ICLR 2024 Papers

International Conference on Learning Representations

Decision breakdown

2,260papers

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

  • Oral
    863.8%
  • Spotlight
    36716.2%
  • Poster
    1,80780.0%

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Incentive-Aware Federated Learning with Training-Time Model Rewards

Zhaoxuan Wu, Mohammad Mohammadi Amiri, Ramesh Raskar, Bryan Kian Hsiang Low

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In federated learning (FL), incentivizing contributions of training resources (e.g., data, compute) from potentially competitive clients is crucial. Existing incentive mechanisms often distribute post-training monetary rewards, which suffer from practical challenges of timeliness and feasibility of the rewards. Rewarding the clients after the completion of training may incentivize them to abort the collaboration, and monetizing the contribution is challenging in practice. To address these problems, we propose an incentive-aware algorithm that offers differentiated training-time model rewards for each client at each FL iteration. We theoretically prove that such a $\textit{local}$ design ensures the $\textit{global}$ objective of client incentivization. Through theoretical analyses, we further identify the issue of error propagation in model rewards and thus propose a stochastic reference-model recovery strategy to ensure theoretically that all the clients eventually obtain the optimal model in the limit. We perform extensive experiments to demonstrate the superior incentivizing performance of our method compared to existing baselines.

Poster
Let's do the time-warp-attend: Learning topological invariants of dynamical systems

Noa Moriel, Matt Ricci, Mor Nitzan

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Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series-based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we propose a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries based on the extraction of topologically invariant features. We focus on the paradigmatic case of the supercritical Hopf bifurcation, which is used to model periodic dynamics across a wide range of applications. Our convolutional attention method is trained with data augmentations that encourage the learning of topological invariants which can be used to detect bifurcation boundaries in unseen systems and to design models of biological systems like oscillatory gene regulatory networks. We further demonstrate our method's use in analyzing real data by recovering distinct proliferation and differentiation dynamics along pancreatic endocrinogenesis trajectory in gene expression space based on single-cell data. Our method provides valuable insights into the qualitative, long-term behavior of a wide range of dynamical systems, and can detect bifurcations or catastrophic transitions in large-scale physical and biological systems.

Poster
A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables

Xinshuai Dong, Biwei Huang, Ignavier Ng, Xiangchen Song, Yujia Zheng, Songyao Jin, Roberto Legaspi, Peter Spirtes, Kun Zhang

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Most existing causal discovery methods rely on the assumption of no latent confounders, limiting their applicability in solving real-life problems. In this paper, we introduce a novel, versatile framework for causal discovery that accommodates the presence of causally-related hidden variables almost everywhere in the causal network (for instance, they can be effects of measured variables), based on rank information of covariance matrix over measured variables. We start by investigating the efficacy of rank in comparison to conditional independence and, theoretically, establish necessary and sufficient conditions for the identifiability of certain latent structural patterns. Furthermore, we develop a Rank-based Latent Causal Discovery algorithm, RLCD, that can efficiently locate hidden variables, determine their cardinalities, and discover the entire causal structure over both measured and hidden ones. We also show that, under certain graphical conditions, RLCD correctly identifies the Markov Equivalence Class of the whole latent causal graph asymptotically. Experimental results on both synthetic and real-world personality data sets demonstrate the efficacy of the proposed approach in finite-sample cases. Our code will be publicly available.

Poster
Does Writing with Language Models Reduce Content Diversity?

Vishakh Padmakumar, He He

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Large language models (LLMs) have led to a surge in collaborative writing with model assistance. As different users incorporate suggestions from the same model, there is a risk of decreased diversity in the produced content, potentially limiting diverse perspectives in public discourse. In this work, we measure the impact of co-writing on diversity via a controlled experiment, where users write argumentative essays in three setups---using a base LLM (GPT3), a feedback-tuned LLM (InstructGPT), and writing without model help. We develop a set of diversity metrics and find that writing with InstructGPT (but not the GPT3) results in a statistically significant reduction in diversity. Specifically, it increases the similarity between the writings of different authors and reduces the overall lexical and content diversity. We additionally find that this effect is mainly attributable to InstructGPT contributing less diverse text to co-written essays. In contrast, the user-contributed text remains unaffected by model collaboration. This suggests that the recent improvement in generation quality from adapting models to human feedback might come at the cost of more homogeneous and less diverse content.

