NeurIPS 2023 论文列表

Conference on Neural Information Processing Systems

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3,584篇论文

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  • Oral
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    40011.2%
  • Poster
    3,10786.7%

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Streaming Algorithms and Lower Bounds for Estimating Correlation Clustering Cost

Sepehr Assadi, Vihan Shah, Chen Wang

展开摘要

Correlation clustering is a fundamental optimization problem at the intersection of machine learning and theoretical computer science. Motivated by applications to big data processing, recent years have witnessed a flurry of results on this problem in the streaming model. In this model, the algorithm needs to process the input $n$-vertex graph by making one or few passes over the stream of its edges and using a limited memory, much smaller than the input size. All previous work on streaming correlation clustering have focused on semi-streaming algorithms with $\Omega(n)$ memory, whereas in this work, we study streaming algorithms with much smaller memory requirement of only $\text{polylog}{(n)}$ bits. This stringent memory requirement is in the same spirit of classical streaming algorithms that instead of recovering a full solution to the problem---which can be prohibitively large with such small memory as is the case in our problem---, aimed to learn certain statistical properties of their inputs. In our case, this translates to determining the ``(correlation) clusterability'' of input graphs, or more precisely, estimating the cost of the optimal correlation clustering solution. As our main result, we present two novel algorithms that in only $\text{polylog}{(n)}$ space are able to estimate the optimal correlation clustering cost up to some constant multiplicative factor plus some extra additive error. One of the algorithms outputs a $3$-multiplicative approximation plus $o(n^2)$ additive approximation, and the other one improves the additive error further down at the cost of increasing the multiplicative factor to some large constant. We then present new lower bounds that justify this mix of both multiplicative and additive error approximation in our algorithms.

Poster
Interaction Measures, Partition Lattices and Kernel Tests for High-Order Interactions

Zhaolu Liu, Robert Peach, Pedro A. M. Mediano, Mauricio Barahona

展开摘要

Models that rely solely on pairwise relationships often fail to capture the complete statistical structure of the complex multivariate data found in diverse domains, such as socio-economic, ecological, or biomedical systems. Non-trivial dependencies between groups of more than two variables can play a significant role in the analysis and modelling of such systems, yet extracting such high-order interactions from data remains challenging. Here, we introduce a hierarchy of $d$-order ($d \geq 2$) interaction measures, increasingly inclusive of possible factorisations of the joint probability distribution, and define non-parametric, kernel-based tests to establish systematically the statistical significance of $d$-order interactions. We also establish mathematical links with lattice theory, which elucidate the derivation of the interaction measures and their composite permutation tests; clarify the connection of simplicial complexes with kernel matrix centring; and provide a means to enhance computational efficiency. We illustrate our results numerically with validations on synthetic data, and through an application to neuroimaging data.

Poster
Large language models implicitly learn to straighten neural sentence trajectories to construct a predictive representation of natural language.

Eghbal A. Hosseini, Evelina Fedorenko

展开摘要

Predicting upcoming events is critical to our ability to effectively interact with our environment and conspecifics. In natural language processing, transformer models, which are trained on next-word prediction, appear to construct a general-purpose representation of language that can support diverse downstream tasks. However, we still lack an understanding of how a predictive objective shapes such representations. Inspired by recent work in vision neuroscience Hénaff et al. (2019), here we test a hypothesis about predictive representations of autoregressive transformer models. In particular, we test whether the neural trajectory of a sequence of words in a sentence becomes progressively more straight as it passes through the layers of the network. The key insight behind this hypothesis is that straighter trajectories should facilitate prediction via linear extrapolation. We quantify straightness using a 1- dimensional curvature metric, and present four findings in support of the trajectory straightening hypothesis: i) In trained models, the curvature progressively decreases from the first to the middle layers of the network. ii) Models that perform better on the next-word prediction objective, including larger models and models trained on larger datasets, exhibit greater decreases in curvature, suggesting that this improved ability to straighten sentence neural trajectories may be the underlying driver of better language modeling performance. iii) Given the same linguistic context, the sequences that are generated by the model have lower curvature than the ground truth (the actual continuations observed in a language corpus), suggesting that the model favors straighter trajectories for making predictions. iv) A consistent relationship holds between the average curvature and the average surprisal of sentences in the middle layers of models, such that sentences with straighter neural trajectories also have lower surprisal. Importantly, untrained models don’t exhibit these behaviors. In tandem, these results support the trajectory straightening hypothesis and provide a possible mechanism for how the geometry of the internal representations of autoregressive models supports next word prediction.

