ICLR 2025 Papers

International Conference on Learning Representations

Decision breakdown

3,703papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    2135.8%
  • Spotlight
    38010.3%
  • Poster
    3,11084.0%

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SqueezeAttention: 2D Management of KV-Cache in LLM Inference via Layer-wise Optimal Budget

Zihao Wang, Bin Cui, Shaoduo Gan

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Optimizing the Key-Value (KV) cache of the Large Language Model (LLM) has been considered critical to saving the cost of inference. Most of the existing KV-cache compression algorithms attempted to sparsify the sequence of tokens by taking advantage of the different importance of tokens. However, most of these methods treat all layers equally, allocating the same KV budget to each layer. This approach is suboptimal, as some layers may be less sensitive to input tokens yet still receive the same budget as others. In this work, we found that by identifying the importance of attention layers, we could optimize the KV-cache jointly from two dimensions, i.e., sequence-wise and layer-wise. Based on our observations regarding layer-wise importance in inference, we propose \sys to precisely optimize the allocation of KV-cache budget among layers on-the-fly and then incorporate three representative sequence-wise algorithms to compress the KV-cache for each layer with its very own budget. Specifically, we first measure each layer's importance by calculating the cosine similarity of the input prompt differences before and after the self-attention layers. Based on this similarity, we then categorize the layers into two groups and adjust their KV budgets accordingly. By optimizing the KV-cache from both sequence's and layer's dimensions, \sys achieves around 30\% to 70\% of the memory reductions and up to 2.2 $\times$ of throughput improvements in a wide range of LLMs and benchmarks. The code is available at https://github.com/hetailang/SqueezeAttention.

Poster
Hyper-Connections

Defa Zhu, Hongzhi Huang, Zihao Huang, Yutao Zeng, Yunyao Mao, Banggu Wu, Qiyang Min, Xun Zhou

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We present hyper-connections, a simple yet effective method that can serve as an alternative to residual connections. This approach specifically addresses common drawbacks observed in residual connection variants, such as the seesaw effect between gradient vanishing and representation collapse. Theoretically, hyper-connections allow the network to adjust the strength of connections between features at different depths and dynamically rearrange layers. We conduct experiments focusing on the pre-training of large language models, including dense and sparse models, where hyper-connections show significant performance improvements over residual connections. Additional experiments conducted on vision tasks also demonstrate similar improvements. We anticipate that this method will be broadly applicable and beneficial across a wide range of AI problems.

Poster
PRDP: Progressively Refined Differentiable Physics

Kanishk Bhatia, Felix Koehler, Nils Thuerey

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The physics solvers employed for neural network training are primarily iterative, and hence, differentiating through them introduces a severe computational burden as iterations grow large. Inspired by works in bilevel optimization, we show that full accuracy of the network is achievable through physics significantly coarser than fully converged solvers. We propose *progressively refined differentiable physics* (PRDP), an approach that identifies the level of physics refinement sufficient for full training accuracy. By beginning with coarse physics, adaptively refining it during training, and stopping refinement at the level adequate for training, it enables significant compute savings without sacrificing network accuracy. Our focus is on differentiating iterative linear solvers for sparsely discretized differential operators, which are fundamental to scientific computing. PRDP is applicable to both unrolled and implicit differentiation. We validate its performance on a variety of learning scenarios involving differentiable physics solvers such as inverse problems, autoregressive neural emulators, and correction-based neural-hybrid solvers. In the challenging example of emulating the Navier-Stokes equations, we reduce training time by 62%.

Poster
Inverse Constitutional AI: Compressing Preferences into Principles

Arduin Findeis, Timo Kaufmann, Eyke Hüllermeier, Samuel Albanie, Robert D. Mullins

