NeurIPS 2023 Papers

Conference on Neural Information Processing Systems

Decision breakdown

3,584papers

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

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

Browse all papers

On Slicing Optimality for Mutual Information

Ammar Fayad, Majd Ibrahim

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Measuring dependence between two random variables is of great importance in various domains but is difficult to compute in today's complex environments with high-dimensional data. Recently, slicing methods have shown to be a scalable approach to measuring mutual information (MI) between high-dimensional variables by projecting these variables into one-dimensional spaces. Unfortunately, these methods use uniform distributions of slicing directions, which generally discard informative features between variables and thus lead to inaccurate quantification of dependence. In this paper, we propose a principled framework that searches for an \textit{optimal} distribution of slices for MI. Importantly, we answer theoretical questions about finding the optimal slicing distribution in the context of MI and develop corresponding theoretical analyses. We also develop a practical algorithm, connecting our theoretical results with modern machine learning frameworks. Through comprehensive experiments in benchmark domains, we demonstrate significant gains in our information measure than state-of-the-art baselines.

Poster
Generalised f-Mean Aggregation for Graph Neural Networks

Ryan Kortvelesy, Steven Morad, Amanda Prorok

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Graph Neural Network (GNN) architectures are defined by their implementations of update and aggregation modules. While many works focus on new ways to parametrise the update modules, the aggregation modules receive comparatively little attention. Because it is difficult to parametrise aggregation functions, currently most methods select a ``standard aggregator'' such as mean, sum, or max. While this selection is often made without any reasoning, it has been shown that the choice in aggregator has a significant impact on performance, and the best choice in aggregator is problem-dependent. Since aggregation is a lossy operation, it is crucial to select the most appropriate aggregator in order to minimise information loss. In this paper, we present GenAgg, a generalised aggregation operator, which parametrises a function space that includes all standard aggregators. In our experiments, we show that GenAgg is able to represent the standard aggregators with much higher accuracy than baseline methods. We also show that using GenAgg as a drop-in replacement for an existing aggregator in a GNN often leads to a significant boost in performance across various tasks.

Poster
Vocabulary-free Image Classification

Alessandro Conti, Enrico Fini, Massimiliano Mancini, Paolo Rota, Yiming Wang, Elisa Ricci

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Recent advances in large vision-language models have revolutionized the image classification paradigm. Despite showing impressive zero-shot capabilities, a pre-defined set of categories, a.k.a. the vocabulary, is assumed at test time for composing the textual prompts. However, such assumption can be impractical when the semantic context is unknown and evolving. We thus formalize a novel task, termed as Vocabulary-free Image Classification (VIC), where we aim to assign to an input image a class that resides in an unconstrained language-induced semantic space, without the prerequisite of a known vocabulary. VIC is a challenging task as the semantic space is extremely large, containing millions of concepts, with hard-to-discriminate fine-grained categories. In this work, we first empirically verify that representing this semantic space by means of an external vision-language database is the most effective way to obtain semantically relevant content for classifying the image. We then propose Category Search from External Databases (CaSED), a method that exploits a pre-trained vision-language model and an external vision-language database to address VIC in a training-free manner. CaSED first extracts a set of candidate categories from captions retrieved from the database based on their semantic similarity to the image, and then assigns to the image the best matching candidate category according to the same vision-language model. Experiments on benchmark datasets validate that CaSED outperforms other complex vision-language frameworks, while being efficient with much fewer parameters, paving the way for future research in this direction.

Poster
Global Identifiability of $\ell_1$-based Dictionary Learning via Matrix Volume Optimization

Jingzhou Hu, Kejun Huang

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We propose a novel formulation for dictionary learning that minimizes the determinant of the dictionary matrix, also known as its volume, subject to the constraint that each row of the sparse coefficient matrix has unit $\ell_1$ norm. The main motivation for the proposed formulation is that it provides global identifiability guarantee of the groundtruth dictionary and sparse coefficient matrices, up to the inherent and inconsequential permutation and scaling ambiguity, if a set of vectors obtained from the coefficient matrix lies inside the $\ell_\infty$ norm ball but contains the $\ell_2$ norm ball in their convex hull. Unlike existing work on identifiability of dictionary learning, our result is global, meaning that a globally optimal solution to our proposed formulation has to be a permuted and rescaled version of the groundtruth factors. Another major improvement in our result is that there is no additional assumption on the dictionary matrix other than it is nonsingular, unlike most other work that require the atoms of the dictionary to be mutually incoherent. We also provide a probabilistic analysis and show that if the sparse coefficient matrix is generated from the widely adopted Bernoulli-Gaussian model, then it is globally identifiable if the sample size is bigger than a constant times $k\log k$, where $k$ is the number atoms in the dictionary, with overwhelming probability. The bound is essentially the same as those local identifiability results, but we show that it is also global. Finally, we propose algorithms to solve the new proposed formulation, specifically one based on the linearized-ADMM with efficient per-iteration updates. The proposed algorithms exhibit surprisingly effective performance in correctly and efficiently recovering the dictionary, as demonstrated in the numerical experiments.