Poster
Inferring the Future by Imagining the Past

Kartik Chandra, Tony Chen, Tzu-Mao Li, Jonathan Ragan-Kelley, Joshua B. Tenenbaum

展开摘要

A single panel of a comic book can say a lot: it can depict not only where the characters currently are, but also their motions, their motivations, their emotions, and what they might do next. More generally, humans routinely infer complex sequences of past and future events from a *static snapshot* of a *dynamic scene*, even in situations they have never seen before. In this paper, we model how humans make such rapid and flexible inferences. Building on a long line of work in cognitive science, we offer a Monte Carlo algorithm whose inferences correlate well with human intuitions in a wide variety of domains, while only using a small, cognitively-plausible number of samples. Our key technical insight is a surprising connection between our inference problem and Monte Carlo path tracing, which allows us to apply decades of ideas from the computer graphics community to this seemingly-unrelated theory of mind task.

Spotlight
Fast Exact Leverage Score Sampling from Khatri-Rao Products with Applications to Tensor Decomposition

Vivek Bharadwaj, Osman Asif Malik, Riley Murray, Laura Grigori, Aydin Buluc, James Demmel

展开摘要

We present a data structure to randomly sample rows from the Khatri-Rao product of several matrices according to the exact distribution of its leverage scores. Our proposed sampler draws each row in time logarithmic in the height of the Khatri-Rao product and quadratic in its column count, with persistent space overhead at most the size of the input matrices. As a result, it tractably draws samples even when the matrices forming the Khatri-Rao product have tens of millions of rows each. When used to sketch the linear least-squares problems arising in Candecomp / PARAFAC decomposition, our method achieves lower asymptotic complexity per solve than recent state-of-the-art methods. Experiments on billion-scale sparse tensors and synthetic data validate our theoretical claims, with our algorithm achieving higher accuracy than competing methods as the decomposition rank grows.

Poster
SG×P : A Sorghum Genotype × Phenotype Prediction Dataset and Benchmark

Zeyu Zhang, Robert Pless, Nadia Shakoor, Austin Carnahan, Abby Stylianou

展开摘要

Large scale field-phenotyping approaches have the potential to solve important questions about the relationship of plant genotype to plant phenotype. Computational approaches to measuring the phenotype (the observable plant features) are required to address the problem at a large scale, but machine learning approaches to extract phenotypes from sensor data have been hampered by limited access to (a) sufficiently large, organized multi-sensor datasets, (b) field trials that have a large scale and significant number of genotypes, (c) full genetic sequencing of those phenotypes, and (d) datasets sufficiently organized so that algorithm centered researchers can directly address the real biological problems. To address this, we present SGxP, a novel benchmark dataset from a large-scale field trial consisting of the complete genotype of over 300 sorghum varieties, and time sequences of imagery from several field plots growing each variety, taken with RGB and laser 3D scanner imaging. To lower the barrier to entry and facilitate further developments, we provide a set of well organized, multi-sensor imagery and corresponding genomic data. We implement baseline deep learning based phenotyping approaches to create baseline results for individual sensors and multi-sensor fusion for detecting genetic mutations with known impacts. We also provide and support an open-ended challenge by identifying thousands of genetic mutations whose phenotypic impacts are currently unknown. A web interface for machine learning researchers and practitioners to share approaches, visualizations and hypotheses supports engagement with plant biologists to further the understanding of the sorghum genotype x phenotype relationship. The full dataset, leaderboard (including baseline results) and discussion forums can be found at http://sorghumsnpbenchmark.com.

Poster
SwiFT: Swin 4D fMRI Transformer

Peter Yongho Kim, Junbeom Kwon, Sunghwan Joo, Sangyoon Bae, Donggyu Lee, Yoonho Jung, Shinjae Yoo, Jiook Cha, Taesup Moon

