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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Accessing Vision Foundation Models via ImageNet-1K

Yitian Zhang, Xu Ma, Yue Bai, Huan Wang, Yun Fu

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Vision foundation models are renowned for the generalization ability due to massive training data. Nevertheless, they demand tremendous training resources, and the training data is often inaccessible, e.g., CLIP, DINOv2, posing great challenges to developing derivatives that could facilitate the research. In this work, we offer a very simple and general solution, named Proteus, to distill foundation models into smaller equivalents on ImageNet-1K without access to the original training data. Specifically, we remove the designs from conventional knowledge distillation settings that result in dataset bias and present three levels of training objectives, i.e., token, patch, and feature, to maximize the efficacy of knowledge transfer. In this manner, Proteus is trained at ImageNet-level costs with surprising ability, facilitating the accessibility of training foundation models for the broader research community. When leveraging DINOv2-g/14 as the teacher, Proteus-L/14 matches the performance of the Oracle method DINOv2-L/14 (142M training data) across 19 benchmarks and outperforms other vision foundation models including CLIP-L/14 (400M), OpenCLIP-L/14 (400M/2B) and SynCLR-L/14 (600M) with a significantly smaller training set of 1.2M images.

Poster
Reducing Hallucinations in Large Vision-Language Models via Latent Space Steering

Sheng Liu, Haotian Ye, James Zou

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Hallucination poses a challenge to the deployment of large vision-language models (LVLMs) in applications. Unlike in large language models (LLMs), hallucination in LVLMs often arises from misalignments between visual inputs and textual outputs. This paper investigates the underlying mechanisms of hallucination, focusing on the unique structure of LVLMs that distinguishes them from LLMs. We identify that hallucinations often arise from the sensitivity of text decoders to vision inputs, a natural phenomenon when image encoders and text decoders are pre-trained separately. Inspired by this, we introduce Visual and Textual Intervention (VTI), a novel technique designed to reduce hallucinations by steering latent space representations during inference to enhance the stability of vision features. As a task-agnostic test-time intervention, VTI can be easily applied to any problem without additional training costs. Extensive experiments demonstrate that it can effectively reduce hallucinations and outperform baseline methods across multiple metrics, highlighting the critical role of vision feature stability in LVLMs.

Spotlight
QERA: an Analytical Framework for Quantization Error Reconstruction

Cheng Zhang, Jeffrey T. H. Wong, Can Xiao, George Anthony Constantinides, Yiren Zhao

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The growing number of parameters and computational demands of large language models (LLMs) present significant challenges for their efficient deployment. Recently, there is an increasing interest in quantizing weights to extremely low precision while offsetting the resulting error with low-rank, high-precision error reconstruction terms. The combination of quantization and low-rank approximation is now popular in both adapter-based, parameter-efficient fine-tuning methods such as LoftQ and low-precision inference techniques including ZeroQuant-V2. Usually, the low-rank terms are calculated via the singular value decomposition (SVD) of the weight quantization error, minimizing the Frobenius and spectral norms of the weight approximation error. Recent methods like LQ-LoRA and LQER introduced hand-crafted heuristics to minimize errors in layer outputs (activations) rather than weights, resulting improved quantization results. However, these heuristic methods lack an analytical solution to guide the design of quantization error reconstruction terms. In this paper, we revisit this problem and formulate an analytical framework, named Quantization Error Reconstruction Analysis (QERA), and offer a closed-form solution to the problem. We show QERA benefits both existing low-precision fine-tuning and inference methods -- QERA achieves a fine-tuned accuracy gain of $\Delta_{\text{acc}}$ = 6.05\% of 2-bit RoBERTa-base on GLUE compared to LoftQ; and obtains $\Delta_{\text{acc}}$ = 2.97\% higher post-training quantization accuracy of 4-bit Llama-3.1-70B on average than ZeroQuant-V2 and $\Delta_{\text{ppl}}$ = $-$ 0.28 lower perplexity on WikiText2 than LQER.

