ICLR 2022 论文列表

International Conference on Learning Representations

录用类型

1,095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
    555.0%
  • Spotlight
    17415.9%
  • Poster
    86679.1%

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Latent Variable Sequential Set Transformers for Joint Multi-Agent Motion Prediction

Roger Girgis, Florian Golemo, Felipe Codevilla, Martin Weiss, Jim Aldon D'Souza, Samira Ebrahimi Kahou, Felix Heide, Christopher Pal

展开摘要

Robust multi-agent trajectory prediction is essential for the safe control of robotic systems. A major challenge is to efficiently learn a representation that approximates the true joint distribution of contextual, social, and temporal information to enable planning. We propose Latent Variable Sequential Set Transformers which are encoder-decoder architectures that generate scene-consistent multi-agent trajectories. We refer to these architectures as “AutoBots”. The encoder is a stack of interleaved temporal and social multi-head self-attention (MHSA) modules which alternately perform equivariant processing across the temporal and social dimensions. The decoder employs learnable seed parameters in combination with temporal and social MHSA modules allowing it to perform inference over the entire future scene in a single forward pass efficiently. AutoBots can produce either the trajectory of one ego-agent or a distribution over the future trajectories for all agents in the scene. For the single-agent prediction case, our model achieves top results on the global nuScenes vehicle motion prediction leaderboard, and produces strong results on the Argoverse vehicle prediction challenge. In the multi-agent setting, we evaluate on the synthetic partition of TrajNet++ dataset to showcase the model’s socially-consistent predictions. We also demonstrate our model on general sequences of sets and provide illustrative experiments modelling the sequential structure of the multiple strokes that make up symbols in the Omniglot data. A distinguishing feature of AutoBots is that all models are trainable on a single desktop GPU (1080 Ti) in under 48h.

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Omni-Dimensional Dynamic Convolution

Chao Li, Aojun Zhou, Anbang Yao

展开摘要

Learning a single static convolutional kernel in each convolutional layer is the common training paradigm of modern Convolutional Neural Networks (CNNs). Instead, recent research in dynamic convolution shows that learning a linear combination of n convolutional kernels weighted with their input-dependent attentions can significantly improve the accuracy of light-weight CNNs, while maintaining efficient inference. However, we observe that existing works endow convolutional kernels with the dynamic property through one dimension (regarding the convolutional kernel number) of the kernel space, but the other three dimensions (regarding the spatial size, the input channel number and the output channel number for each convolutional kernel) are overlooked. Inspired by this, we present Omni-dimensional Dynamic Convolution (ODConv), a more generalized yet elegant dynamic convolution design, to advance this line of research. ODConv leverages a novel multi-dimensional attention mechanism with a parallel strategy to learn complementary attentions for convolutional kernels along all four dimensions of the kernel space at any convolutional layer. As a drop-in replacement of regular convolutions, ODConv can be plugged into many CNN architectures. Extensive experiments on the ImageNet and MS-COCO datasets show that ODConv brings solid accuracy boosts for various prevailing CNN backbones including both light-weight and large ones, e.g., 3.77%~5.71%|1.86%~3.72% absolute top-1 improvements to MobivleNetV2|ResNet family on the ImageNet dataset. Intriguingly, thanks to its improved feature learning ability, ODConv with even one single kernel can compete with or outperform existing dynamic convolution counterparts with multiple kernels, substantially reducing extra parameters. Furthermore, ODConv is also superior to other attention modules for modulating the output features or the convolutional weights. Code and models will be available at https://github.com/OSVAI/ODConv.

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Interpretable Unsupervised Diversity Denoising and Artefact Removal

Mangal Prakash, Mauricio Delbracio, Peyman Milanfar, Florian Jug

展开摘要

Image denoising and artefact removal are complex inverse problems admitting multiple valid solutions. Unsupervised diversity restoration, that is, obtaining a diverse set of possible restorations given a corrupted image, is important for ambiguity removal in many applications such as microscopy where paired data for supervised training are often unobtainable. In real world applications, imaging noise and artefacts are typically hard to model, leading to unsatisfactory performance of existing unsupervised approaches. This work presents an interpretable approach for unsupervised and diverse image restoration. To this end, we introduce a capable architecture called Hierarchical DivNoising (HDN) based on hierarchical Variational Autoencoder. We show that HDN learns an interpretable multi-scale representation of artefacts and we leverage this interpretability to remove imaging artefacts commonly occurring in microscopy data. Our method achieves state-of-the-art results on twelve benchmark image denoising datasets while providing access to a whole distribution of sensibly restored solutions. Additionally, we demonstrate on three real microscopy datasets that HDN removes artefacts without supervision, being the first method capable of doing so while generating multiple plausible restorations all consistent with the given corrupted image.