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Feedback data is widely used for fine-tuning and evaluating state-of-the-art AI models. Pairwise text preferences, where human or AI annotators select the “better” of two options, are particularly common. Such preferences are used to train (reward) models or to rank models with aggregate statistics. For many applications it is desirable to understand annotator preferences in addition to modelling them  – not least because extensive prior work has shown various unintended biases in preference datasets. Yet, preference datasets remain challenging to interpret. Neither black-box reward models nor statistics can answer why one text is preferred over another. Manual interpretation of the numerous (long) response pairs is usually equally infeasible. In this paper, we introduce the Inverse Constitutional AI (ICAI) problem, formulating the interpretation of pairwise text preference data as a compression task. In constitutional AI, a set of principles (a constitution) is used to provide feedback and fine-tune AI models. ICAI inverts this process: given a feedback dataset, we aim to extract a constitution that best enables a large language model (LLM) to reconstruct the original annotations. We propose a corresponding ICAI algorithm and validate its generated constitutions quantitatively based on annotation reconstruction accuracy on several datasets: (a) synthetic feedback data with known principles; (b) AlpacaEval cross-annotated human feedback data; (c) crowdsourced Chatbot Arena data; and (d) PRISM data from diverse demographic groups. As an example application, we further demonstrate the detection of biases in human feedback data. As a short and interpretable representation of the original dataset, generated constitutions have many potential use cases: they may help identify undesirable annotator biases, better understand model performance, scale feedback to unseen data, or assist with adapting AI models to individual user or group preferences. We release the source code for our algorithm and experiments at https://github.com/rdnfn/icai.

Poster
An Efficient Framework for Crediting Data Contributors of Diffusion Models

MingYu Lu, Chris Lin, Chanwoo Kim, Su-In Lee

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As diffusion models are deployed in real-world settings and their performance driven by training data, appraising the contribution of data contributors is crucial to creating incentives for sharing quality data and to implementing policies for data compensation. Depending on the use case, model performance corresponds to various global properties of the distribution learned by a diffusion model (e.g., overall aesthetic quality). Hence, here we address the problem of attributing global properties of diffusion models to data contributors. The Shapley value provides a principled approach to valuation by uniquely satisfying game-theoretic axioms of fairness. However, estimating Shapley values for diffusion models is computationally impractical because it requires retraining and rerunning inference on many subsets of data contributors. We introduce a method to efficiently retrain and rerun inference for Shapley value estimation, by leveraging model pruning and fine-tuning. We evaluate the utility of our method with three use cases: (i) image quality for a DDPM trained on a CIFAR dataset, (ii) demographic diversity for an LDM trained on CelebA-HQ, and (iii) aesthetic quality for a Stable Diffusion model LoRA-finetuned on Post-Impressionist artworks. Our results empirically demonstrate that our framework can identify important data contributors across global properties, outperforming existing attribution methods for diffusion models.

Poster
Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling

Yuma Ichikawa, Yamato Arai

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Learning-based methods have gained attention as general-purpose solvers due to their ability to automatically learn problem-specific heuristics, reducing the need for manually crafted heuristics. However, these methods often face scalability challenges. To address these issues, the improved Sampling algorithm for Combinatorial Optimization (iSCO), using discrete Langevin dynamics, has been proposed, demonstrating better performance than several learning-based solvers. This study proposes a different approach that integrates gradient-based update through continuous relaxation, combined with Quasi-Quantum Annealing (QQA). QQA smoothly transitions the objective function, starting from a simple convex function, minimized at half-integral values, to the original objective function, where the relaxed variables are minimized only in the discrete space. Furthermore, we incorporate parallel run communication leveraging GPUs to enhance exploration capabilities and accelerate convergence. Numerical experiments demonstrate that our method is a competitive general-purpose solver, achieving performance comparable to iSCO and learning-based solvers across various benchmark problems. Notably, our method exhibits superior speed-quality trade-offs for large-scale instances compared to iSCO, learning-based solvers, commercial solvers, and specialized algorithms.

Poster
VideoPhy: Evaluating Physical Commonsense for Video Generation

Hritik Bansal, Zongyu Lin, Tianyi Xie, Zeshun Zong, Michal Yarom, Yonatan Bitton, Chenfanfu Jiang, Yizhou Sun, Kai-Wei Chang, Aditya Grover

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Recent advances in internet-scale video data pretraining have led to the development of text-to-video generative models that can create high-quality videos across a broad range of visual concepts, synthesize realistic motions and render complex objects. Hence, these generative models have the potential to become general-purpose simulators of the physical world. However, it is unclear how far we are from this goal with the existing text-to-video generative models. To this end, we present VideoPhy, a benchmark designed to assess whether the generated videos follow physical commonsense for real-world activities (e.g. marbles will roll down when placed on a slanted surface). Specifically, we curate diverse prompts that involve interactions between various material types in the physical world (e.g., solid-solid, solid-fluid, fluid-fluid). We then generate videos conditioned on these captions from diverse state-of-the-art text-to-video generative models, including open models (e.g., CogVideoX) and closed models (e.g., Lumiere, Dream Machine). Our human evaluation reveals that the existing models severely lack the ability to generate videos adhering to the given text prompts, while also lack physical commonsense. Specifically, the best performing model, CogVideoX-5B, generates videos that adhere to the caption and physical laws for 39.6% of the instances. VideoPhy thus highlights that the video generative models are far from accurately simulating the physical world. Finally, we propose an auto-evaluator, VideoCon-Physics, to assess the performance reliably for the newly released models. The code is available here: https://github.com/Hritikbansal/videophy.