Poster
SPAM: Spike-Aware Adam with Momentum Reset for Stable LLM Training

Tianjin Huang, Ziquan Zhu, Gaojie Jin, Lu Liu, Zhangyang Wang, Shiwei Liu

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Large Language Models (LLMs) have demonstrated exceptional performance across diverse tasks, yet their training remains highly resource intensive and susceptible to critical challenges such as training instability. A predominant source of this instability stems from gradient and loss spikes, which disrupt the learning process, often leading to costly interventions like checkpoint recovery and experiment restarts, further amplifying inefficiencies. This paper presents a comprehensive investigation into gradient spikes observed during LLM training, revealing their prevalence across multiple architectures and datasets. Our analysis shows that these spikes can be up to 1000× larger than typical gradients, substantially deteriorating model performance. To address this issue, we propose Spike-Aware Adam with Momentum Reset (SPAM), a novel optimizer designed to counteract gradient spikes through momentum reset and spike-aware gradient clipping. Extensive experiments, including both pre-training and fine-tuning, demonstrate that SPAM consistently surpasses Adam and its variants across a range of model scales. Additionally, SPAM facilitates memory-efficient training by enabling sparse momentum, where only a subset of momentum terms are maintained and updated. When operating under memory constraints, SPAM outperforms state-of-the-art memory-efficient optimizers such as GaLore and Adam-Mini. Our work underscores the importance of mitigating gradient spikes in LLM training and introduces an effective optimization strategy that enhances both training stability and resource efficiency at scale. Code is submitted.

Poster
DaWin: Training-free Dynamic Weight Interpolation for Robust Adaptation

Changdae Oh, Yixuan Li, Kyungwoo Song, Sangdoo Yun, Dongyoon Han

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Adapting a pre-trained foundation model on downstream tasks should ensure robustness against distribution shifts without the need to retrain the whole model. Although existing weight interpolation methods are simple yet effective, we argue their static nature limits downstream performance while achieving efficiency. In this work, we propose DaWin, a training-free dynamic weight interpolation method that leverages the entropy of individual models over each unlabeled test sample to assess model expertise, and compute per-sample interpolation coefficients dynamically. Unlike previous works that typically rely on additional training to learn such coefficients, our approach requires no training. Then, we propose a mixture modeling approach that greatly reduces inference overhead raised by dynamic interpolation. We validate DaWin on the large-scale visual recognition benchmarks, spanning 14 tasks across robust fine-tuning -- ImageNet and derived five distribution shift benchmarks -- and multi-task learning with eight classification tasks. Results demonstrate that DaWin achieves significant performance gain in considered settings, with minimal computational overhead. We further discuss DaWin's analytic behavior to explain its empirical success.

Poster
OASIS Uncovers: High-Quality T2I Models, Same Old Stereotypes

Sepehr Dehdashtian, Gautam Sreekumar, Vishnu Boddeti

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Images generated by text-to-image (T2I) models often exhibit visual biases and stereotypes of concepts such as culture and profession. Existing quantitative measures of stereotypes are based on statistical parity that does not align with the sociological definition of stereotypes and, therefore, incorrectly categorizes biases as stereotypes. Instead of oversimplifying stereotypes as biases, we propose a quantitative measure of stereotypes that aligns with its sociological definition. We then propose OASIS to measure the stereotypes in a generated dataset and understand their origins within the T2I model. OASIS includes two scores to measure stereotypes from a generated image dataset: **(M1)** Stereotype Score to measure the distributional violation of stereotypical attributes, and **(M2)** WALS to measure spectral variance in the images along a stereotypical attribute. OASIS also includes two methods to understand the origins of stereotypes in T2I models: **(U1)** StOP to discover attributes that the T2I model internally associates with a given concept, and **(U2)** SPI to quantify the emergence of stereotypical attributes in the latent space of the T2I model during image generation. Despite the considerable progress in image fidelity, using OASIS, we conclude that newer T2I models such as FLUX.1 and SDv3 contain strong stereotypical predispositions about concepts and still generate images with widespread stereotypical attributes. Additionally, the quantity of stereotypes worsens for nationalities with lower Internet footprints.