展开摘要

Modeling spatiotemporal brain dynamics from high-dimensional data, such as functional Magnetic Resonance Imaging (fMRI), is a formidable task in neuroscience. Existing approaches for fMRI analysis utilize hand-crafted features, but the process of feature extraction risks losing essential information in fMRI scans. To address this challenge, we present SwiFT (Swin 4D fMRI Transformer), a Swin Transformer architecture that can learn brain dynamics directly from fMRI volumes in a memory and computation-efficient manner. SwiFT achieves this by implementing a 4D window multi-head self-attention mechanism and absolute positional embeddings. We evaluate SwiFT using multiple large-scale resting-state fMRI datasets, including the Human Connectome Project (HCP), Adolescent Brain Cognitive Development (ABCD), and UK Biobank (UKB) datasets, to predict sex, age, and cognitive intelligence. Our experimental outcomes reveal that SwiFT consistently outperforms recent state-of-the-art models. Furthermore, by leveraging its end-to-end learning capability, we show that contrastive loss-based self-supervised pre-training of SwiFT can enhance performance on downstream tasks. Additionally, we employ an explainable AI method to identify the brain regions associated with sex classification. To our knowledge, SwiFT is the first Swin Transformer architecture to process dimensional spatiotemporal brain functional data in an end-to-end fashion. Our work holds substantial potential in facilitating scalable learning of functional brain imaging in neuroscience research by reducing the hurdles associated with applying Transformer models to high-dimensional fMRI.

Poster
Tight Bounds for Volumetric Spanners and Applications

Aditya Bhaskara, Sepideh Mahabadi, Ali Vakilian

展开摘要

Given a set of points of interest, a volumetric spanner is a subset of the points using which all the points can be expressed using "small" coefficients (measured in an appropriate norm). Formally, given a set of vectors $X = [v_1, v_2, \dots, v_n]$, the goal is to find $T \subseteq [n]$ such that every $v \in X$ can be expressed as $\sum_{i\in T} \alpha_i v_i$, with $\Vert \alpha \Vert$ being small. This notion, which has also been referred to as a well-conditioned basis, has found several applications, including bandit linear optimization, determinant maximization, and matrix low rank approximation. In this paper, we give almost optimal bounds on the size of volumetric spanners for all $\ell_p$ norms, and show that they can be constructed using a simple local search procedure. We then show the applications of our result to other tasks and in particular the problem of finding coresets for the Minimum Volume Enclosing Ellipsoid (MVEE) problem.

Poster
Large Language Models are Fixated by Red Herrings: Exploring Creative Problem Solving and Einstellung Effect using the Only Connect Wall Dataset

Saeid Alavi Naeini, Raeid Saqur, mozhgan saeidi, John Michael Giorgi, Babak Taati

展开摘要

The quest for human imitative AI has been an enduring topic in AI research since inception. The technical evolution and emerging capabilities of the latest cohort of large language models (LLMs) have reinvigorated the subject beyond academia to cultural zeitgeist. While recent NLP evaluation benchmark tasks test some aspects of human-imitative behaviour (e.g., BIG-bench's `human-like behavior' tasks), few, if not none, examine *creative problem solving* abilities. Creative problem solving in humans is a well-studied topic in cognitive neuroscience with standardized tests that predominantly use ability to associate (heterogeneous) connections among clue words as a metric for creativity. Exposure to misleading stimuli --- distractors dubbed *red herrings* --- impede human performance in such tasks via the *fixation effect* and Einstellung paradigm. In cognitive neuroscience studies, such fixations are experimentally induced by pre-exposing participants to orthographically similar incorrect words to subsequent word-fragments or clues. The popular British quiz show Only Connect's *Connecting Wall* segment essentially mimics Mednick's Remote Associates Test (RAT) formulation with built-in, deliberate red herrings, that makes it an ideal proxy dataset to explore and study fixation effect and Einstellung paradigm from cognitive neuroscience in LLMs. In addition to presenting the novel Only Connect Wall (OCW) dataset, we also report results from our evaluation of selected pre-trained language models and LLMs (including OpenAI's GPT series) on creative problem solving tasks like grouping clue words by heterogeneous connections, and identifying correct open knowledge domain connections in respective groups. We synthetically generate two additional datasets: OCW-Randomized, OCW-WordNet to further analyze our red-herrings hypothesis in language models. The code and link to the dataset is available at [url](https://github.com/TaatiTeam/OCW).

Poster
Revisiting Area Convexity: Faster Box-Simplex Games and Spectrahedral Generalizations

Arun Jambulapati, Kevin Tian

展开摘要

We investigate area convexity [Sherman17], a mysterious tool introduced to tackle optimization problems under the challenging $\ell_\infty$ geometry. We develop a deeper understanding of its relationship with conventional analyses of extragradient methods [Nemirovski04, Nesterov07]. We also give improved solvers for the subproblems required by variants of the [Sherman17] algorithm, designed through the lens of relative smoothness [BBT17, LFN18}. Leveraging these new tools, we give a state-of-the-art first-order algorithm for solving box-simplex games (a primal-dual formulation of $\ell_\infty$ regression) in a $d \times n$ matrix with bounded rows, using $O(\log d \cdot \epsilon^{-1})$ matrix-vector queries. As a consequence, we obtain improved complexities for approximate maximum flow, optimal transport, min-mean-cycle, and other basic combinatorial optimization problems. We also develop a near-linear time algorithm for a matrix generalization of box-simplex games, capturing a family of problems closely related to semidefinite programs recently used as subroutines in robust statistics and numerical linear algebra.