Poster
Simple, Scalable and Effective Clustering via One-Dimensional Projections

Moses Charikar, Monika Henzinger, Lunjia Hu, Maximilian Vötsch, Erik Waingarten

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Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in a $d$-dimensional space (represented by an $n\times d$ matrix $X$) into $k$ clusters. On massive datasets with moderate to large $k$, the multiplicative $k$ factor can become very expensive. We introduce a simple randomized clustering algorithm that provably runs in expected time $O(\mathsf{nnz}(X) + n\log n)$ for arbitrary $k$. Here $\mathsf{nnz}(X)$ is the total number of non-zero entries in the input dataset $X$, which is upper bounded by $nd$ and can be significantly smaller for sparse datasets. We prove that our algorithm achieves approximation ratio $\widetilde{O}(k^4)$ on any input dataset for the $k$-means objective, and our experiments show that the quality of the clusters found by our algorithm is usually much better than this worst-case bound. We use our algorithm for $k$-means clustering and for coreset construction; our experiments show that it gives a new tradeoff between running time and cluster quality compared to previous state-of-the-art methods for these tasks. Our theoretical analysis is based on novel results of independent interest. We show that the approximation ratio achieved after a random one-dimensional projection can be lifted to the original points and that $k$-means++ seeding can be implemented in expected time $O(n\log n)$ in one dimension.

Poster
DatasetDM: Synthesizing Data with Perception Annotations Using Diffusion Models

Weijia Wu, Yuzhong Zhao, Hao Chen, Yuchao Gu, Rui Zhao, Yefei He, Hong Zhou, Mike Zheng Shou, Chunhua Shen

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Current deep networks are very data-hungry and benefit from training on large-scale datasets, which are often time-consuming to collect and annotate. By contrast, synthetic data can be generated infinitely using generative models such as DALL-E and diffusion models, with minimal effort and cost. In this paper, we present DatasetDM, a generic dataset generation model that can produce diverse synthetic images and the corresponding high-quality perception annotations (e.g., segmentation masks, and depth). Our method builds upon the pre-trained diffusion model and extends text-guided image synthesis to perception data generation. We show that the rich latent code of the diffusion model can be effectively decoded as accurate perception annotations using a decoder module. Training the decoder only needs less than 1% (around 100 images) of manually labeled images, enabling the generation of an infinitely large annotated dataset. Then these synthetic data can be used for training various perception models on downstream tasks. To showcase the power of the proposed approach, we generate datasets with rich dense pixel-wise labels for a wide range of downstream tasks, including semantic15 segmentation, instance segmentation, and depth estimation. Notably, it achieves 1) state-of-the-art results on semantic segmentation and instance segmentation; 2) significantly more efficient and robust in domain generalization than the real data; 3) state-of-the-art results in zero-shot segmentation setting; and 4) flexibility for efficient application and novel task composition (e.g., image editing)

Poster
GeoDE: a Geographically Diverse Evaluation Dataset for Object Recognition

Vikram V. Ramaswamy, Sing Yu Lin, Dora Zhao, Aaron Bryan Adcock, Laurens van der Maaten, Deepti Ghadiyaram, Olga Russakovsky

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Current dataset collection methods typically scrape large amounts of data from the web. While this technique is extremely scalable, data collected in this way tends to reinforce stereotypical biases, can contain personally identifiable information, and typically originates from Europe and North America. In this work, we rethink the dataset collection paradigm and introduce GeoDE, a geographically diverse dataset with 61,940 images from 40 classes and 6 world regions, and no personally identifiable information, collected by soliciting images from people across the world. We analyse GeoDE to understand differences in images collected in this manner compared to web-scraping. Despite the smaller size of this dataset, we demonstrate its use as both an evaluation and training dataset, allowing us to highlight shortcomings in current models, as well as demonstrate improved performance even when training on this small dataset. We release the full dataset and code at https://geodiverse-data-collection.cs.princeton.edu/