Poster
Ada-K Routing: Boosting the Efficiency of MoE-based LLMs

Tongtian Yue, Longteng Guo, Jie Cheng, Xuange Gao, Hua Huang, Jing Liu

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In the era of Large Language Models (LLMs), Mixture-of-Experts (MoE) architectures offer a promising approach to managing computational costs while scaling up model parameters. Conventional MoE-based LLMs typically employ static Top-K routing, which activates a fixed and equal number of experts for each token regardless of their significance within the context. In this paper, we propose a novel Ada-K routing strategy that dynamically adjusts the number of activated experts for each token, thereby improving the balance between computational efficiency and model performance. Specifically, our strategy incorporates learnable and lightweight allocator modules that decide customized expert resource allocation tailored to the contextual needs for each token. These allocators are designed to be fully pluggable, making it broadly applicable across all mainstream MoE-based LLMs. We leverage the Proximal Policy Optimization (PPO) algorithm to facilitate an end-to-end learning process for this non-differentiable decision-making framework. Extensive evaluations on four popular baseline models demonstrate that our Ada-K routing method significantly outperforms conventional Top-K routing. Compared to Top-K, our method achieves over 25% reduction in FLOPs and more than 20% inference speedup while still improving performance across various benchmarks. Moreover, the training of Ada-K is highly efficient. Even for Mixtral-8x22B, a MoE-based LLM with more than 140B parameters, the training time is limited to 8 hours. Detailed analysis shows that harder tasks, middle layers, and content words tend to activate more experts, providing valuable insights for future adaptive MoE system designs. Both the training code and model checkpoints will be publicly available.

Poster
Enhancing Zeroth-order Fine-tuning for Language Models with Low-rank Structures

Yiming Chen, Yuan Zhang, Liyuan Cao, Kun Yuan, Zaiwen Wen

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Parameter-efficient fine-tuning (PEFT) significantly reduces memory costs when adapting large language models (LLMs) for downstream applications. However, traditional first-order (FO) fine-tuning algorithms incur substantial memory overhead due to the need to store activation values for back-propagation during gradient computation, particularly in long-context fine-tuning tasks. Zeroth-order (ZO) algorithms offer a promising alternative by approximating gradients using finite differences of function values, thus eliminating the need for activation storage. Nevertheless, existing ZO methods struggle to capture the low-rank gradient structure common in LLM fine-tuning, leading to suboptimal performance. This paper proposes a low-rank ZO gradient estimator and introduces a novel **lo**w-rank **ZO** algorithm (LOZO) that effectively captures this structure in LLMs. We provide convergence guarantees for LOZO by framing it as a subspace optimization method. Additionally, its low-rank nature enables LOZO to integrate with momentum techniques while incurring negligible extra memory costs. Extensive experiments across various model sizes and downstream tasks demonstrate that LOZO and its momentum-based variant outperform existing ZO methods and closely approach the performance of FO algorithms.

Poster
DebGCD: Debiased Learning with Distribution Guidance for Generalized Category Discovery

Yuanpei Liu, Kai Han

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In this paper, we tackle the problem of Generalized Category Discovery (GCD). Given a dataset containing both labelled and unlabelled images, the objective is to categorize all images in the unlabelled subset, irrespective of whether they are from known or unknown classes. In GCD, an inherent label bias exists between known and unknown classes due to the lack of ground-truth labels for the latter. State-of-the-art methods in GCD leverage parametric classifiers trained through self-distillation with soft labels, leaving the bias issue unattended. Besides, they treat all unlabelled samples uniformly, neglecting variations in certainty levels and resulting in suboptimal learning. Moreover, the explicit identification of semantic distribution shifts between known and unknown classes, a vital aspect for effective GCD, has been neglected. To address these challenges, we introduce DebGCD, a Debiased learning with distribution guidance framework for GCD. Initially, DebGCD co-trains an auxiliary debiased classifier in the same feature space as the GCD classifier, progressively enhancing the GCD features. Moreover, we introduce a semantic distribution detector in a separate feature space to implicitly boost the learning efficacy of GCD. Additionally, we employ a curriculum learning strategy based on semantic distribution certainty to steer the debiased learning at an optimized pace. Thorough evaluations on GCD benchmarks demonstrate the consistent state-of-the-art performance of our framework, highlighting its superiority. Project page: [https://visual-ai.github.io/debgcd/](https://visual-ai.github.io/debgcd/)