Spotlight
Discrete Latent Plans via Semantic Skill Abstractions

Haobin Jiang, Jiangxing Wang, Zongqing Lu

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Skill learning from language instructions is a critical challenge in developing intelligent agents that can generalize across diverse tasks and follow complex human instructions. Hierarchical methods address this by decomposing the learning problem into multiple levels, where the high-level and low-level policies are mediated through a latent plan space. Effective modeling and learning of this latent plan space are key to enabling robust and interpretable skill learning. In this paper, we introduce LADS, a hierarchical approach that learns language-conditioned discrete latent plans through semantic skill abstractions. Our method decouples the learning of the latent plan space from the language-conditioned high-level policy to improve training stability. First, we incorporate a trajectory encoder to learn a discrete latent space with the low-level policy, regularized by language instructions. Next, we model the high-level policy as a categorical distribution over these discrete latent plans to capture the multi-modality of the dataset. Through experiments in simulated control environments, we demonstrate that LADS outperforms state-of-the-art methods in both skill learning and compositional generalization.

Poster
RobustKV: Defending Large Language Models against Jailbreak Attacks via KV Eviction

Tanqiu Jiang, ZiAn Wang, Jiacheng Liang, Changjiang Li, Yuhui Wang, Ting Wang

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Jailbreak attacks circumvent LLMs' built-in safeguards by concealing harmful queries within adversarial prompts. While most existing defenses attempt to mitigate the effects of adversarial prompts, they often prove inadequate as adversarial prompts can take arbitrary, adaptive forms. This paper introduces RobustKV, a novel jailbreak defense that takes a fundamentally different approach by selectively removing critical tokens of harmful queries from key-value (KV) caches. Intuitively, for an adversarial prompt to be effective, its tokens must achieve sufficient `importance' (measured by attention scores), which consequently lowers the importance of tokens in the concealed harmful query. Therefore, by carefully evicting the KVs of low-ranked tokens, RobustKV minimizes the harmful query's presence in the KV cache, thus preventing the LLM from generating informative responses. Extensive evaluation using benchmark datasets and models demonstrates that RobustKV effectively counters state-of-the-art jailbreak attacks while maintaining the LLM's performance on benign queries. Notably, RobustKV creates an interesting effectiveness-evasiveness dilemma for the adversary, leading to its robustness against adaptive attacks.{(Warning: This paper contains potentially harmful content generated by LLMs.)}

Poster
Learning to engineer protein flexibility

Petr Kouba, Joan Planas-Iglesias, Jiri Damborsky, Jiri Sedlar, Stanislav Mazurenko, Josef Sivic

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Generative machine learning models are increasingly being used to design novel proteins. However, their major limitation is the inability to account for protein flexibility, a property crucial for protein function. Learning to engineer flexibility is difficult because the relevant data is scarce, heterogeneous, and costly to obtain using computational and experimental methods. Our contributions are three-fold. First, we perform a comprehensive comparison of methods for evaluating protein flexibility and identify relevant data for learning. Second, we overcome the data scarcity issue by leveraging a pre-trained protein language model. We design and train flexibility predictors utilizing either only sequential or both sequential and structural information on the input. Third, we introduce a method for fine-tuning a protein inverse folding model to make it steerable toward desired flexibility at specified regions. We demonstrate that our method Flexpert enables guidance of inverse folding models toward increased flexibility. This opens up a transformative possibility of engineering protein flexibility.