Poster
On the Power of the Weisfeiler-Leman Test for Graph Motif Parameters

Matthias Lanzinger, Pablo Barcelo

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Seminal research in the field of graph neural networks (GNNs) has revealed a direct correspondence between the expressive capabilities of GNNs and the $k$-dimensional Weisfeiler-Leman ($k$WL) test, a widely-recognized method for verifying graph isomorphism. This connection has reignited interest in comprehending the specific graph properties effectively distinguishable by the $k$WL test. A central focus of research in this field revolves around determining the least dimensionality $k$, for which $k$WL can discern graphs with different number of occurrences of a pattern graph $p$. We refer to such a least $k$ as the WL-dimension of this pattern counting problem. This inquiry traditionally delves into two distinct counting problems related to patterns: subgraph counting and induced subgraph counting. Intriguingly, despite their initial appearance as separate challenges with seemingly divergent approaches, both of these problems are interconnected components of a more comprehensive problem: "graph motif parameters". In this paper, we provide a precise characterization of the WL-dimension of labeled graph motif parameters. As specific instances of this result, we obtain characterizations of the WL-dimension of the subgraph counting and induced subgraph counting problem for every labeled pattern $p$. Particularly noteworthy is our resolution of a problem left open in previous work concerning induced copies. We additionally demonstrate that in cases where the $k$WL test distinguishes between graphs with varying occurrences of a pattern $p$, the exact number of occurrences of $p$ can be computed uniformly using only local information of the last layer of a corresponding GNN. We finally delve into the challenge of recognizing the WL-dimension of various graph parameters. We give a polynomial time algorithm for determining the WL-dimension of the subgraph counting problem for given pattern $p$, answering an open question from previous work. We additionally show how to utilize deep results from the field of graph motif parameters, together with our characterization, to determine the WL-dimension of induced subgraph counting and counting $k$-graphlets.

Poster
AlpaGasus: Training a Better Alpaca with Fewer Data

Lichang Chen, Shiyang Li, Jun Yan, Hai Wang, Kalpa Gunaratna, Vikas Yadav, Zheng Tang, Vijay Srinivasan, Tianyi Zhou, Heng Huang, Hongxia Jin

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Large language models~(LLMs) strengthen instruction-following capability through instruction-finetuning (IFT) on supervised instruction/response data. However, widely used IFT datasets (e.g., Alpaca's 52k data) surprisingly contain many low-quality instances with incorrect or irrelevant responses, which are misleading and detrimental to IFT. In this paper, we propose a simple and effective data selection strategy that automatically identifies and removes low-quality data using a strong LLM (e.g., ChatGPT). To this end, we introduce Alpagasus, which is finetuned on only 9k high-quality data filtered from the 52k Alpaca data. Alpagasus significantly outperforms the original Alpaca as evaluated by GPT-4 on multiple test sets and the controlled human study. Its 13B variant matches $>90\%$ performance of its teacher LLM (i.e., Text-Davinci-003) on test tasks. It also provides 5.7x faster training, reducing the training time for a 7B variant from 80 minutes (for Alpaca) to 14 minutes \footnote{We apply IFT for the same number of epochs as Alpaca(7B) but on fewer data, using 4$\times$NVIDIA A100 (80GB) GPUs and following the original Alpaca setting and hyperparameters.}. In the experiment, we also demonstrate that our method can work not only for machine-generated datasets but also for human-written datasets. Overall, Alpagasus demonstrates a novel data-centric IFT paradigm that can be generally applied to instruction-tuning data, leading to faster training and better instruction-following models.