Poster
LANTERN: Accelerating Visual Autoregressive Models with Relaxed Speculative Decoding

Doohyuk Jang, Sihwan Park, June Yong Yang, Yeonsung Jung, Jihun Yun, Souvik Kundu, Sung-Yub Kim, Eunho Yang

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Auto-Regressive (AR) models have recently gained prominence in image generation, often matching or even surpassing the performance of diffusion models. However, one major limitation of AR models is their sequential nature, which processes tokens one at a time, slowing down generation compared to models like GANs or diffusion-based methods that operate more efficiently. While speculative decoding has proven effective for accelerating LLMs by generating multiple tokens in a single forward, its application in visual AR models remains largely unexplored. In this work, we identify a challenge in this setting, which we term \textit{token selection ambiguity}, wherein visual AR models frequently assign uniformly low probabilities to tokens, hampering the performance of speculative decoding. To overcome this challenge, we propose a relaxed acceptance condition referred to as LANTERN that leverages the interchangeability of tokens in latent space. This relaxation restores the effectiveness of speculative decoding in visual AR models by enabling more flexible use of candidate tokens that would otherwise be prematurely rejected. Furthermore, by incorporating a total variation distance bound, we ensure that these speed gains are achieved without significantly compromising image quality or semantic coherence. Experimental results demonstrate the efficacy of our method in providing a substantial speed-up over speculative decoding. In specific, compared to a na\"ive application of the state-of-the-art speculative decoding, LANTERN increases speed-ups by $\mathbf{1.75}\times$ and $\mathbf{1.82}\times$, as compared to greedy decoding and random sampling, respectively, when applied to LlamaGen, a contemporary visual AR model. The code is publicly available at \url{https://github.com/jadohu/LANTERN}.

Poster
Semi-Supervised CLIP Adaptation by Enforcing Semantic and Trapezoidal Consistency

Kai Gan, Bo Ye, Min-Ling Zhang, Tong Wei

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Vision-language pre-training models, such as CLIP, have demonstrated strong capability in rapidly adapting to downstream tasks through fine-tuning, and have been widely applied across various tasks. However, when the downstream tasks are constrained by limited image-text paired data, CLIP struggles to effectively address the domain gap between the pre-training and the target tasks. To address this limitation, we propose a novel semi-supervised CLIP training method coined SemiCLIP that leverages a small amount of image-text pairs alongside a large volume of images without text descriptions to enhance CLIP’s cross-modal alignment. To effectively utilize unlabeled images, we introduce semantic concept mining to improve task-specific visual representations by matching images with relevant concepts mined from labeled data. Leveraging matched semantic concepts, we construct learnable surrogate captions for unlabeled images and optimize a trapezoidal consistency to regulate the geometric structure of image-text pairs in the representation space. Experimental results demonstrate that our approach significantly improves the adaptability of CLIP in target tasks with limited labeled data, achieving gains ranging from 1.72\% -- 6.58\% for zero-shot classification accuracy and 2.32\% -- 3.23\% for image-text retrieval performance on standard benchmarks. The source code is available at https://github.com/Gank0078/SemiCLIP.

Poster
SiMHand: Mining Similar Hands for Large-Scale 3D Hand Pose Pre-training

Nie Lin, Takehiko Ohkawa, Yifei Huang, Mingfang Zhang, Minjie Cai, Ming Li, Ryosuke Furuta, Yoichi Sato

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We present a framework for pre-training of 3D hand pose estimation from in-the-wild hand images sharing with similar hand characteristics, dubbed SiMHand. Pre-training with large-scale images achieves promising results in various tasks, but prior methods for 3D hand pose pre-training have not fully utilized the potential of diverse hand images accessible from in-the-wild videos. To facilitate scalable pre-training, we first prepare an extensive pool of hand images from in-the-wild videos and design our pre-training method with contrastive learning. Specifically, we collect over 2.0M hand images from recent human-centric videos, such as 100DOH and Ego4D. To extract discriminative information from these images, we focus on the similarity of hands: pairs of non-identical samples with similar hand poses. We then propose a novel contrastive learning method that embeds similar hand pairs closer in the feature space. Our method not only learns from similar samples but also adaptively weights the contrastive learning loss based on inter-sample distance, leading to additional performance gains. Our experiments demonstrate that our method outperforms conventional contrastive learning approaches that produce positive pairs solely from a single image with data augmentation. We achieve significant improvements over the state-of-the-art method (PeCLR) in various datasets, with gains of 15% on FreiHand, 10% on DexYCB, and 4% on AssemblyHands. Our code is available at https://github.com/ut-vision/SiMHand.