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Learning meta-features for AutoML

Herilalaina Rakotoarison, Louisot Milijaona, Andry RASOANAIVO, Michele Sebag, Marc Schoenauer

展开摘要

This paper tackles the AutoML problem, aimed to automatically select an ML algorithm and its hyper-parameter configuration most appropriate to the dataset at hand. The proposed approach, MetaBu, learns new meta-features via an Optimal Transport procedure, aligning the manually designed \mf s with the space of distributions on the hyper-parameter configurations. MetaBu meta-features, learned once and for all, induce a topology on the set of datasets that is exploited to define a distribution of promising hyper-parameter configurations amenable to AutoML. Experiments on the OpenML CC-18 benchmark demonstrate that using MetaBu meta-features boosts the performance of state of the art AutoML systems, AutoSklearn (Feurer et al. 2015) and Probabilistic Matrix Factorization (Fusi et al. 2018). Furthermore, the inspection of MetaBu meta-features gives some hints into when an ML algorithm does well. Finally, the topology based on MetaBu meta-features enables to estimate the intrinsic dimensionality of the OpenML benchmark w.r.t. a given ML algorithm or pipeline. The source code is available at https://github.com/luxusg1/metabu.

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On the Importance of Firth Bias Reduction in Few-Shot Classification

Saba Ghaffari, Ehsan Saleh, David Forsyth, Yu-Xiong Wang

展开摘要

Learning accurate classifiers for novel categories from very few examples, known as few-shot image classification, is a challenging task in statistical machine learning and computer vision. The performance in few-shot classification suffers from the bias in the estimation of classifier parameters; however, an effective underlying bias reduction technique that could alleviate this issue in training few-shot classifiers has been overlooked. In this work, we demonstrate the effectiveness of Firth bias reduction in few-shot classification. Theoretically, Firth bias reduction removes the $O(N^{-1})$ first order term from the small-sample bias of the Maximum Likelihood Estimator. Here we show that the general Firth bias reduction technique simplifies to encouraging uniform class assignment probabilities for multinomial logistic classification, and almost has the same effect in cosine classifiers. We derive an easy-to-implement optimization objective for Firth penalized multinomial logistic and cosine classifiers, which is equivalent to penalizing the cross-entropy loss with a KL-divergence between the predictions and the uniform label distribution. Then, we empirically evaluate that it is consistently effective across the board for few-shot image classification, regardless of (1) the feature representations from different backbones, (2) the number of samples per class, and (3) the number of classes. Furthermore, we demonstrate the effectiveness of Firth bias reduction on cross-domain and imbalanced data settings. Our implementation is available at https://github.com/ehsansaleh/firth_bias_reduction.

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Controlling Directions Orthogonal to a Classifier

Yilun Xu, Hao He, Tianxiao Shen, Tommi S. Jaakkola

展开摘要

We propose to identify directions invariant to a given classifier so that these directions can be controlled in tasks such as style transfer. While orthogonal decomposition is directly identifiable when the given classifier is linear, we formally define a notion of orthogonality in the non-linear case. We also provide a surprisingly simple method for constructing the orthogonal classifier (a classifier utilizing directions other than those of the given classifier). Empirically, we present three use cases where controlling orthogonal variation is important: style transfer, domain adaptation, and fairness. The orthogonal classifier enables desired style transfer when domains vary in multiple aspects, improves domain adaptation with label shifts and mitigates the unfairness as a predictor. The code is available at https://github.com/Newbeeer/orthogonal_classifier

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How Do Vision Transformers Work?

Namuk Park, Songkuk Kim

展开摘要

The success of multi-head self-attentions (MSAs) for computer vision is now indisputable. However, little is known about how MSAs work. We present fundamental explanations to help better understand the nature of MSAs. In particular, we demonstrate the following properties of MSAs and Vision Transformers (ViTs): (1) MSAs improve not only accuracy but also generalization by flattening the loss landscapes. Such improvement is primarily attributable to their data specificity, not long-range dependency. On the other hand, ViTs suffer from non-convex losses. Large datasets and loss landscape smoothing methods alleviate this problem; (2) MSAs and Convs exhibit opposite behaviors. For example, MSAs are low-pass filters, but Convs are high-pass filters. Therefore, MSAs and Convs are complementary; (3) Multi-stage neural networks behave like a series connection of small individual models. In addition, MSAs at the end of a stage play a key role in prediction. Based on these insights, we propose AlterNet, a model in which Conv blocks at the end of a stage are replaced with MSA blocks. AlterNet outperforms CNNs not only in large data regimes but also in small data regimes. The code is available at https://github.com/xxxnell/how-do-vits-work.