Poster
TabReD: Analyzing Pitfalls and Filling the Gaps in Tabular Deep Learning Benchmarks

Ivan Rubachev, Nikolay Kartashev, Yury Gorishniy, Artem Babenko

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Advances in machine learning research drive progress in real-world applications. To ensure this progress, it is important to understand the potential pitfalls on the way from a novel method's success on academic benchmarks to its practical deployment. In this work, we analyze existing tabular deep learning benchmarks and find two common characteristics of tabular data in typical industrial applications that are underrepresented in the datasets usually used for evaluation in the literature. First, in real-world deployment scenarios, distribution of data often changes over time. To account for this distribution drift, time-based train/test splits should be used in evaluation. However, existing academic tabular datasets often lack timestamp metadata to enable such evaluation. Second, a considerable portion of datasets in production settings stem from extensive data acquisition and feature engineering pipelines. This can have an impact on the absolute and relative number of predictive, uninformative, and correlated features compared to academic datasets. In this work, we aim to understand how recent research advances in tabular deep learning transfer to these underrepresented conditions. To this end, we introduce TabReD -- a collection of eight industry-grade tabular datasets. We reassess a large number of tabular ML models and techniques on TabReD. We demonstrate that evaluation on both time-based data splits and richer feature sets leads to different methods ranking, compared to evaluation on random splits and smaller number of features, which are common in academic benchmarks. Furthermore, simple MLP-like architectures and GBDT show the best results on the TabReD datasets, while other methods are less effective in the new setting.

Spotlight
Projection Head is Secretly an Information Bottleneck

Zhuo Ouyang, Kaiwen Hu, Qi Zhang, Yifei Wang, Yisen Wang

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Recently, contrastive learning has risen to be a promising paradigm for extracting meaningful data representations. Among various special designs, adding a projection head on top of the encoder during training and removing it for downstream tasks has proven to significantly enhance the performance of contrastive learning. However, despite its empirical success, the underlying mechanism of the projection head remains under-explored. In this paper, we develop an in-depth theoretical understanding of the projection head from the information-theoretic perspective. By establishing the theoretical guarantees on the downstream performance of the features before the projector, we reveal that an effective projector should act as an information bottleneck, filtering out the information irrelevant to the contrastive objective. Based on theoretical insights, we introduce modifications to projectors with training and structural regularizations. Empirically, our methods exhibit consistent improvement in the downstream performance across various real-world datasets, including CIFAR-10, CIFAR-100, and ImageNet-100. We believe our theoretical understanding on the role of the projection head will inspire more principled and advanced designs in this field. Code is available at \url{https://github.com/PKU-ML/Projector_Theory}.

Poster
Finding Shared Decodable Concepts and their Negations in the Brain

Cory Daniel Efird, Alex Murphy, Joel Zylberberg, Alona Fyshe

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Prior work has offered evidence for functional localization in the brain; different anatomical regions preferentially activate for certain types of visual input. For example, the fusiform face area preferentially activates for visual stimuli that include a face. However, the spectrum of visual semantics is extensive, and only a few semantically-tuned patches of cortex have so far been identified in the human brain. Using a multimodal (natural language and image) neural network architecture (CLIP, \cite{CLIP}, we train a highly accurate contrastive model that maps brain responses during naturalistic image viewing to CLIP embeddings. We then use a novel adaptation of the DBSCAN clustering algorithm to cluster the parameters of these participant-specific contrastive models. This reveals what we call Shared Decodable Concepts (SDCs): clusters in CLIP space that are decodable from common sets of voxels across multiple participants. Examining the images most and least associated with each SDC cluster gives us additional insight into the semantic properties of each SDC. We note SDCs for previously reported visual features (e.g. orientation tuning in early visual cortex) as well as visual semantic concepts such as faces, places and bodies. In cases where our method finds multiple clusters for a visuo-semantic concept, the least associated images allow us to dissociate between confounding factors. For example, we discovered two clusters of food images, one driven by color, the other by shape. We also uncover previously unreported areas with visuo-semantic sensitivity such as regions of extrastriate body area (EBA) tuned for legs/hands and sensitivity to numerosity in right intraparietal sulcus, sensitivity associated with visual perspective (close/far) and more. Thus, our contrastive-learning methodology better characterizes new and existing visuo-semantic representations in the brain by leveraging multimodal neural network representations and a novel adaptation of clustering algorithms.