Poster
OVOR: OnePrompt with Virtual Outlier Regularization for Rehearsal-Free Class-Incremental Learning

Wei-Cheng Huang, Chun-Fu Chen, Hsiang Hsu

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Recent works have shown that by using large pre-trained models along with learnable prompts, rehearsal-free methods for class-incremental learning (CIL) settings can achieve superior performance to prominent rehearsal-based ones. Rehearsal-free CIL methods struggle with distinguishing classes from different tasks, as those are not trained together. In this work we propose a regularization method based on virtual outliers to tighten decision boundaries of the classifier, such that confusion of classes among different tasks is mitigated. Recent prompt-based methods often require a pool of task-specific prompts, in order to prevent overwriting knowledge of previous tasks with that of the new task, leading to extra computation in querying and composing an appropriate prompt from the pool. This additional cost can be eliminated, without sacrificing accuracy, as we reveal in the paper. We illustrate that a simplified prompt-based method can achieve results comparable to previous state-of-the-art (SOTA) methods equipped with a prompt pool, using much less learnable parameters and lower inference cost. Our regularization method has demonstrated its compatibility with different prompt-based methods, boosting those previous SOTA rehearsal-free CIL methods' accuracy on the ImageNet-R and CIFAR-100 benchmarks. Our source code is available at https://github.com/jpmorganchase/ovor.

Poster
Neural-Symbolic Recursive Machine for Systematic Generalization

Qing Li, Yixin Zhu, Yitao Liang, Ying Nian Wu, Song-Chun Zhu, Siyuan Huang

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Current learning models often struggle with human-like systematic generalization, particularly in learning compositional rules from limited data and extrapolating them to novel combinations. We introduce the Neural-Symbolic Recursive Ma- chine ( NSR), whose core is a Grounded Symbol System ( GSS), allowing for the emergence of combinatorial syntax and semantics directly from training data. The NSR employs a modular design that integrates neural perception, syntactic parsing, and semantic reasoning. These components are synergistically trained through a novel deduction-abduction algorithm. Our findings demonstrate that NSR’s design, imbued with the inductive biases of equivariance and compositionality, grants it the expressiveness to adeptly handle diverse sequence-to-sequence tasks and achieve unparalleled systematic generalization. We evaluate NSR’s efficacy across four challenging benchmarks designed to probe systematic generalization capabilities: SCAN for semantic parsing, PCFG for string manipulation, HINT for arithmetic reasoning, and a compositional machine translation task. The results affirm NSR ’s superiority over contemporary neural and hybrid models in terms of generalization and transferability.

Poster
MVDream: Multi-view Diffusion for 3D Generation

Yichun Shi, Peng Wang, Jianglong Ye, Long Mai, Kejie Li, Xiao Yang

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We introduce MVDream, a diffusion model that is able to generate consistent multi-view images from a given text prompt. Learning from both 2D and 3D data, a multi-view diffusion model can achieve the generalizability of 2D diffusion models and the consistency of 3D renderings. We demonstrate that such a multi-view diffusion model is implicitly a generalizable 3D prior agnostic to 3D representations. It can be applied to 3D generation via Score Distillation Sampling, significantly enhancing the consistency and stability of existing 2D-lifting methods. It can also learn new concepts from a few 2D examples, akin to DreamBooth, but for 3D generation.

Poster
ZeroFlow: Scalable Scene Flow via Distillation

Kyle Vedder, Neehar Peri, Nathaniel Eliot Chodosh, Ishan Khatri, ERIC EATON, Dinesh Jayaraman, Yang Liu, Deva Ramanan, James Hays

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Scene flow estimation is the task of describing the 3D motion field between temporally successive point clouds. State-of-the-art methods use strong priors and test-time optimization techniques, but require on the order of tens of seconds to process full-size point clouds, making them unusable as computer vision primitives for real-time applications such as open world object detection. Feedforward methods are considerably faster, running on the order of tens to hundreds of milliseconds for full-size point clouds, but require expensive human supervision. To address both limitations, we propose _Scene Flow via Distillation_, a simple, scalable distillation framework that uses a label-free optimization method to produce pseudo-labels to supervise a feedforward model. Our instantiation of this framework, _ZeroFlow_, achieves **state-of-the-art** performance on the _Argoverse 2 Self-Supervised Scene Flow Challenge_ while using zero human labels by simply training on large-scale, diverse unlabeled data. At test-time, ZeroFlow is over 1000$\times$ faster than label-free state-of-the-art optimization-based methods on full-size point clouds (34 FPS vs 0.028 FPS) and over 1000$\times$ cheaper to train on unlabeled data compared to the cost of human annotation (\\$394 vs ~\\$750,000). To facilitate further research, we will release our code, trained model weights, and high quality pseudo-labels for the Argoverse 2 and Waymo Open datasets.

