NeurIPS 2023 论文列表

Conference on Neural Information Processing Systems

录用类型

3,584篇论文

按官方录用论文列表统计,可能与会议公布的数字略有出入。

  • Oral
    772.1%
  • Spotlight
    40011.2%
  • Poster
    3,10786.7%

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Semi-Implicit Denoising Diffusion Models (SIDDMs)

yanwu xu, Mingming Gong, Shaoan Xie, Wei Wei, Matthias Grundmann, Kayhan Batmanghelich, Tingbo Hou

展开摘要

Despite the proliferation of generative models, achieving fast sampling during inference without compromising sample diversity and quality remains challenging. Existing models such as Denoising Diffusion Probabilistic Models (DDPM) deliver high-quality, diverse samples but are slowed by an inherently high number of iterative steps. The Denoising Diffusion Generative Adversarial Networks (DDGAN) attempted to circumvent this limitation by integrating a GAN model for larger jumps in the diffusion process. However, DDGAN encountered scalability limitations when applied to large datasets. To address these limitations, we introduce a novel approach that tackles the problem by matching implicit and explicit factors. More specifically, our approach involves utilizing an implicit model to match the marginal distributions of noisy data and the explicit conditional distribution of the forward diffusion. This combination allows us to effectively match the joint denoising distributions. Unlike DDPM but similar to DDGAN, we do not enforce a parametric distribution for the reverse step, enabling us to take large steps during inference. Similar to the DDPM but unlike DDGAN, we take advantage of the exact form of the diffusion process. We demonstrate that our proposed method obtains comparable generative performance to diffusion-based models and vastly superior results to models with a small number of sampling steps.

Poster
On Private and Robust Bandits

Yulian Wu, Xingyu Zhou, Youming Tao, Di Wang

展开摘要

We study private and robust multi-armed bandits (MABs), where the agent receives Huber's contaminated heavy-tailed rewards and meanwhile needs to ensure differential privacy. We consider both the finite $k$-th raw moment and the finite $k$-th central moment settings for heavy-tailed rewards distributions with $k\ge 2$. We first present its minimax lower bound, characterizing the information-theoretic limit of regret with respect to privacy budget, contamination level, and heavy-tailedness. Then, we propose a meta-algorithm that builds on a private and robust mean estimation sub-routine \texttt{PRM} that essentially relies on reward truncation and the Laplace mechanism. For the above two different heavy-tailed settings, we give corresponding schemes of \texttt{PRM}, which enable us to achieve nearly-optimal regrets. Moreover, our two proposed truncation-based or histogram-based \texttt{PRM} schemes achieve the optimal trade-off between estimation accuracy, privacy and robustness. Finally, we support our theoretical results and show the effectiveness of our algorithms with experimental studies.

Poster
Best Arm Identification with Fixed Budget: A Large Deviation Perspective

Po-An Wang, Ruo-Chun Tzeng, Alexandre Proutiere

展开摘要

We consider the problem of identifying the best arm in stochastic Multi-Armed Bandits (MABs) using a fixed sampling budget. Characterizing the minimal instance-specific error probability for this problem constitutes one of the important remaining open problems in MABs. When arms are selected using a static sampling strategy, the error probability decays exponentially with the number of samples at a rate that can be explicitly derived via Large Deviation techniques. Analyzing the performance of algorithms with adaptive sampling strategies is however much more challenging. In this paper, we establish a connection between the Large Deviation Principle (LDP) satisfied by the empirical proportions of arm draws and that satisfied by the empirical arm rewards. This connection holds for any adaptive algorithm, and is leveraged (i) to improve error probability upper bounds of some existing algorithms, such as the celebrated SR (Successive Rejects) algorithm \cite{audibert2010best}, and (ii) to devise and analyze new algorithms. In particular, we present CR (Continuous Rejects), a truly adaptive algorithm that can reject arms in {\it any} round based on the observed empirical gaps between the rewards of various arms. Applying our Large Deviation results, we prove that CR enjoys better performance guarantees than existing algorithms, including SR. Extensive numerical experiments confirm this observation.

Spotlight
Differentiable sorting for censored time-to-event data.