Poster
SEVA: Leveraging sketches to evaluate alignment between human and machine visual abstraction

展开摘要

Sketching is a powerful tool for creating abstract images that are sparse but meaningful. Sketch understanding poses fundamental challenges for general-purpose vision algorithms because it requires robustness to the sparsity of sketches relative to natural visual inputs and because it demands tolerance for semantic ambiguity, as sketches can reliably evoke multiple meanings. While current vision algorithms have achieved high performance on a variety of visual tasks, it remains unclear to what extent they understand sketches in a human-like way. Here we introduce $\texttt{SEVA}$, a new benchmark dataset containing approximately 90K human-generated sketches of 128 object concepts produced under different time constraints, and thus systematically varying in sparsity. We evaluated a suite of state-of-the-art vision algorithms on their ability to correctly identify the target concept depicted in these sketches and to generate responses that are strongly aligned with human response patterns on the same sketch recognition task. We found that vision algorithms that better predicted human sketch recognition performance also better approximated human uncertainty about sketch meaning, but there remains a sizable gap between model and human response patterns. To explore the potential of models that emulate human visual abstraction in generative tasks, we conducted further evaluations of a recently developed sketch generation algorithm (Vinker et al., 2022) capable of generating sketches that vary in sparsity. We hope that public release of this dataset and evaluation protocol will catalyze progress towards algorithms with enhanced capacities for human-like visual abstraction.

Poster
SatBird: a Dataset for Bird Species Distribution Modeling using Remote Sensing and Citizen Science Data

Mélisande Teng, Amna Elmustafa, Benjamin Akera, Yoshua Bengio, Hager Radi, Hugo Larochelle, David Rolnick

展开摘要

Biodiversity is declining at an unprecedented rate, impacting ecosystem services necessary to ensure food, water, and human health and well-being. Understanding the distribution of species and their habitats is crucial for conservation policy planning. However, traditional methods in ecology for species distribution models (SDMs) generally focus either on narrow sets of species or narrow geographical areas and there remain significant knowledge gaps about the distribution of species. A major reason for this is the limited availability of data traditionally used, due to the prohibitive amount of effort and expertise required for traditional field monitoring. The wide availability of remote sensing data and the growing adoption of citizen science tools to collect species observations data at low cost offer an opportunity for improving biodiversity monitoring and enabling the modelling of complex ecosystems. We introduce a novel task for mapping bird species to their habitats by predicting species encounter rates from satellite images, and present SatBird, a satellite dataset of locations in the USA with labels derived from presence-absence observation data from the citizen science database eBird, considering summer (breeding) and winter seasons. We also provide a dataset in Kenya representing low-data regimes. We additionally provide environmental data and species range maps for each location. We benchmark a set of baselines on our dataset, including SOTA models for remote sensing tasks. SatBird opens up possibilities for scalably modelling properties of ecosystems worldwide.

Poster
MoCa: Measuring Human-Language Model Alignment on Causal and Moral Judgment Tasks

Allen Nie, Yuhui Zhang, Atharva Amdekar, Christopher J Piech, Tatsunori Hashimoto, Tobias Gerstenberg

展开摘要

Human commonsense understanding of the physical and social world is organized around intuitive theories. These theories support making causal and moral judgments. When something bad happens, we naturally ask: who did what, and why? A rich literature in cognitive science has studied people's causal and moral intuitions. This work has revealed a number of factors that systematically influence people's judgments, such as the violation of norms and whether the harm is avoidable or inevitable. We collected a dataset of stories from 24 cognitive science papers and developed a system to annotate each story with the factors they investigated. Using this dataset, we test whether large language models (LLMs) make causal and moral judgments about text-based scenarios that align with those of human participants. On the aggregate level, alignment has improved with more recent LLMs. However, using statistical analyses, we find that LLMs weigh the different factors quite differently from human participants. These results show how curated, challenge datasets combined with insights from cognitive science can help us go beyond comparisons based merely on aggregate metrics: we uncover LLMs implicit tendencies and show to what extent these align with human intuitions.