Poster
Partial Multi-Label Learning with Probabilistic Graphical Disambiguation

Jun-Yi Hang, Min-Ling Zhang

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In partial multi-label learning (PML), each training example is associated with a set of candidate labels, among which only some labels are valid. As a common strategy to tackle PML problem, disambiguation aims to recover the ground-truth labeling information from such inaccurate annotations. However, existing approaches mainly rely on heuristics or ad-hoc rules to disambiguate candidate labels, which may not be universal enough in complicated real-world scenarios. To provide a principled way for disambiguation, we make a first attempt to explore the probabilistic graphical model for PML problem, where a directed graph is tailored to infer latent ground-truth labeling information from the generative process of partial multi-label data. Under the framework of stochastic gradient variational Bayes, a unified variational lower bound is derived for this graphical model, which is further relaxed probabilistically so that the desired prediction model can be induced with simultaneously identified ground-truth labeling information. Comprehensive experiments on multiple synthetic and real-world data sets show that our approach outperforms the state-of-the-art counterparts.

Poster
Adversarial Examples Might be Avoidable: The Role of Data Concentration in Adversarial Robustness

Ambar Pal, Jeremias Sulam, Rene Vidal

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The susceptibility of modern machine learning classifiers to adversarial examples has motivated theoretical results suggesting that these might be unavoidable. However, these results can be too general to be applicable to natural data distributions. Indeed, humans are quite robust for tasks involving vision. This apparent conflict motivates a deeper dive into the question: Are adversarial examples truly unavoidable? In this work, we theoretically demonstrate that a key property of the data distribution -- concentration on small-volume subsets of the input space -- determines whether a robust classifier exists. We further demonstrate that, for a data distribution concentrated on a union of low-dimensional linear subspaces, utilizing structure in data naturally leads to classifiers that enjoy data-dependent polyhedral robustness guarantees, improving upon methods for provable certification in certain regimes.

Poster
Improving Few-Shot Generalization by Exploring and Exploiting Auxiliary Data

Alon Albalak, Colin Raffel, William Yang Wang

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Few-shot learning is valuable in many real-world applications, but learning a generalizable model without overfitting to the few labeled datapoints is challenging. In this work, we focus on Few-shot Learning with Auxiliary Data (FLAD), a training paradigm that assumes access to auxiliary data during few-shot learning in hopes of improving generalization. Previous works have proposed automated methods for mixing auxiliary and target data, but these methods typically scale linearly (or worse) with the number of auxiliary datasets, limiting their practicality. In this work we relate FLAD to the explore-exploit dilemma that is central to the multi-armed bandit setting and derive algorithms whose computational complexity is independent of the number of auxiliary datasets, allowing us to scale to 100x more auxiliary datasets than prior methods. We propose two algorithms -- EXP3-FLAD and UCB1-FLAD -- and compare them with prior FLAD methods that either explore or exploit, finding that the combination of exploration and exploitation is crucial. Through extensive experimentation we find that our methods outperform all pre-existing FLAD methods by 4% and lead to the first 3 billion parameter language models that outperform the 175 billion parameter GPT-3. Overall, our work suggests that the discovery of better, more efficient mixing strategies for FLAD may provide a viable path towards substantially improving generalization in few-shot learning.

Poster
Deep Non-line-of-sight Imaging from Under-scanning Measurements

Yue Li, Yueyi Zhang, Juntian Ye, Feihu Xu, Zhiwei Xiong

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Active confocal non-line-of-sight (NLOS) imaging has successfully enabled seeing around corners relying on high-quality transient measurements. However, acquiring spatial-dense transient measurement is time-consuming, raising the question of how to reconstruct satisfactory results from under-scanning measurements (USM). The existing solutions, involving the traditional algorithms, however, are hindered by unsatisfactory results or long computing times. To this end, we propose the first deep-learning-based approach to NLOS imaging from USM. Our proposed end-to-end network is composed of two main components: the transient recovery network (TRN) and the volume reconstruction network (VRN). Specifically, TRN takes the under-scanning measurements as input, utilizes a multiple kernel feature extraction module and a multiple feature fusion module, and outputs sufficient-scanning measurements at the high-spatial resolution. Afterwards, VRN incorporates the linear physics prior of the light-path transport model and reconstructs the hidden volume representation. Besides, we introduce regularized constraints that enhance the perception of more local details while suppressing smoothing effects. The proposed method achieves superior performance on both synthetic data and public real-world data, as demonstrated by extensive experimental results with different under-scanning grids. Moreover, the proposed method delivers impressive robustness at an extremely low scanning grid (i.e., 8$\times$8) and offers high-speed inference (i.e., 50 times faster than the existing iterative solution).