Andre Vauvelle, Benjamin Wild, Roland Eils, Spiros Denaxas

展开摘要

Survival analysis is a crucial semi-supervised task in machine learning with significant real-world applications, especially in healthcare. The most common approach to survival analysis, Cox’s partial likelihood, can be interpreted as a ranking model optimized on a lower bound of the concordance index. We follow these connections further, with listwise ranking losses that allow for a relaxation of the pairwise independence assumption. Given the inherent transitivity of ranking, we explore differentiable sorting networks as a means to introduce a stronger transitive inductive bias during optimization. Despite their potential, current differentiable sorting methods cannot account for censoring, a crucial aspect of many real-world datasets. We propose a novel method, Diffsurv, to overcome this limitation by extending differentiable sorting methods to handle censored tasks. Diffsurv predicts matrices of possible permutations that accommodate the label uncertainty introduced by censored samples. Our experiments reveal that Diffsurv outperforms established baselines in various simulated and real-world risk prediction scenarios. Furthermore, we demonstrate the algorithmic advantages of Diffsurv by presenting a novel method for top-k risk prediction that surpasses current methods.

Poster
Global Convergence Analysis of Local SGD for Two-layer Neural Network without Overparameterization

Yajie Bao, Amarda Shehu, Mingrui Liu

展开摘要

Local SGD, a cornerstone algorithm in federated learning, is widely used in training deep neural networks and shown to have strong empirical performance. A theoretical understanding of such performance on nonconvex loss landscapes is currently lacking. Analysis of the global convergence of SGD is challenging, as the noise depends on the model parameters. Indeed, many works narrow their focus to GD and rely on injecting noise to enable convergence to the local or global optimum. When expanding the focus to local SGD, existing analyses in the nonconvex case can only guarantee finding stationary points or assume the neural network is overparameterized so as to guarantee convergence to the global minimum through neural tangent kernel analysis. In this work, we provide the first global convergence analysis of the vanilla local SGD for two-layer neural networks \emph{without overparameterization} and \textit{without injecting noise}, when the input data is Gaussian. The main technical ingredients of our proof are \textit{a self-correction mechanism} and \textit{a new exact recursive characterization of the direction of global model parameters}. The self-correction mechanism guarantees the algorithm reaches a good region even if the initialization is in a bad region. A good (bad) region means updating the model by gradient descent will move closer to (away from) the optimal solution. The main difficulty in establishing a self-correction mechanism is to cope with the gradient dependency between two layers. To address this challenge, we divide the landscape of the objective into several regions to carefully control the interference of two layers during the correction process. As a result, we show that local SGD can correct the two layers and enter the good region in polynomial time. After that, we establish a new exact recursive characterization of the direction of global parameters, which is the key to showing convergence to the global minimum with linear speedup in the number of machines and reduced communication rounds. Experiments on synthetic data confirm theoretical results.

Poster
Learning Provably Robust Estimators for Inverse Problems via Jittering

Anselm Krainovic, Mahdi Soltanolkotabi, Reinhard Heckel

展开摘要

Deep neural networks provide excellent performance for inverse problems such as denoising. However, neural networks can be sensitive to adversarial or worst-case perturbations. This raises the question of whether such networks can be trained efficiently to be worst-case robust. In this paper, we investigate whether jittering, a simple regularization technique that adds isotropic Gaussian noise during training, is effective for learning worst-case robust estimators for inverse problems. While well studied for prediction in classification tasks, the effectiveness of jittering for inverse problems has not been systematically investigated. In this paper, we present a novel analytical characterization of the optimal $\ell_2$-worst-case robust estimator for linear denoising and show that jittering yields optimal robust denoisers. Furthermore, we examine jittering empirically via training deep neural networks (U-nets) for natural image denoising, deconvolution, and accelerated magnetic resonance imaging (MRI). The results show that jittering significantly enhances the worst-case robustness, but can be suboptimal for inverse problems beyond denoising. Moreover, our results imply that training on real data which often contains slight noise is somewhat robustness enhancing.