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On Improving Adversarial Transferability of Vision Transformers

Muzammal Naseer, Kanchana Ranasinghe, Salman Khan, Fahad Khan, Fatih Porikli

展开摘要

Vision transformers (ViTs) process input images as sequences of patches via self-attention; a radically different architecture than convolutional neural networks (CNNs). This makes it interesting to study the adversarial feature space of ViT models and their transferability. In particular, we observe that adversarial patterns found via conventional adversarial attacks show very \emph{low} black-box transferability even for large ViT models. We show that this phenomenon is only due to the sub-optimal attack procedures that do not leverage the true representation potential of ViTs. A deep ViT is composed of multiple blocks, with a consistent architecture comprising of self-attention and feed-forward layers, where each block is capable of independently producing a class token. Formulating an attack using only the last class token (conventional approach) does not directly leverage the discriminative information stored in the earlier tokens, leading to poor adversarial transferability of ViTs.Using the compositional nature of ViT models, we enhance transferability of existing attacks by introducing two novel strategies specific to the architecture of ViT models. \emph{(i) Self-Ensemble:} We propose a method to find multiple discriminative pathways by dissecting a single ViT model into an ensemble of networks. This allows explicitly utilizing class-specific information at each ViT block. \emph{(ii) Token Refinement:} We then propose to refine the tokens to further enhance the discriminative capacity at each block of ViT.Our token refinement systematically combines the class tokens with structural information preserved within the patch tokens. An adversarial attack when applied to such refined tokens within the ensemble of classifiers found in a single vision transformer has significantly higher transferability and thereby brings out the true generalization potential of the ViT's adversarial space. Code: https://t.ly/hBbW.

Spotlight
Score-Based Generative Modeling with Critically-Damped Langevin Diffusion

Tim Dockhorn, Arash Vahdat, Karsten Kreis

展开摘要

Score-based generative models (SGMs) have demonstrated remarkable synthesis quality. SGMs rely on a diffusion process that gradually perturbs the data towards a tractable distribution, while the generative model learns to denoise. The complexity of this denoising task is, apart from the data distribution itself, uniquely determined by the diffusion process. We argue that current SGMs employ overly simplistic diffusions, leading to unnecessarily complex denoising processes, which limit generative modeling performance. Based on connections to statistical mechanics, we propose a novel critically-damped Langevin diffusion (CLD) and show that CLD-based SGMs achieve superior performance. CLD can be interpreted as running a joint diffusion in an extended space, where the auxiliary variables can be considered "velocities" that are coupled to the data variables as in Hamiltonian dynamics. We derive a novel score matching objective for CLD and show that the model only needs to learn the score function of the conditional distribution of the velocity given data, an easier task than learning scores of the data directly. We also derive a new sampling scheme for efficient synthesis from CLD-based diffusion models. We find that CLD outperforms previous SGMs in synthesis quality for similar network architectures and sampling compute budgets. We show that our novel sampler for CLD significantly outperforms solvers such as Euler–Maruyama. Our framework provides new insights into score-based denoising diffusion models and can be readily used for high-resolution image synthesis. Project page and code: https://nv-tlabs.github.io/CLD-SGM.

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Transition to Linearity of Wide Neural Networks is an Emerging Property of Assembling Weak Models

Chaoyue Liu, Libin Zhu, Misha Belkin

展开摘要

Wide neural networks with linear output layer have been shown to be near-linear, and to have near-constant neural tangent kernel (NTK), in a region containing the optimization path of gradient descent. These findings seem counter-intuitive since in general neural networks are highly complex models. Why does a linear structure emerge when the neural networks become wide? In this work, we provide a new perspective on this "transition to linearity" by considering a neural network as an assembly model recursively built from a set of sub-models corresponding to individual neurons. In this view, we show that the linearity of wide neural networks is, in fact, an emerging property of assembling a large number of diverse ``weak'' sub-models, none of which dominate the assembly.