Poster
Bayesian target optimisation for high-precision holographic optogenetics

Marcus Triplett, Marta Agnieszka Gajowa, Hillel Adesnik, Liam Paninski

展开摘要

Two-photon optogenetics has transformed our ability to probe the structure and function of neural circuits. However, achieving precise optogenetic control of neural ensemble activity has remained fundamentally constrained by the problem of off-target stimulation (OTS): the inadvertent activation of nearby non-target neurons due to imperfect confinement of light onto target neurons. Here we propose a novel computational approach to this problem called Bayesian target optimisation. Our approach uses nonparametric Bayesian inference to model neural responses to optogenetic stimulation, and then optimises the laser powers and optical target locations needed to achieve a desired activity pattern with minimal OTS. We validate our approach in simulations and using data from in vitro experiments, showing that Bayesian target optimisation considerably reduces OTS across all conditions we test. Together, these results establish our ability to overcome OTS, enabling optogenetic stimulation with substantially improved precision.

Spotlight
Cognitive Model Discovery via Disentangled RNNs

Kevin J Miller, Maria K Eckstein, Matthew Botvinick, Zeb Kurth-Nelson

展开摘要

Computational cognitive models are a fundamental tool in behavioral neuroscience. They embody in software precise hypotheses about the cognitive mechanisms underlying a particular behavior. Constructing these models is typically a difficult iterative process that requires both inspiration from the literature and the creativity of an individual researcher. Here, we adopt an alternative approach to learn parsimonious cognitive models directly from data. We fit behavior data using a recurrent neural network that is penalized for carrying excess information between timesteps, leading to sparse, interpretable representations and dynamics. When fitting synthetic behavioral data from known cognitive models, our method recovers the underlying form of those models. When fit to choice data from rats performing a bandit task, our method recovers simple and interpretable models that make testable predictions about neural mechanisms.

Poster
CAPP-130: A Corpus of Chinese Application Privacy Policy Summarization and Interpretation

Pengyun Zhu, Long Wen, Jinfei Liu, Feng Xue, Jian Lou, Zhibo Wang, Kui Ren

展开摘要

A privacy policy serves as an online internet protocol crafted by service providers, which details how service providers collect, process, store, manage, and use personal information when users engage with applications. However, these privacy policies are often filled with technobabble and legalese, making them "incomprehensible''. As a result, users often agree to all terms unknowingly, even some terms may conflict with the law, thereby posing a considerable risk to personal privacy information. One potential solution to alleviate this challenge is to automatically summarize privacy policies using NLP techniques. However, existing techniques primarily focus on extracting key sentences, resulting in comparatively shorter agreements, but failing to address the poor readability caused by the "incomprehensible'' of technobabble and legalese. Moreover, research on Chinese application privacy policy summarization is currently almost nonexistent, and there is a lack of a high-quality corpus suitable for addressing readability issues. To tackle these challenges, we introduce a fine-grained CAPP-130 corpus and a TCSI-pp framework. CAPP-130 contains 130 Chinese privacy policies from popular applications that have been carefully annotated and interpreted by legal experts, resulting in 52,489 annotations and 20,555 rewritten sentences. TCSI-pp first extracts sentences related to the topic specified by users and then uses a generative model to rewrite the sentences into comprehensible summarization. Built upon TSCI-pp, we construct a summarization tool TSCI-pp-zh by selecting RoBERTa from six classification models for sentence extraction and selecting mT5 from five generative models for sentence rewriting. Experimental results show that TCSI-pp-zh outperforms GPT-4 and other baselines in Chinese application privacy policy summarization, demonstrating exceptional readability and reliability. Our data, annotation guidelines, benchmark models, and source code are publicly available at https://github.com/EnlightenedAI/CAPP-130.

Poster
Training biologically plausible recurrent neural networks on cognitive tasks with long-term dependencies