Poster
Diffusion-TTA: Test-time Adaptation of Discriminative Models via Generative Feedback

Mihir Prabhudesai, Tsung-Wei Ke, Alexander Cong Li, Deepak Pathak, Katerina Fragkiadaki

展开摘要

The advancements in generative modeling, particularly the advent of diffusion models, have sparked a fundamental question: how can these models be effectively used for discriminative tasks? In this work, we find that generative models can be great test-time adapters for discriminative models. Our method, Diffusion-TTA, adapts pre-trained discriminative models such as image classifiers, segmenters and depth predictors, to each unlabelled example in the test set using generative feedback from a diffusion model. We achieve this by modulating the conditioning of the diffusion model using the output of the discriminative model. We then maximize the image likelihood objective by backpropagating the gradients to discriminative model’s parameters. We show Diffusion-TTA significantly enhances the accuracy of various large-scale pre-trained discriminative models, such as, ImageNet classifiers, CLIP models, image pixel labellers and image depth predictors. Diffusion-TTA outperforms existing test-time adaptation methods, including TTT-MAE and TENT, and particularly shines in online adaptation setups, where the discriminative model is continually adapted to each example in the test set. We provide access to code, results, and visualizations on our website: diffusion-tta.github.io/

Poster
BiSLS/SPS: Auto-tune Step Sizes for Stable Bi-level Optimization

Chen Fan, Gaspard Choné-Ducasse, Mark Schmidt, Christos Thrampoulidis

展开摘要

The popularity of bi-level optimization (BO) in deep learning has spurred a growing interest in studying gradient-based BO algorithms. However, existing algorithms involve two coupled learning rates that can be affected by approximation errors when computing hypergradients, making careful fine-tuning necessary to ensure fast convergence. To alleviate this issue, we investigate the use of recently proposed adaptive step-size methods, namely stochastic line search (SLS) and stochastic Polyak step size (SPS), for computing both the upper and lower-level learning rates. First, we revisit the use of SLS and SPS in single-level optimization without the additional interpolation condition that is typically assumed in prior works. For such settings, we investigate new variants of SLS and SPS that improve upon existing suggestions in the literature and are simpler to implement. Importantly, these two variants can be seen as special instances of general family of methods with an envelope-type step-size. This unified envelope strategy allows for the extension of the algorithms and their convergence guarantees to BO settings. Finally, our extensive experiments demonstrate that the new algorithms, which are available in both SGD and Adam versions, can find large learning rates with minimal tuning and converge faster than corresponding vanilla SGD or Adam BO algorithms that require fine-tuning.

Poster
Rethinking Conditional Diffusion Sampling with Progressive Guidance

Anh-Dung Dinh, Daochang Liu, Chang Xu

展开摘要

This paper tackles two critical challenges encountered in classifier guidance for diffusion generative models, i.e., the lack of diversity and the presence of adversarial effects. These issues often result in a scarcity of diverse samples or the generation of non-robust features. The underlying cause lies in the mechanism of classifier guidance, where discriminative gradients push samples to be recognized as conditions aggressively. This inadvertently suppresses information with common features among relevant classes, resulting in a limited pool of features with less diversity or the absence of robust features for image construction. We propose a generalized classifier guidance method called Progressive Guidance, which mitigates the problems by allowing relevant classes' gradients to contribute to shared information construction when the image is noisy in early sampling steps. In the later sampling stage, we progressively enhance gradients to refine the details in the image toward the primary condition. This helps to attain a high level of diversity and robustness compared to the vanilla classifier guidance. Experimental results demonstrate that our proposed method further improves the image quality while offering a significant level of diversity as well as robust features.

Poster
Optimistic Rates for Multi-Task Representation Learning

Austin Watkins, Enayat Ullah, Thanh Nguyen-Tang, Raman Arora

展开摘要

We study the problem of transfer learning via Multi-Task Representation Learning (MTRL), wherein multiple source tasks are used to learn a good common representation, and a predictor is trained on top of it for the target task. Under standard regularity assumptions on the loss function and task diversity, we provide new statistical rates on the excess risk of the target task, which demonstrate the benefit of representation learning. Importantly, our rates are optimistic, i.e., they interpolate between the standard $O(m^{-1/2})$ rate and the fast $O(m^{-1})$ rate, depending on the difficulty of the learning task, where $m$ is the number of samples for the target task. Besides the main result, we make several new contributions, including giving optimistic rates for excess risk of source tasks (multi-task learning (MTL)), a local Rademacher complexity theorem for MTRL and MTL, as well as a chain rule for local Rademacher complexity for composite predictor classes.