Poster
Grounded Decoding: Guiding Text Generation with Grounded Models for Embodied Agents

Wenlong Huang, Fei Xia, Dhruv Shah, Danny Driess, Andy Zeng, Yao Lu, Pete Florence, Igor Mordatch, Sergey Levine, Karol Hausman, brian ichter

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Recent progress in large language models (LLMs) has demonstrated the ability to learn and leverage Internet-scale knowledge through pre-training with autoregressive models. Unfortunately, applying such models to settings with embodied agents, such as robots, is challenging due to their lack of experience with the physical world, inability to parse non-language observations, and ignorance of rewards or safety constraints that robots may require. On the other hand, language-conditioned robotic policies that learn from interaction data can provide the necessary grounding that allows the agent to be correctly situated in the real world, but such policies are limited by the lack of high-level semantic understanding due to the limited breadth of the interaction data available for training them. Thus, if we want to make use of the semantic knowledge in a language model while still situating it in an embodied setting, we must construct an action sequence that is both likely according to the language model and also realizable according to grounded models of the environment. We frame this as a problem similar to probabilistic filtering: decode a sequence that both has high probability under the language model and high probability under a set of grounded model objectives. We demonstrate how such grounded models can be obtained across three simulation and real-world domains, and that the proposed decoding strategy is able to solve complex, long-horizon embodiment tasks in a robotic setting by leveraging the knowledge of both models.

Poster
Make Pre-trained Model Reversible: From Parameter to Memory Efficient Fine-Tuning

Baohao Liao, Shaomu Tan, Christof Monz

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Parameter-efficient fine-tuning (PEFT) of pre-trained language models (PLMs) has emerged as a highly successful approach, with training only a small number of parameters without sacrificing performance and becoming the de-facto learning paradigm with the increasing size of PLMs. However, existing PEFT methods are not memory-efficient, because they still require caching most of the intermediate activations for the gradient calculation, akin to fine-tuning. One effective way to reduce the activation memory is to apply a reversible model, so the intermediate activations are not necessary to be cached and can be recomputed. Nevertheless, modifying a PLM to its reversible variant is not straightforward, since the reversible model has a distinct architecture from the currently released PLMs. In this paper, we first investigate what is a key factor for the success of existing PEFT methods, and realize that it's essential to preserve the PLM's starting point when initializing a PEFT method. With this finding, we propose memory-efficient fine-tuning (MEFT) that inserts adapters into a PLM, preserving the PLM's starting point and making it reversible without additional pre-training. We evaluate MEFT on the GLUE benchmark and five question-answering tasks with various backbones, BERT, RoBERTa, BART and OPT. MEFT significantly reduces the activation memory up to 84% of full fine-tuning with a negligible amount of trainable parameters. Moreover, MEFT achieves the same score on GLUE and a comparable score on the question-answering tasks as full fine-tuning. A similar finding is also observed for the image classification task.

Poster
LLM-Pruner: On the Structural Pruning of Large Language Models

Xinyin Ma, Gongfan Fang, Xinchao Wang

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Large language models (LLMs) have shown remarkable capabilities in language understanding and generation. However, such impressive capability typically comes with a substantial model size, which presents significant challenges in both the deployment, inference, and training stages. With LLM being a general-purpose task solver, we explore its compression in a task-agnostic manner, which aims to preserve the multi-task solving and language generation ability of the original LLM. One challenge to achieving this is the enormous size of the training corpus of LLM, which makes both data transfer and model post-training over-burdensome. Thus, we tackle the compression of LLMs within the bound of two constraints: being task-agnostic and minimizing the reliance on the original training dataset. Our method, named LLM-pruner, adopts structural pruning that selectively removes non-critical coupled structures based on gradient information, maximally preserving the majority of the LLM's functionality. To this end, the performance of pruned models can be efficiently recovered through tuning techniques, LoRA, in merely 3 hours, requiring only 50K data. We validate the LLM-Pruner on three LLMs, including LLaMA, Vicuna, and ChatGLM, and demonstrate that the compressed models still exhibit satisfactory capabilities in zero-shot classification and generation. The code will be made public.