Poster
ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate

Chi-Min Chan, Weize Chen, Yusheng Su, Jianxuan Yu, Wei Xue, Shanghang Zhang, Jie Fu, Zhiyuan Liu

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Text evaluation has historically posed significant challenges, often demanding substantial labor and time cost. With the emergence of large language models (LLMs), researchers have explored LLMs' potential as alternatives for human evaluation. While these single-agent-based approaches show promise, experimental results suggest that further advancements are needed to bridge the gap between their current effectiveness and human-level evaluation quality. Recognizing that best practices of human evaluation processes often involve multiple human annotators collaborating in the evaluation, we resort to a multi-agent debate framework, moving beyond single-agent prompting strategies. In this paper, we construct a multi-agent referee team called $\textbf{ChatEval}$ to autonomously discuss and evaluate the quality of different texts. Our experiments on two benchmarks illustrate that ChatEval delivers superior accuracy and correlation in alignment with human assessment. Furthermore, we find that the diverse role prompts (different personas) are essential in the multi-agent debate process; that is, utilizing the same role description in the prompts can lead to a degradation in performance. Our qualitative analysis also shows that ChatEval transcends mere textual scoring, offering a human-mimicking evaluation process for reliable assessments.

Poster
A Symmetry-Aware Exploration of Bayesian Neural Network Posteriors

Olivier Laurent, Emanuel Aldea, Gianni Franchi

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The distribution of modern deep neural networks (DNNs) weights -- crucial for uncertainty quantification and robustness -- is an eminently complex object due to its extremely high dimensionality. This paper presents one of the first large-scale explorations of the posterior distribution of deep Bayesian Neural Networks (BNNs), expanding its study to real-world vision tasks and architectures. Specifically, we investigate the optimal approach for approximating the posterior, analyze the connection between posterior quality and uncertainty quantification, delve into the impact of modes on the posterior, and explore methods for visualizing the posterior. Moreover, we uncover weight-space symmetries as a critical aspect for understanding the posterior. To this extent, we develop an in-depth assessment of the impact of both permutation and scaling symmetries that tend to obfuscate the Bayesian posterior. While the first type of transformation is known for duplicating modes, we explore the relationship between the latter and L2 regularization, challenging previous misconceptions. Finally, to help the community improve our understanding of the Bayesian posterior, we release the first large-scale checkpoint dataset, including thousands of real-world models, along with our code.

Poster
SEINE: Short-to-Long Video Diffusion Model for Generative Transition and Prediction

Xinyuan Chen, Yaohui Wang, Lingjun Zhang, Shaobin Zhuang, Xin Ma, Jiashuo Yu, Yali Wang, Dahua Lin, Yu Qiao, Ziwei Liu

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Recently video generation has achieved substantial progress with realistic results. Nevertheless, existing AI-generated videos are usually very short clips ("shot-level'') depicting a single scene. To deliver a coherent long video ("story-level''), it is desirable to have creative transition and prediction effects across different clips. This paper presents a short-to-long video diffusion model, SEINE, that focuses on generative transition and prediction. The goal is to generate high-quality long videos with smooth and creative transitions between scenes and varying lengths of shot-level videos. Specifically, we propose a random-mask video diffusion model to automatically generate transitions based on textual descriptions. By providing the images of different scenes as inputs, combined with text-based control, our model generates transition videos that ensure coherence and visual quality. Furthermore, the model can be readily extended to various tasks such as image-to-video animation and autoregressive video prediction. To conduct a comprehensive evaluation of this new generative task, we propose three assessing criteria for smooth and creative transition: temporal consistency, semantic similarity, and video-text semantic alignment. Extensive experiments validate the effectiveness of our approach over existing methods for generative transition and prediction, enabling the creation of story-level long videos.

