=2$) by Arthur and Vassilvitskii (2007), who showed that it guarantees in expectation an $O(2^{2\alpha}\cdot \log k)$-approximate solution to the ($k$,$\alpha$)-clustering cost (where distances are raised to the power $\alpha$) for any $\alpha\ge 1$. More recently, Balcan, Dick, and White (2018) observed experimentally that using $D^\alpha$ seeding with $\alpha>2$ can lead to a better solution with respect to the standard $k$-means objective (i.e. the $(k,2)$-clustering cost). In this paper, we provide a rigorous understanding of this phenomenon. For any $\alpha>2$, we show that $D^\alpha$ seeding guarantees in expectation an approximation factor of \begin{equation*} O_\alpha \left(\left(\frac{\sigma_{\textrm{max}}}{\sigma_{\textrm{min}}}\right)^{2-4/\alpha}\cdot (g_\alpha \cdot \min \lbrace\ell,\log k\rbrace)^{2/\alpha}\right) \end{equation*} with respect to the standard $k$-means cost of any underlying clustering; where $g_\alpha$ is a parameter capturing the concentration of the points in each cluster, $\sigma_{\textrm{max}}$ and $\sigma_{\textrm{min}}$ are the maximum and minimum standard deviation of the clusters around their center, and $\ell$ is the number of distinct mixing weights in the underlying clustering (after rounding them to the nearest power of $2$). For instance, if the underlying clustering is defined by a mixture of $k$ Gaussian distributions with equal cluster variance (up to a constant-factor), then our result implies that: (1) if there are a constant number of mixing weights, any constant $\alpha>2$ yields a constant-factor approximation; (2) if the mixing weights are arbitrary, any constant $\alpha>2$ yields an $O\left(\log^{2/\alpha}k\right)$-approximation, and $\alpha=\Theta(\log\log k)$ yields an $O(\log\log k)^3$-approximation. We complement these results by some lower bounds showing that the dependency on $g_\alpha$ and $\sigma_{\textrm{max}}/\sigma_{\textrm{min}}$ is tight. Finally, we provide an experimental validation of the effects of the aforementioned parameters when using $D^\alpha$ seeding.

Poster