Poster
Selective Unlearning via Representation Erasure Using Domain Adversarial Training

Nazanin Mohammadi Sepahvand, Eleni Triantafillou, Hugo Larochelle, Doina Precup, James J. Clark, Daniel M. Roy, Gintare Karolina Dziugaite

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When deploying machine learning models in the real world, we often face the challenge of “unlearning” specific data points or subsets after training. Inspired by Domain-Adversarial Training of Neural Networks (DANN), we propose a novel algorithm,SURE, for targeted unlearning.SURE treats the process as a domain adaptation problem, where the “forget set” (data to be removed) and a validation set from the same distribution form two distinct domains. We train a domain classifier to discriminate between representations from the forget and validation sets.Using a gradient reversal strategy similar to DANN, we perform gradient updates to the representations to “fool” the domain classifier and thus obfuscate representations belonging to the forget set. Simultaneously, gradient descent is applied to the retain set (original training data minus the forget set) to preserve its classification performance. Unlike other unlearning approaches whose training objectives are built based on model outputs, SURE directly manipulates the representations.This is key to ensure robustness against a set of more powerful attacks than currently considered in the literature, that aim to detect which examples were unlearned through access to learned embeddings. Our thorough experiments reveal that SURE has a better unlearning quality to utility trade-off compared to other standard unlearning techniques for deep neural networks.

Poster
Adapters for Altering LLM Vocabularies: What Languages Benefit the Most?

HyoJung Han, Akiko Eriguchi, Haoran Xu, Hieu Hoang, Marine Carpuat, Huda Khayrallah

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Vocabulary adaptation, which integrates new vocabulary into pre-trained language models, enables expansion to new languages and mitigates token over-fragmentation. However, existing approaches are limited by their reliance on heuristics or external embeddings. We propose VocADT, a novel method for vocabulary adaptation using adapter modules that are trained to learn the optimal linear combination of existing embeddings while keeping the model’s weights fixed. VocADT offers a flexible and scalable solution without depending on external resources or language constraints. Across 11 languages—with diverse scripts, resource availability, and fragmentation—we demonstrate that VocADT outperforms the original Mistral model (Jiang et al., 2023) and other baselines across various multilingual tasks including natural language understanding and machine translation. We find that Latin-script languages and highly fragmented languages benefit the most from vocabulary adaptation. We further fine-tune the adapted model on the generative task of machine translation and find that vocabulary adaptation is still beneficial after fine-tuning and that VocADT is the most effective.

Poster
An Asynchronous Bundle Method for Distributed Learning Problems

Daniel Cederberg, Xuyang Wu, Stephen P. Boyd, Mikael Johansson

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We propose a novel asynchronous bundle method to solve distributed learning problems. Compared to existing asynchronous methods, our algorithm computes the next iterate based on a more accurate approximation of the objective function and does not require any prior information about the maximal information delay in the system. This makes the proposed method fast and easy to tune. We prove that the algorithm converges in both deterministic and stochastic (mini-batch) settings, and quantify how the convergence times depend on the level of asynchrony. The practical advantages of our method are illustrated through numerical experiments on classification problems of varying complexities and scales.

Poster
Agent Skill Acquisition for Large Language Models via CycleQD

So Kuroki, Taishi Nakamura, Takuya Akiba, Yujin Tang

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Training large language models to acquire specific skills remains a challenging endeavor. Conventional training approaches often struggle with data distribution imbalances and inadequacies in objective functions that do not align well with task-specific performance. To address these challenges, we introduce CycleQD, a novel approach that leverages the Quality Diversity framework through a cyclic adaptation of the algorithm, along with a model merging based crossover and an SVD-based mutation. In CycleQD, each task’s performance metric is alternated as the quality measure while the others serve as the behavioral characteristics. This cyclic focus on individual tasks allows for concentrated effort on one task at a time, eliminating the need for data ratio tuning and simplifying the design of the objective function. Empirical results from AgentBench indicate that applying CycleQD to LLAMA3-8B-INSTRUCT based models not only enables them to surpass traditional fine-tuning methods in coding, operating systems, and database tasks, but also achieves performance on par with GPT-3.5-TURBO, which potentially contains much more parameters, across these domains. Crucially, this enhanced performance is achieved while retaining robust language capabilities, as evidenced by its performance on widely adopted language benchmark tasks. We highlight the key design choices in CycleQD, detailing how these contribute to its effectiveness. Furthermore, our method is general and can be applied to image segmentation models, highlighting its applicability across different domains.