Poster
Gradual Optimization Learning for Conformational Energy Minimization

Artem Tsypin, Leonid Anatolievich Ugadiarov, Kuzma Khrabrov, Alexander Telepov, Egor Rumiantsev, Alexey Skrynnik, Aleksandr Panov, Dmitry P. Vetrov, Elena Tutubalina, Artur Kadurin

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Molecular conformation optimization is crucial to computer-aided drug discovery and materials design. Traditional energy minimization techniques rely on iterative optimization methods that use molecular forces calculated by a physical simulator (oracle) as anti-gradients. However, this is a computationally expensive approach that requires many interactions with a physical simulator. One way to accelerate this procedure is to replace the physical simulator with a neural network. Despite recent progress in neural networks for molecular conformation energy prediction, such models are prone to errors due to distribution shift, leading to inaccurate energy minimization. We find that the quality of energy minimization with neural networks can be improved by providing optimization trajectories as additional training data. Still, obtaining complete optimization trajectories demands a lot of additional computations. To reduce the required additional data, we present the Gradual Optimization Learning Framework (GOLF) for energy minimization with neural networks. The framework consists of an efficient data-collecting scheme and an external optimizer. The external optimizer utilizes gradients from the energy prediction model to generate optimization trajectories, and the data-collecting scheme selects additional training data to be processed by the physical simulator. Our results demonstrate that the neural network trained with GOLF performs \textit{on par} with the oracle on a benchmark of diverse drug-like molecules using significantly less additional data.

Poster
Denoising Diffusion Bridge Models

Linqi Zhou, Aaron Lou, Samar Khanna, Stefano Ermon

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Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion models must rely on cumbersome methods like guidance or projected sampling to incorporate this information in the generative process. In our work, we propose Denoising Diffusion Bridge Models (DDBMs), a natural alternative to this paradigm based on *diffusion bridges*, a family of processes that interpolate between two paired distributions given as endpoints. Our method learns the score of the diffusion bridge from data and maps from one endpoint distribution to the other by solving a (stochastic) differential equation based on the learned score. Our method naturally unifies several classes of generative models, such as score-based diffusion models and OT-Flow-Matching, allowing us to adapt existing design and architectural choices to our more general problem. Empirically, we apply DDBMs to challenging image datasets in both pixel and latent space. On standard image translation problems, DDBMs achieve significant improvement over baseline methods, and, when we reduce the problem to image generation by setting the source distribution to random noise, DDBMs achieve comparable FID scores to state-of-the-art methods despite being built for a more general task.

Poster
Bayesian Low-rank Adaptation for Large Language Models

Adam X. Yang, Maxime Robeyns, Xi Wang, Laurence Aitchison

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Parameter-efficient fine-tuning (PEFT) has emerged as a new paradigm for cost-efficient fine-tuning of large language models (LLMs), with low-rank adaptation (LoRA) being a widely adopted choice. However, fine-tuned LLMs often become overconfident especially when fine-tuned on small datasets. Bayesian methods, with their inherent ability to estimate uncertainty, serve as potent tools to mitigate overconfidence and enhance calibration. In this work, we introduce Laplace-LoRA, a straightforward yet effective Bayesian method, which applies the Laplace approximation to the LoRA parameters and, considerably boosts the calibration of fine-tuned LLMs.

Poster
SequenceMatch: Imitation Learning for Autoregressive Sequence Modelling with Backtracking

Chris Cundy, Stefano Ermon

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In many domains, autoregressive models can attain high likelihood on the task of predicting the next observation. However, this maximum-likelihood (MLE) objective does not necessarily match a downstream use-case of autoregressively generating high-quality sequences. The MLE objective weights sequences proportionally to their frequency under the data distribution, with no guidance for the model's behaviour out of distribution (OOD): leading to compounding error during autoregressive generation. In order to address this compounding error problem, we formulate sequence generation as an imitation learning (IL) problem. This allows us to minimize a variety of divergences between the distribution of sequences generated by an autoregressive model and sequences from a dataset, including divergences with weight on OOD generated sequences. The IL framework also allows us to incorporate backtracking by introducing a backspace action into the generation process. This further mitigates the compounding error problem by allowing the model to revert a sampled token if it takes the sequence OOD. Our resulting method, SequenceMatch, can be implemented without adversarial training or major architectural changes. We identify the SequenceMatch-χ2 divergence as a more suitable training objective for autoregressive models which are used for generation. We show that empirically, SequenceMatch training leads to improvements over MLE on text generation with language models and arithmetic