Poster
Unlocking Feature Visualization for Deep Network with MAgnitude Constrained Optimization

Thomas FEL, Thibaut Boissin, Victor Boutin, Agustin Martin Picard, Paul Novello, Julien Colin, Drew Linsley, Tom ROUSSEAU, Remi Cadene, Lore Goetschalckx, Laurent Gardes, Thomas Serre

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Feature visualization has gained significant popularity as an explainability method, particularly after the influential work by Olah et al. in 2017. Despite its success, its widespread adoption has been limited due to issues in scaling to deeper neural networks and the reliance on tricks to generate interpretable images. Here, we describe MACO, a simple approach to address these shortcomings. It consists in optimizing solely an image's phase spectrum while keeping its magnitude constant to ensure that the generated explanations lie in the space of natural images. Our approach yields significantly better results -- both qualitatively and quantitatively -- unlocking efficient and interpretable feature visualizations for state-of-the-art neural networks. We also show that our approach exhibits an attribution mechanism allowing to augment feature visualizations with spatial importance. Furthermore, we enable quantitative evaluation of feature visualizations by introducing 3 metrics: transferability, plausibility, and alignment with natural images. We validate our method on various applications and we introduce a website featuring MACO visualizations for all classes of the ImageNet dataset, which will be made available upon acceptance. Overall, our study unlocks feature visualizations for the largest, state-of-the-art classification networks without resorting to any parametric prior image model, effectively advancing a field that has been stagnating since 2017 (Olah et al, 2017).

Poster
Glance and Focus: Memory Prompting for Multi-Event Video Question Answering

Ziyi Bai, Ruiping Wang, Xilin Chen

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Video Question Answering (VideoQA) has emerged as a vital tool to evaluate agents’ ability to understand human daily behaviors. Despite the recent success of large vision language models in many multi-modal tasks, complex situation reasoning over videos involving multiple human-object interaction events still remains challenging. In contrast, humans can easily tackle it by using a series of episode memories as anchors to quickly locate question-related key moments for reasoning. To mimic this effective reasoning strategy, we propose the Glance- Focus model. One simple way is to apply an action detection model to predict a set of actions as key memories. However, these actions within a closed set vocabulary are hard to generalize to various video domains. Instead of that, we train an Encoder-Decoder to generate a set of dynamic event memories at the glancing stage. Apart from using supervised bipartite matching to obtain the event memories, we further design an unsupervised memory generation method to get rid of dependence on event annotations. Next, at the focusing stage, these event memories act as a bridge to establish the correlation between the questions with high-level event concepts and low-level lengthy video content. Given the question, the model first focuses on the generated key event memory, then focuses on the most relevant moment for reasoning through our designed multi-level cross- attention mechanism. We conduct extensive experiments on four Multi-Event VideoQA benchmarks including STAR, EgoTaskQA, AGQA, and NExT-QA. Our proposed model achieves state-of-the-art results, surpassing current large models in various challenging reasoning tasks. The code and models are available at https://github.com/ByZ0e/Glance-Focus.

Poster
Stability-penalty-adaptive follow-the-regularized-leader: Sparsity, game-dependency, and best-of-both-worlds

Taira Tsuchiya, Shinji Ito, Junya Honda

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Adaptivity to the difficulties of a problem is a key property in sequential decision-making problems to broaden the applicability of algorithms. Follow-the-regularized-leader (FTRL) has recently emerged as one of the most promising approaches for obtaining various types of adaptivity in bandit problems. Aiming to further generalize this adaptivity, we develop a generic adaptive learning rate, called stability-penalty-adaptive (SPA) learning rate for FTRL. This learning rate yields a regret bound jointly depending on stability and penalty of the algorithm, into which the regret of FTRL is typically decomposed. With this result, we establish several algorithms with three types of adaptivity: sparsity, game-dependency, and best-of-both-worlds (BOBW). Despite the fact that sparsity appears frequently in real problems, existing sparse multi-armed bandit algorithms with $k$-arms assume that the sparsity level $s \leq k$ is known in advance, which is often not the case in real-world scenarios. To address this issue, we first establish $s$-agnostic algorithms with regret bounds of $\tilde{O}(\sqrt{sT})$ in the adversarial regime for $T$ rounds, which matches the existing lower bound up to a logarithmic factor. Meanwhile, BOBW algorithms aim to achieve a near-optimal regret in both the stochastic and adversarial regimes. Leveraging the SPA learning rate and the technique for $s$-agnostic algorithms combined with a new analysis to bound the variation in FTRL output in response to changes in a regularizer, we establish the first BOBW algorithm with a sparsity-dependent bound. Additionally, we explore partial monitoring and demonstrate that the proposed SPA learning rate framework allows us to achieve a game-dependent bound and the BOBW simultaneously.