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Scarf: Self-Supervised Contrastive Learning using Random Feature Corruption

Dara Bahri, Heinrich Jiang, Yi Tay, Donald Metzler

展开摘要

Self-supervised contrastive representation learning has proved incredibly successful in the vision and natural language domains, enabling state-of-the-art performance with orders of magnitude less labeled data. However, such methods are domain-specific and little has been done to leverage this technique on real-world \emph{tabular} datasets. We propose \textsc{Scarf}, a simple, widely-applicable technique for contrastive learning, where views are formed by corrupting a random subset of features. When applied to pre-train deep neural networks on the 69 real-world, tabular classification datasets from the OpenML-CC18 benchmark, \textsc{Scarf} not only improves classification accuracy in the fully-supervised setting but does so also in the presence of label noise and in the semi-supervised setting where only a fraction of the available training data is labeled. We show that \textsc{Scarf} complements existing strategies and outperforms alternatives like autoencoders. We conduct comprehensive ablations, detailing the importance of a range of factors.

Spotlight
Generalized Decision Transformer for Offline Hindsight Information Matching

Hiroki Furuta, Yutaka Matsuo, Shixiang Shane Gu

展开摘要

How to extract as much learning signal from each trajectory data has been a key problem in reinforcement learning (RL), where sample inefficiency has posed serious challenges for practical applications. Recent works have shown that using expressive policy function approximators and conditioning on future trajectory information -- such as future states in hindsight experience replay (HER) or returns-to-go in Decision Transformer (DT) -- enables efficient learning of multi-task policies, where at times online RL is fully replaced by offline behavioral cloning (BC), e.g. sequence modeling. We demonstrate that all these approaches are doing hindsight information matching (HIM) -- training policies that can output the rest of trajectory that matches some statistics of future state information. We present Generalized Decision Transformer (GDT) for solving any HIM problem, and show how different choices for the feature function and the anti-causal aggregator not only recover DT as a special case, but also lead to novel Categorical DT (CDT) and Bi-directional DT (BDT) for matching different statistics of the future. For evaluating CDT and BDT, we define offline multi-task state-marginal matching (SMM) and imitation learning (IL) as two generic HIM problems, propose a Wasserstein distance loss as a metric for both, and empirically study them on MuJoCo continuous control benchmarks. Categorical DT, which simply replaces anti-causal summation with anti-causal binning in DT, enables arguably the first effective offline multi-task SMM algorithm that generalizes well to unseen (and even synthetic) multi-modal reward or state-feature distributions. Bi-directional DT, which uses an anti-causal second transformer as the aggregator, can learn to model any statistics of the future and outperforms DT variants in offline multi-task IL, i.e. one-shot IL. Our generalized formulations from HIM and GDT greatly expand the role of powerful sequence modeling architectures in modern RL.

Spotlight
Dynamics-Aware Comparison of Learned Reward Functions

Blake Wulfe, Logan Michael Ellis, Jean Mercat, Rowan Thomas McAllister, Adrien Gaidon

展开摘要

The ability to learn reward functions plays an important role in enabling the deployment of intelligent agents in the real world. However, $\textit{comparing}$ reward functions, for example as a means of evaluating reward learning methods, presents a challenge. Reward functions are typically compared by considering the behavior of optimized policies, but this approach conflates deficiencies in the reward function with those of the policy search algorithm used to optimize it. To address this challenge, Gleave et al. (2020) propose the Equivalent-Policy Invariant Comparison (EPIC) distance. EPIC avoids policy optimization, but in doing so requires computing reward values at transitions that may be impossible under the system dynamics. This is problematic for learned reward functions because it entails evaluating them outside of their training distribution, resulting in inaccurate reward values that we show can render EPIC ineffective at comparing rewards. To address this problem, we propose the Dynamics-Aware Reward Distance (DARD), a new reward pseudometric. DARD uses an approximate transition model of the environment to transform reward functions into a form that allows for comparisons that are invariant to reward shaping while only evaluating reward functions on transitions close to their training distribution. Experiments in simulated physical domains demonstrate that DARD enables reliable reward comparisons without policy optimization and is significantly more predictive than baseline methods of downstream policy performance when dealing with learned reward functions.

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Probabilistic Implicit Scene Completion

Dongsu Zhang, Changwoon Choi, Inbum Park, Young Min Kim

展开摘要

We propose a probabilistic shape completion method extended to the continuous geometry of large-scale 3D scenes. Real-world scans of 3D scenes suffer from a considerable amount of missing data cluttered with unsegmented objects. The problem of shape completion is inherently ill-posed, and high-quality result requires scalable solutions that consider multiple possible outcomes. We employ the Generative Cellular Automata that learns the multi-modal distribution and transform the formulation to process large-scale continuous geometry. The local continuous shape is incrementally generated as a sparse voxel embedding, which contains the latent code for each occupied cell. We formally derive that our training objective for the sparse voxel embedding maximizes the variational lower bound of the complete shape distribution and therefore our progressive generation constitutes a valid generative model. Experiments show that our model successfully generates diverse plausible scenes faithful to the input, especially when the input suffers from a significant amount of missing data. We also demonstrate that our approach outperforms deterministic models even in less ambiguous cases with a small amount of missing data, which infers that probabilistic formulation is crucial for high-quality geometry completion on input scans exhibiting any levels of completeness.