Poster
Sketch2Diagram: Generating Vector Diagrams from Hand-Drawn Sketches

Itsumi Saito, Haruto Yoshida, Keisuke Sakaguchi

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We address the challenge of automatically generating high-quality vector diagrams from hand-drawn sketches. Vector diagrams are essential for communicating complex ideas across various fields, offering flexibility and scalability. While recent research has progressed in generating diagrams from text descriptions, converting hand-drawn sketches into vector diagrams remains largely unexplored due to the lack of suitable datasets. To address this gap, we introduce SketikZ, a dataset comprising 3,231 pairs of hand-drawn sketches and thier corresponding TikZ codes as well as reference diagrams. Our evaluations reveal the limitations of state-of-the-art vision and language models (VLMs), positioning SketikZ as a key benchmark for future research in sketch-to-diagram conversion. Along with SketikZ, we present ImgTikZ, an image-to-TikZ model that integrates a 6.7B parameter code-specialized open-source large language model (LLM) with a pre-trained vision encoder. Despite its relatively compact size, ImgTikZ performs comparably to GPT-4o. This success is driven by using our two data augmentation techniques and a multi-candidate inference strategy. Our findings open promising directions for future research in sketch-to-diagram conversion and broader image-to-code generation tasks. SketikZ is publicly available.

Poster
SoundCTM: Unifying Score-based and Consistency Models for Full-band Text-to-Sound Generation

Koichi Saito, Dongjun Kim, Takashi Shibuya, Chieh-Hsin Lai, Zhi Zhong, Yuhta Takida, Yuki Mitsufuji

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Sound content creation, essential for multimedia works such as video games and films, often involves extensive trial-and-error, enabling creators to semantically reflect their artistic ideas and inspirations, which evolve throughout the creation process, into the sound. Recent high-quality diffusion-based Text-to-Sound (T2S) generative models provide valuable tools for creators. However, these models often suffer from slow inference speeds, imposing an undesirable burden that hinders the trial-and-error process. While existing T2S distillation models address this limitation through $1$-step generation, the sample quality of $1$-step generation remains insufficient for production use. Additionally, while multi-step sampling in those distillation models improves sample quality itself, the semantic content changes due to their lack of deterministic sampling capabilities. Thus, developing a T2S generative model that allows creators to efficiently conduct trial-and-error while producing high-quality sound remains a key challenge. To address these issues, we introduce Sound Consistency Trajectory Models (SoundCTM), which allow flexible transitions between high-quality $1$-step sound generation and superior sound quality through multi-step deterministic sampling. This allows creators to efficiently conduct trial-and-error with $1$-step generation to semantically align samples with their intention, and subsequently refine sample quality with preserving semantic content through deterministic multi-step sampling. To develop SoundCTM, we reframe the CTM training framework, originally proposed in computer vision, and introduce a novel feature distance using the teacher network for a distillation loss. Additionally, while distilling classifier-free guided trajectories, we introduce a $\nu$-sampling, a new algorithm that offers another source of quality improvement. For the $\nu$-sampling, we simultaneously train both conditional and unconditional student models. For production-level generation, we scale up our model to 1B trainable parameters, making SoundCTM-DiT-1B the first large-scale distillation model in the sound community to achieve both promising high-quality $1$-step and multi-step full-band (44.1kHz) generation. Audio samples are available at \url{https://anonymus-soundctm.github.io/soundctm_iclr/}.