Wayne WM Soo, Vishwa Goudar, Xiao-Jing Wang

展开摘要

Training recurrent neural networks (RNNs) has become a go-to approach for generating and evaluating mechanistic neural hypotheses for cognition. The ease and efficiency of training RNNs with backpropagation through time and the availability of robustly supported deep learning libraries has made RNN modeling more approachable and accessible to neuroscience. Yet, a major technical hindrance remains. Cognitive processes such as working memory and decision making involve neural population dynamics over a long period of time within a behavioral trial and across trials. It is difficult to train RNNs to accomplish tasks where neural representations and dynamics have long temporal dependencies without gating mechanisms such as LSTMs or GRUs which currently lack experimental support and prohibit direct comparison between RNNs and biological neural circuits. We tackled this problem based on the idea of specialized skip-connections through time to support the emergence of task-relevant dynamics, and subsequently reinstitute biological plausibility by reverting to the original architecture. We show that this approach enables RNNs to successfully learn cognitive tasks that prove impractical if not impossible to learn using conventional methods. Over numerous tasks considered here, we achieve less training steps and shorter wall-clock times, particularly in tasks that require learning long-term dependencies via temporal integration over long timescales or maintaining a memory of past events in hidden-states. Our methods expand the range of experimental tasks that biologically plausible RNN models can learn, thereby supporting the development of theory for the emergent neural mechanisms of computations involving long-term dependencies.

Poster
Degraded Polygons Raise Fundamental Questions of Neural Network Perception

Leonard Tang, Dan Ley

展开摘要

It is well-known that modern computer vision systems often exhibit behaviors misaligned with those of humans: from adversarial attacks to image corruptions, deep learning vision models suffer in a variety of settings that humans capably handle. In light of these phenomena, here we introduce another, orthogonal perspective studying the human-machine vision gap. We revisit the task of recovering images under degradation, first introduced over 30 years ago in the Recognition-by-Components theory of human vision. Specifically, we study the performance and behavior of neural networks on the seemingly simple task of classifying regular polygons at varying orders of degradation along their perimeters. To this end, we implement the Automated Shape Recoverability Test for rapidly generating large-scale datasets of perimeter-degraded regular polygons, modernizing the historically manual creation of image recoverability experiments. We then investigate the capacity of neural networks to recognize and recover such degraded shapes when initialized with different priors. Ultimately, we find that neural networks’ behavior on this simple task conflicts with human behavior, raising a fundamental question of the robustness and learning capabilities of modern computer vision models

Poster
Spatial-frequency channels, shape bias, and adversarial robustness

Ajay Subramanian, Elena Sizikova, Najib J. Majaj, Denis G. Pelli

展开摘要

What spatial frequency information do humans and neural networks use to recognize objects? In neuroscience, critical band masking is an established tool that can reveal the frequency-selective filters used for object recognition. Critical band masking measures the sensitivity of recognition performance to noise added at each spatial frequency. Existing critical band masking studies show that humans recognize periodic patterns (gratings) and letters by means of a spatial-frequency filter (or "channel") that has a frequency bandwidth of one octave (doubling of frequency). Here, we introduce critical band masking as a task for network-human comparison and test 14 humans and 76 neural networks on 16-way ImageNet categorization in the presence of narrowband noise. We find that humans recognize objects in natural images using the same one-octave-wide channel that they use for letters and gratings, making it a canonical feature of human object recognition. Unlike humans, the neural network channel is very broad, 2-4 times wider than the human channel. This means that the network channel extends to frequencies higher and lower than those that humans are sensitive to. Thus, noise at those frequencies will impair network performance and spare human performance. Adversarial and augmented-image training are commonly used to increase network robustness and shape bias. Does this training align network and human object recognition channels? Three network channel properties (bandwidth, center frequency, peak noise sensitivity) correlate strongly with shape bias (51% variance explained) and robustness of adversarially-trained networks (66% variance explained). Adversarial training increases robustness but expands the channel bandwidth even further beyond the human bandwidth. Thus, critical band masking reveals that the network channel is more than twice as wide as the human channel, and that adversarial training only makes it worse. Networks with narrower channels might be more robust.

Oral
Tree-Based Diffusion Schrödinger Bridge with Applications to Wasserstein Barycenters

Maxence Noble, Valentin De Bortoli, Arnaud Doucet, Alain Durmus

展开摘要

Multi-marginal Optimal Transport (mOT), a generalization of OT, aims at minimizing the integral of a cost function with respect to a distribution with some prescribed marginals. In this paper, we consider an entropic version of mOT with a tree-structured quadratic cost, i.e., a function that can be written as a sum of pairwise cost functions between the nodes of a tree. To address this problem, we develop Tree-based Diffusion Schr\"odinger Bridge (TreeDSB), an extension of the Diffusion Schr\"odinger Bridge (DSB) algorithm. TreeDSB corresponds to a dynamic and continuous state-space counterpart of the multimarginal Sinkhorn algorithm. A notable use case of our methodology is to compute Wasserstein barycenters which can be recast as the solution of a mOT problem on a star-shaped tree. We demonstrate that our methodology can be applied in high-dimensional settings such as image interpolation and Bayesian fusion.

Spotlight