Poster
DesCo: Learning Object Recognition with Rich Language Descriptions

Liunian Harold Li, Zi-Yi Dou, Nanyun Peng, Kai-Wei Chang

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Recent development in vision-language approaches has instigated a paradigm shift in learning visual recognition models from language supervision. These approaches align objects with language queries (e.g. "a photo of a cat") and thus improve the models' adaptability to novel objects and domains. Recent studies have attempted to query these models with complex language expressions that include specifications of fine-grained details, such as colors, shapes, and relations. However, simply incorporating language descriptions into queries does not guarantee accurate interpretation by the models. In fact, our experiments show that GLIP, a state-of-the-art vision-language model for object detection, often disregards contextual information in the language descriptions and instead relies heavily on detecting objects solely by their names. To tackle the challenge, we propose a new description-conditioned (DesCo) paradigm of learning object recognition models with rich language descriptions consisting of two innovations: 1) we employ a large language model as a commonsense knowledge engine to generate rich language descriptions of objects; 2) we design context-sensitive queries to improve the model's ability in deciphering intricate nuances embedded within descriptions and enforce the model to focus on context rather than object names alone. On two novel object detection benchmarks, LVIS and OminiLabel, under the zero-shot detection setting, our approach achieves 34.8 APr minival (+9.1) and 29.3 AP (+3.6), respectively, surpassing the prior state-of-the-art models, GLIP and FIBER, by a large margin.

Poster
Quantifying & Modeling Multimodal Interactions: An Information Decomposition Framework

Paul Pu Liang, Yun Cheng, Xiang Fan, Chun Kai Ling, Suzanne Nie, Richard J. Chen, Zihao Deng, Nicholas Allen, Randy Auerbach, Faisal Mahmood, Ruslan Salakhutdinov, Louis-Philippe Morency

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The recent explosion of interest in multimodal applications has resulted in a wide selection of datasets and methods for representing and integrating information from different modalities. Despite these empirical advances, there remain fundamental research questions: How can we quantify the interactions that are necessary to solve a multimodal task? Subsequently, what are the most suitable multimodal models to capture these interactions? To answer these questions, we propose an information-theoretic approach to quantify the degree of redundancy, uniqueness, and synergy relating input modalities with an output task. We term these three measures as the PID statistics of a multimodal distribution (or PID for short), and introduce two new estimators for these PID statistics that scale to high-dimensional distributions. To validate PID estimation, we conduct extensive experiments on both synthetic datasets where the PID is known and on large-scale multimodal benchmarks where PID estimations are compared with human annotations. Finally, we demonstrate their usefulness in (1) quantifying interactions within multimodal datasets, (2) quantifying interactions captured by multimodal models, (3) principled approaches for model selection, and (4) three real-world case studies engaging with domain experts in pathology, mood prediction, and robotic perception where our framework helps to recommend strong multimodal models for each application.

Poster
A graphon-signal analysis of graph neural networks

Ron Levie

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We present an approach for analyzing message passing graph neural networks (MPNNs) based on an extension of graphon analysis to a so called graphon-signal analysis. A MPNN is a function that takes a graph and a signal on the graph (a graph-signal) and returns some value. Since the input space of MPNNs is non-Euclidean, i.e., graphs can be of any size and topology, properties such as generalization are less well understood for MPNNs than for Euclidean neural networks. We claim that one important missing ingredient in past work is a meaningful notion of graph-signal similarity measure, that endows the space of inputs to MPNNs with a regular structure. We present such a similarity measure, called the graphon-signal cut distance, which makes the space of all graph-signals a dense subset of a compact metric space -- the graphon-signal space. Informally, two deterministic graph-signals are close in cut-distance if they ``look like'' they were sampled from the same random graph-signal model. Hence, our cut distance is a natural notion of graph-signal similarity, which allows comparing any pair of graph-signals of any size and topology. We prove that MPNNs are Lipschitz continuous functions over the graphon-signal metric space. We then give two applications of this result: 1) a generalization bound for MPNNs, and, 2) the stability of MPNNs to subsampling of graph-signals. Our results apply to any regular enough MPNN on any distribution of graph-signals, making the analysis rather universal.

Poster