Poster
Streaming Algorithms For $\ell_p$ Flows and $\ell_p$ Regression

Amit Chakrabarti, Jeffrey Jiang, David Woodruff, Taisuke Yasuda

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We initiate the study of one-pass streaming algorithms for underdetermined $\ell_p$ linear regression problems of the form $$ \min_{\mathbf A\mathbf x = \mathbf b} \lVert\mathbf x\rVert_p \,, \qquad \text{where } \mathbf A \in \mathbb R^{n \times d} \text{ with } n \ll d \,, $$ which generalizes basis pursuit ($p = 1$) and least squares solutions to underdetermined linear systems ($p = 2$). We study the column-arrival streaming model, in which the columns of $\mathbf A$ are presented one by one in a stream. When $\mathbf A$ is the incidence matrix of a graph, this corresponds to an edge insertion graph stream, and the regression problem captures $\ell_p$ flows which includes transshipment ($p = 1$), electrical flows ($p = 2$), and max flow ($p = \infty$) on undirected graphs as special cases. Our goal is to design algorithms which use space much less than the entire stream, which has a length of $d$. For the task of estimating the cost of the $\ell_p$ regression problem for $p\in[2,\infty]$, we show a streaming algorithm which constructs a sparse instance supported on $\tilde O(\varepsilon^{-2}n)$ columns of $\mathbf A$ which approximates the cost up to a $(1\pm\varepsilon)$ factor, which corresponds to $\tilde O(\varepsilon^{-2}n^2)$ bits of space in general and an $\tilde O(\varepsilon^{-2}n)$ space semi-streaming algorithm for constructing $\ell_p$ flow sparsifiers on graphs. This extends to $p\in(1, 2)$ with $\tilde O(\varepsilon^{2}n^{q/2})$ columns, where $q$ is the H\"older conjugate exponent of $p$. For $p = 2$, we show that $\Omega(n^2)$ bits of space are required in general even for outputting a constant factor solution. For $p = 1$, we show that the cost cannot be estimated even to an $o(\sqrt n)$ factor in $\mathrm{poly}(n)$ space. On the other hand, if we are interested in outputting a solution $\mathbf x$, then we show that $(1+\varepsilon)$-approximations require $\Omega(d)$ space for $p > 1$, and in general, $\kappa$-approximations require $\tilde\Omega(d/\kappa^{2q})$ space for $p > 1$. We complement these lower bounds with the first sublinear space upper bounds for this problem, showing that we can output a $\kappa$-approximation using space only $\mathrm{poly}(n) \cdot \tilde O(d/\kappa^q)$ for $p > 1$, as well as a $\sqrt n$-approximation using $\mathrm{poly}(n, \log d)$ space for $p = 1$.

Spotlight
A Multi-Power Law for Loss Curve Prediction Across Learning Rate Schedules

Kairong Luo, Haodong Wen, Shengding Hu, Zhenbo Sun, Zhiyuan Liu, Maosong Sun, Kaifeng Lyu, Wenguang Chen

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Training large models is both resource-intensive and time-consuming, making it crucial to understand the quantitative relationship between model performance and hyperparameters. In this paper, we derive an empirical law that predicts pretraining loss for large language models for every intermediate training step across various learning rate schedules, including constant, cosine, and step decay schedules. Our proposed law takes a multi-power form, combining a power law based on the sum of learning rates and additional power laws to account for a loss reduction effect as learning rate decays. We validate this law extensively on Llama-2 models of varying sizes and demonstrate that, after fitting on a few learning rate schedules, it accurately predicts the loss curves for unseen schedules of different shapes and horizons. Moreover, by minimizing the predicted final pretraining loss across learning rate schedules, we are able to find a schedule that outperforms the widely-used cosine learning rate schedule. Interestingly, this automatically discovered schedule bears some resemblance to the recently proposed Warmup-Stable-Decay (WSD) schedule (Hu et al, 2024) but achieves a slightly lower final loss. We believe these results could offer valuable insights for understanding the dynamics of pretraining and for designing learning rate schedules to improve efficiency.

Poster