Poster
Causal Identification for Complex Functional Longitudinal Studies

Andrew Ying

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Real-time monitoring in modern medical research introduces functional longitudinal data, characterized by continuous-time measurements of outcomes, treatments, and confounders. This complexity leads to uncountably infinite treatment-confounder feedbacks, which traditional causal inference methodologies cannot handle. Inspired by the coarsened data framework, we adopt stochastic process theory, measure theory, and net convergence to propose a nonparametric causal identification framework. This framework generalizes classical g-computation, inverse probability weighting, and doubly robust formulas, accommodating time-varying outcomes subject to mortality and censoring for functional longitudinal data. We examine our framework through Monte Carlo simulations. Our approach addresses significant gaps in current methodologies, providing a solution for functional longitudinal data and paving the way for future estimation work in this domain.

Poster
Denoising Task Difficulty-based Curriculum for Training Diffusion Models

Jin-Young Kim, Hyojun Go, Soonwoo Kwon, Hyun-Gyoon Kim

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Diffusion-based generative models have emerged as powerful tools in the realm of generative modeling. Despite extensive research on denoising across various timesteps and noise levels, a conflict persists regarding the relative difficulties of the denoising tasks. While various studies argue that lower timesteps present more challenging tasks, others contend that higher timesteps are more difficult. To address this conflict, our study undertakes a comprehensive examination of task difficulties, focusing on convergence behavior and changes in relative entropy between consecutive probability distributions across timesteps. Our observational study reveals that denoising at earlier timesteps poses challenges characterized by slower convergence and higher relative entropy, indicating increased task difficulty at these lower timesteps. Building on these observations, we introduce an easy-to-hard learning scheme, drawing from curriculum learning, to enhance the training process of diffusion models. By organizing timesteps or noise levels into clusters and training models with ascending orders of difficulty, we facilitate an order-aware training regime, progressing from easier to harder denoising tasks, thereby deviating from the conventional approach of training diffusion models simultaneously across all timesteps. Our approach leads to improved performance and faster convergence by leveraging benefits of curriculum learning, while maintaining orthogonality with existing improvements in diffusion training techniques. We validate these advantages through comprehensive experiments in image generation tasks, including unconditional, class-conditional, and text-to-image generation.

Poster
Interpreting and Editing Vision-Language Representations to Mitigate Hallucinations

Nicholas Jiang, Anish Kachinthaya, Suzanne Petryk, Yossi Gandelsman

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We investigate the internal representations of vision-language models (VLMs) to address hallucinations, a persistent challenge despite advances in model size and training. We project VLMs’ internal image representations to their language vocabulary and observe more confident output probabilities on real objects than hallucinated objects. We additionally use these output probabilities to spatially localize real objects. Building on this approach, we introduce a knowledge erasure algorithm that removes hallucinations by linearly orthogonalizing image features with respect to hallucinated object features. We show that targeted edits to a model’s latent representations can reduce hallucinations by up to 25.7% on the COCO2014 dataset while preserving performance. Our findings demonstrate how a deeper understanding of VLMs’ latent representations can enhance reliability and enable novel capabilities, such as zero-shot segmentation.

Poster
Data Pruning by Information Maximization

Haoru Tan, Sitong Wu, Wei Huang, Shizhen Zhao, Xiaojuan Qi

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In this paper, we present InfoMax, a novel data pruning method, also known as coreset selection, designed to maximize the information content of selected samples while minimizing redundancy. By doing so, InfoMax enhances the overall informativeness of the coreset. The information of individual samples is measured by importance scores, which capture their influence or difficulty in model learning. To quantify redundancy, we use pairwise sample similarities, based on the premise that similar samples contribute similarly to the learning process. We formalize the coreset selection problem as a discrete quadratic programming (DQP) task, with the objective of maximizing the total information content, represented as the sum of individual sample contributions minus the redundancies introduced by similar samples within the coreset. To ensure practical scalability, we introduce an efficient gradient-based solver, complemented by sparsification techniques applied to the similarity matrix and dataset partitioning strategies. This enables InfoMax to seamlessly scale to datasets with millions of samples. Extensive experiments demonstrate the superior performance of InfoMax in various data pruning tasks, including image classification, vision-language pre-training, and instruction tuning for large language models.