Poster
Partial Matrix Completion

Elad Hazan, Adam Tauman Kalai, Varun Kanade, Clara Mohri, Y. Jennifer Sun

展开摘要

The matrix completion problem involves reconstructing a low-rank matrix by using a given set of revealed (and potentially noisy) entries. Although existing methods address the completion of the entire matrix, the accuracy of the completed entries can vary significantly across the matrix, due to differences in the sampling distribution. For instance, users may rate movies primarily from their country or favorite genres, leading to inaccurate predictions for the majority of completed entries. We propose a novel formulation of the problem as Partial Matrix Completion, where the objective is to complete a substantial subset of the entries with high confidence. Our algorithm efficiently handles the unknown and arbitrarily complex nature of the sampling distribution, ensuring high accuracy for all completed entries and sufficient coverage across the matrix. Additionally, we introduce an online version of the problem and present a low-regret efficient algorithm based on iterative gradient updates. Finally, we conduct a preliminary empirical evaluation of our methods.

Poster
Content-based Unrestricted Adversarial Attack

Zhaoyu Chen, Bo Li, Shuang Wu, Kaixun Jiang, Shouhong Ding, Wenqiang Zhang

展开摘要

Unrestricted adversarial attacks typically manipulate the semantic content of an image (e.g., color or texture) to create adversarial examples that are both effective and photorealistic, demonstrating their ability to deceive human perception and deep neural networks with stealth and success. However, current works usually sacrifice unrestricted degrees and subjectively select some image content to guarantee the photorealism of unrestricted adversarial examples, which limits its attack performance. To ensure the photorealism of adversarial examples and boost attack performance, we propose a novel unrestricted attack framework called Content-based Unrestricted Adversarial Attack. By leveraging a low-dimensional manifold that represents natural images, we map the images onto the manifold and optimize them along its adversarial direction. Therefore, within this framework, we implement Adversarial Content Attack (ACA) based on Stable Diffusion and can generate high transferable unrestricted adversarial examples with various adversarial contents. Extensive experimentation and visualization demonstrate the efficacy of ACA, particularly in surpassing state-of-the-art attacks by an average of 13.3-50.4\% and 16.8-48.0\% in normally trained models and defense methods, respectively.

Poster
OpenProteinSet: Training data for structural biology at scale

Gustaf Ahdritz, Nazim Bouatta, Sachin Kadyan, Lukas Jarosch, Dan Berenberg, Ian Fisk, Andrew Martin Watkins, Stephen Ra, Richard Bonneau, Mohammed AlQuraishi

展开摘要

Multiple sequence alignments (MSAs) of proteins encode rich biological information and have been workhorses in bioinformatic methods for tasks like protein design and protein structure prediction for decades. Recent breakthroughs like AlphaFold2 that use transformers to attend directly over large quantities of raw MSAs have reaffirmed their importance. Generation of MSAs is highly computationally intensive, however, and no datasets comparable to those used to train AlphaFold2 have been made available to the research community, hindering progress in machine learning for proteins. To remedy this problem, we introduce OpenProteinSet, an open-source corpus of more than 16 million MSAs, associated structural homologs from the Protein Data Bank, and AlphaFold2 protein structure predictions. We have previously demonstrated the utility of OpenProteinSet by successfully retraining AlphaFold2 on it. We expect OpenProteinSet to be broadly useful as training and validation data for 1) diverse tasks focused on protein structure, function, and design and 2) large-scale multimodal machine learning research.

Poster
AdaVAE: Bayesian Structural Adaptation for Variational Autoencoders

Paribesh Regmi, Rui Li

展开摘要

The neural network structures of generative models and their corresponding inference models paired in variational autoencoders (VAEs) play a critical role in the models' generative performance. However, powerful VAE network structures are hand-crafted and fixed prior to training, resulting in a one-size-fits-all approach that requires heavy computation to tune for given data. Moreover, existing VAE regularization methods largely overlook the importance of network structures and fail to prevent overfitting in deep VAE models with cascades of hidden layers. To address these issues, we propose a Bayesian inference framework that automatically adapts VAE network structures to data and prevent overfitting as they grow deeper. We model the number of hidden layers with a beta process to infer the most plausible encoding/decoding network depths warranted by data and perform layer-wise dropout regularization with a conjugate Bernoulli process. We develop a scalable estimator that performs joint inference on both VAE network structures and latent variables. Our experiments show that the inference framework effectively prevents overfitting in both shallow and deep VAE models, yielding state-of-the-art performance. We demonstrate that our framework is compatible with different types of VAE backbone networks and can be applied to various VAE variants, further improving their performance.