Poster
QLLM: Accurate and Efficient Low-Bitwidth Quantization for Large Language Models

Jing Liu, Ruihao Gong, Xiuying Wei, Zhiwei Dong, Jianfei Cai, Bohan Zhuang

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Large Language Models (LLMs) have demonstrated unparalleled efficacy in natural language processing. However, their high computational demands and memory overheads hinder their broad deployment. To address this, two quantization strategies emerge, including Quantization-Aware Training (QAT) and Post-Training Quantization (PTQ). For LLMs, the billions of parameters make the QAT impractical due to the prohibitive training cost and thus PTQ becomes more prevalent. In existing studies, activation outliers in particular channels are identified as the biggest challenge to PTQ accuracy. They propose to transform the magnitudes from activations to weights, which however offers limited alleviation or suffers from unstable gradients, resulting in a severe performance drop at low-bitwidth. In this paper, we propose QLLM, an accurate and efficient low-bitwidth PTQ method designed for LLMs. QLLM introduces an adaptive channel reassembly technique that reallocates the magnitude of outliers to other channels, thereby mitigating their impact on the quantization range. This is achieved by channel disassembly and channel assembly, which first breaks down the outlier channels into several sub-channels to ensure a more balanced distribution of activation magnitudes. Then similar channels are merged to maintain the original channel number for efficiency. Additionally, an adaptive strategy is designed to autonomously determine the optimal number of sub-channels for channel disassembly. To further compensate for the performance loss caused by quantization, we propose an efficient tuning method that only learns a small number of low-rank weights while freezing the pre-trained quantized model. After training, these low-rank parameters can be fused into the frozen weights without affecting inference. Extensive experiments on LLaMA-1 and LLaMA-2 show that QLLM is able to obtain accurate quantized models efficiently. For example, QLLM quantizes the 4-bit LLaMA-2-70B within 10 hours on a single A100-80G GPU, outperforming the previous state-of-the-art method by 7.89% on the average accuracy across five zero-shot tasks. Code is available at [ZIP Lab](https://github.com/ziplab/QLLM) and [ModelTC](https://github.com/ModelTC/QLLM).

Poster
CLIP the Bias: How Useful is Balancing Data in Multimodal Learning?

Ibrahim Alabdulmohsin, Xiao Wang, Andreas Peter Steiner, Priya Goyal, Alexander D'Amour, Xiaohua Zhai

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We study data-balancing for mitigating biases in contrastive language-image pretraining (CLIP), identifying areas of strength and limitation. First, we reaffirm prior conclusions that CLIP can inadvertently absorb stereotypes. To counter this, we present a novel algorithm, called Multi-Modal Moment Matching (M4), designed to reduce both representation and association biases in multimodal data. We use M4 to conduct an in-depth analysis taking into account various factors, such as the model, representation, and data size. Our study also explores the dynamic nature of how CLIP learns/unlearns biases. In particular, we find that fine-tuning is effective in countering representation biases, though its impact diminishes for association biases. Also, data balancing has a mixed impact on quality: it tends to improve classification but can hurt retrieval. Interestingly, data and architectural improvements seem to mitigate the negative impact of data balancing on performance; e.g. applying M4 to SigLIP-B/16 with data quality filters improves COCO image-to-text retrieval @5 from 86% (without data balancing) to 87% and ImageNet 0-shot classification from 77% to 77.5%! Finally, we conclude with recommendations for improving the efficacy of data balancing in multimodal systems.

Poster
Multimarginal Generative Modeling with Stochastic Interpolants

Michael Samuel Albergo, Nicholas Matthew Boffi, Michael Lindsey, Eric Vanden-Eijnden

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Given a set of $K$ probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for optimizing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

Poster