Poster
Edge Prompt Tuning for Graph Neural Networks

Xingbo Fu, Yinhan He, Jundong Li

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Pre-training powerful Graph Neural Networks (GNNs) with unlabeled graph data in a self-supervised manner has emerged as a prominent technique in recent years. However, inevitable objective gaps often exist between pre-training and downstream tasks. To bridge this gap, graph prompt tuning techniques design and learn graph prompts by manipulating input graphs or reframing downstream tasks as pre-training tasks without fine-tuning the pre-trained GNN models. While recent graph prompt tuning methods have proven effective in adapting pre-trained GNN models for downstream tasks, they overlook the crucial role of edges in graph prompt design, which can significantly affect the quality of graph representations for downstream tasks. In this study, we propose EdgePrompt, a simple yet effective graph prompt tuning method from the perspective of edges. Unlike previous studies that design prompt vectors on node features, EdgePrompt manipulates input graphs by learning additional prompt vectors for edges and incorporates the edge prompts through message passing in the pre-trained GNN models to better embed graph structural information for downstream tasks. Our method is compatible with prevalent GNN architectures pre-trained under various pre-training strategies and is universal for different downstream tasks. We provide comprehensive theoretical analyses of our method regarding its capability of handling node classification and graph classification as downstream tasks. Extensive experiments on ten graph datasets under four pre-training strategies demonstrate the superiority of our proposed method against six baselines. Our code is available at https://github.com/xbfu/EdgePrompt.

Poster
Joint Fine-tuning and Conversion of Pretrained Speech and Language Models towards Linear Complexity

Mutian He, Philip N. Garner

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Architectures such as Linformer and Mamba have recently emerged as competitive linear time replacements for transformers. However, corresponding large pretrained models are often unavailable, especially in non-text domains. To remedy this, we present a Cross-Architecture Layerwise Distillation (CALD) approach that jointly converts a transformer model to a linear time substitute and fine-tunes it to a target task. We also compare several means to guide the fine-tuning to optimally retain the desired inference capability from the original model. The methods differ in their use of the target model and the trajectory of the parameters. In a series of empirical studies on language processing, language modeling, and speech processing, we show that CALD can effectively recover the result of the original model, and that the guiding strategy contributes to the result. Some reasons for the variation are suggested.

Poster
LevAttention: Time, Space and Streaming Efficient Algorithm for Heavy Attentions

Ravindran Kannan, Chiranjib Bhattacharyya, Praneeth Kacham, David Woodruff

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A central problem related to transformers can be stated as follows: given two $n \times d$ matrices $Q$ and $K$, and a non-negative function $f$, define the matrix $A$ as follows: (1) apply the function $f$ to each entry of the $n \times n$ matrix $Q K^T$, and then (2) normalize each of the row sums of $A$ to be equal to $1$. The matrix $A$ can be computed in $O(n^2 d)$ time assuming $f$ can be applied to a number in constant time, but the quadratic dependence on $n$ is prohibitive in applications where it corresponds to long context lengths. For a large class of functions $f$, we show how to find all the "large attention scores", i.e., entries of $A$ which are at least a positive value $\varepsilon$, in time with linear dependence on $n$ (i.e., $n \cdot \textrm{poly}(d/\varepsilon)$) for a positive parameter $\varepsilon > 0$. Our class of functions include all functions $f$ of the form $f(x) = |x|^p$, as explored recently in transformer models. Using recently developed tools from randomized numerical linear algebra, we prove that for any $K$, there is a "universal set" $U \subset [n]$ of size independent of $n$, such that for any $Q$ and any row $i$, the large attention scores $A_{i,j}$ in row $i$ of $A$ all have $j \in U$. We also find $U$ in $n \cdot \textrm{poly}(d/\varepsilon)$ time. Notably, we (1) make no assumptions on the data, (2) our workspace does not grow with $n$, and (3) our algorithms can be computed in streaming and parallel settings. We empirically show the benefits of our scheme for vision transformers, showing how to train new models that use our universal set while training as well, showing that our model is able to consistently select "important keys'" during training. We also provide theoretical motivation by formulating a planted model in which our efficient algorithms provably identify relevant keys for each query.

Poster