Poster
SiT Dataset: Socially Interactive Pedestrian Trajectory Dataset for Social Navigation Robots

Jongwook Bae, Jungho Kim, Junyong Yun, Changwon Kang, Jeongseon Choi, Chanhyeok Kim, Junho Lee, Jungwook Choi, Jun Won Choi

展开摘要

To ensure secure and dependable mobility in environments shared by humans and robots, social navigation robots should possess the capability to accurately perceive and predict the trajectories of nearby pedestrians. In this paper, we present a novel dataset of pedestrian trajectories, referred to as Social Interactive Pedestrian Trajectory (SiT) dataset, which can be used to train pedestrian detection, tracking, and trajectory prediction models needed to design social navigation robots. Our dataset includes sequential raw data captured by two 3D LiDARs and five cameras covering a 360-degree view, two inertial measurement units (IMUs), and real-time kinematic positioning (RTK), as well as annotations including 2D & 3D boxes, object classes, and object IDs. Thus far, various human trajectory datasets have been introduced to support the development of pedestrian motion forecasting models. Our SiT dataset differs from these datasets in the following three respects. First, whereas the pedestrian trajectory data in other datasets were obtained from static scenes, our data was collected while the robot navigated in a crowded environment, capturing human-robot interactive scenarios in motion. Second, unlike many autonomous driving datasets where pedestrians are usually at a distance from vehicles and found on pedestrian paths, our dataset offers a distinctive view of navigation robots interacting closely with humans in crowded settings.Third, our dataset has been carefully organized to facilitate the training and evaluation of end-to-end prediction models encompassing 3D detection, 3D multi-object tracking, and trajectory prediction. This design allows for an end-to-end unified modular approach across different tasks. We introduce a comprehensive benchmark for assessing models across all aforementioned tasks and present the performance of multiple baseline models as part of our evaluation. Our dataset provides a strong foundation for future research in pedestrian trajectory prediction, which could expedite the development of safe and agile social navigation robots. The SiT dataset, development kit, and trained models are publicly available at: https://spalaboratory.github.io/SiT/

Poster
One Fits All: Power General Time Series Analysis by Pretrained LM

Tian Zhou, Peisong Niu, Xue Wang, Liang Sun, Rong Jin

展开摘要

Although we have witnessed great success of pre-trained models in natural language processing (NLP) and computer vision (CV), limited progress has been made for general time series analysis. Unlike NLP and CV where a unified model can be used to perform different tasks, specially designed approach still dominates in each time series analysis task such as classification, anomaly detection, forecasting, and few-shot learning. The main challenge that blocks the development of pre-trained model for time series analysis is the lack of a large amount of data for training. In this work, we address this challenge by leveraging language or CV models, pre-trained from billions of tokens, for time series analysis. Specifically, we refrain from altering the self-attention and feedforward layers of the residual blocks in the pre-trained language or image model. This model, known as the Frozen Pretrained Transformer (FPT), is evaluated through fine-tuning on all major types of tasks involving time series. Our results demonstrate that pre-trained models on natural language or images can lead to a comparable or state-of-the-art performance in all main time series analysis tasks, as illustrated in Figure1. We also found both theoretically and empirically that the self-attention module behaviors similarly to principle component analysis (PCA), an observation that helps explains how transformer bridges the domain gap and a crucial step towards understanding the universality of a pre-trained transformer. The code is publicly available at https://anonymous.4open.science/r/Pretrained-LM-for-TSForcasting-C561.

Spotlight
Triangulation Residual Loss for Data-efficient 3D Pose Estimation

Jiachen Zhao, Tao Yu, Liang An, Yipeng Huang, Fang Deng, Qionghai Dai

展开摘要

This paper presents Triangulation Residual loss (TR loss) for multiview 3D pose estimation in a data-efficient manner. Existing 3D supervised models usually require large-scale 3D annotated datasets, but the amount of existing data is still insufficient to train supervised models to achieve ideal performance, especially for animal pose estimation. To employ unlabeled multiview data for training, previous epipolar-based consistency provides a self-supervised loss that considers only the local consistency in pairwise views, resulting in limited performance and heavy calculations. In contrast, TR loss enables self-supervision with global multiview geometric consistency. Starting from initial 2D keypoint estimates, the TR loss can fine-tune the corresponding 2D detector without 3D supervision by simply minimizing the smallest singular value of the triangulation matrix in an end-to-end fashion. Our method achieves the state-of-the-art 25.8mm MPJPE and competitive 28.7mm MPJPE with only 5\% 2D labeled training data on the Human3.6M dataset. Experiments on animals such as mice demonstrate our TR loss's data-efficient training ability.

Poster
Labeling Neural Representations with Inverse Recognition

Kirill Bykov, Laura Kopf, Shinichi Nakajima, Marius Kloft, Marina MC Höhne

展开摘要

Deep Neural Networks (DNNs) demonstrate remarkable capabilities in learning complex hierarchical data representations, but the nature of these representations remains largely unknown. Existing global explainability methods, such as Network Dissection, face limitations such as reliance on segmentation masks, lack of statistical significance testing, and high computational demands. We propose Inverse Recognition (INVERT), a scalable approach for connecting learned representations with human-understandable concepts by leveraging their capacity to discriminate between these concepts. In contrast to prior work, INVERT is capable of handling diverse types of neurons, exhibits less computational complexity, and does not rely on the availability of segmentation masks. Moreover, INVERT provides an interpretable metric assessing the alignment between the representation and its corresponding explanation and delivering a measure of statistical significance. We demonstrate the applicability of INVERT in various scenarios, including the identification of representations affected by spurious correlations, and the interpretation of the hierarchical structure of decision-making within the models.

Poster
Fed-GraB: Federated Long-tailed Learning with Self-Adjusting Gradient Balancer

Zikai Xiao, Zihan Chen, Songshang Liu, Hualiang Wang, Yang Feng, Jin Hao, Joey Tianyi Zhou, Jian Wu, Howard Hao Yang, Zuozhu Liu

展开摘要

Data privacy and long-tailed distribution are the norms rather than the exception in many real-world tasks. This paper investigates a federated long-tailed learning (Fed-LT) task in which each client holds a locally heterogeneous dataset; if the datasets can be globally aggregated, they jointly exhibit a long-tailed distribution. Under such a setting, existing federated optimization and/or centralized long-tailed learning methods hardly apply due to challenges in (a) characterizing the global long-tailed distribution under privacy constraints and (b) adjusting the local learning strategy to cope with the head-tail imbalance. In response, we propose a method termed $\texttt{Fed-GraB}$, comprised of a Self-adjusting Gradient Balancer (SGB) module that re-weights clients' gradients in a closed-loop manner, based on the feedback of global long-tailed distribution evaluated by a Direct Prior Analyzer (DPA) module. Using $\texttt{Fed-GraB}$, clients can effectively alleviate the distribution drift caused by data heterogeneity during the model training process and obtain a global model with better performance on the minority classes while maintaining the performance of the majority classes. Extensive experiments demonstrate that $\texttt{Fed-GraB}$ achieves state-of-the-art performance on representative datasets such as CIFAR-10-LT, CIFAR-100-LT, ImageNet-LT, and iNaturalist.

Poster
Pengi: An Audio Language Model for Audio Tasks

Soham Deshmukh, Benjamin Elizalde, Rita Singh, Huaming Wang

展开摘要

In the domain of audio processing, Transfer Learning has facilitated the rise of Self-Supervised Learning and Zero-Shot Learning techniques. These approaches have led to the development of versatile models capable of tackling a wide array of tasks, while delivering state-of-the-art performance. However, current models inherently lack the capacity to produce the requisite language for open-ended tasks, such as Audio Captioning or Audio Question Answering. We introduce Pengi, a novel Audio Language Model that leverages Transfer Learning by framing all audio tasks as text-generation tasks. It takes as input, an audio recording, and text, and generates free-form text as output. The input audio is represented as a sequence of continuous embeddings by an audio encoder. A text encoder does the same for the corresponding text input. Both sequences are combined as a prefix to prompt a pre-trained frozen language model. The unified architecture of Pengi enables open-ended tasks and close-ended tasks without any additional fine-tuning or task-specific extensions. When evaluated on 21 downstream tasks, our approach yields state-of-the-art performance in several of them. Our results show that connecting language models with audio models is a major step towards general-purpose audio understanding.

Poster