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EViT: Expediting Vision Transformers via Token Reorganizations

Youwei Liang, Chongjian GE, Zhan Tong, Yibing Song, Jue Wang, Pengtao Xie

展开摘要

Vision Transformers (ViTs) take all the image patches as tokens and construct multi-head self-attention (MHSA) among them. Complete leverage of these image tokens brings redundant computations since not all the tokens are attentive in MHSA. Examples include that tokens containing semantically meaningless or distractive image backgrounds do not positively contribute to the ViT predictions. In this work, we propose to reorganize image tokens during the feed-forward process of ViT models, which is integrated into ViT during training. For each forward inference, we identify the attentive image tokens between MHSA and FFN (i.e., feed-forward network) modules, which is guided by the corresponding class token attention. Then, we reorganize image tokens by preserving attentive image tokens and fusing inattentive ones to expedite subsequent MHSA and FFN computations. To this end, our method EViT improves ViTs from two perspectives. First, under the same amount of input image tokens, our method reduces MHSA and FFN computation for efficient inference. For instance, the inference speed of DeiT-S is increased by 50% while its recognition accuracy is decreased by only 0.3% for ImageNet classification. Second, by maintaining the same computational cost, our method empowers ViTs to take more image tokens as input for recognition accuracy improvement, where the image tokens are from higher resolution images. An example is that we improve the recognition accuracy of DeiT-S by 1% for ImageNet classification at the same computational cost of a vanilla DeiT-S. Meanwhile, our method does not introduce more parameters to ViTs. Experiments on the standard benchmarks show the effectiveness of our method. The code is available at https://github.com/youweiliang/evit

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GNN-LM: Language Modeling based on Global Contexts via GNN

Yuxian Meng, Shi Zong, Xiaoya Li, Xiaofei Sun, Tianwei Zhang, Fei Wu, Jiwei Li

展开摘要

Inspired by the notion that "it to copy is easier than to memorize", in this work, we introduce GNN-LM, which extends vanilla neural language model (LM) by allowing to reference similar contexts in the entire training corpus. We build a directed heterogeneous graph between an input context and its semantically related neighbors selected from the training corpus, where nodes are tokens in the input context and retrieved neighbor contexts, and edges represent connections between nodes. Graph neural networks (GNNs) are constructed upon the graph to aggregate information from similar contexts to decode the token. This learning paradigm provides direct access to the reference contexts and helps improve a model's generalization ability. We conduct comprehensive experiments to validate the effectiveness of the GNN-LM: GNN-LM achieves a new state-of-the-art perplexity of 14.8 on WikiText-103 (a 3.9 point improvement over its counterpart of the vanilla LM model), and shows substantial improvement on One Billion Word and Enwiki8 datasets against strong baselines. In-depth ablation studies are performed to understand the mechanics of GNN-LM. The code can be found at https://github.com/ShannonAI/GNN-LM.

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Scalable Sampling for Nonsymmetric Determinantal Point Processes

Insu Han, Mike Gartrell, Jennifer Gillenwater, Elvis Dohmatob, amin karbasi

展开摘要

A determinantal point process (DPP) on a collection of $M$ items is a model, parameterized by a symmetric kernel matrix, that assigns a probability to every subset of those items. Recent work shows that removing the kernel symmetry constraint, yielding nonsymmetric DPPs (NDPPs), can lead to significant predictive performance gains for machine learning applications. However, existing work leaves open the question of scalable NDPP sampling. There is only one known DPP sampling algorithm, based on Cholesky decomposition, that can directly apply to NDPPs as well. Unfortunately, its runtime is cubic in $M$, and thus does not scale to large item collections. In this work, we first note that this algorithm can be transformed into a linear-time one for kernels with low-rank structure. Furthermore, we develop a scalable sublinear-time rejection sampling algorithm by constructing a novel proposal distribution. Additionally, we show that imposing certain structural constraints on the NDPP kernel enables us to bound the rejection rate in a way that depends only on the kernel rank. In our experiments we compare the speed of all of these samplers for a variety of real-world tasks.

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Understanding the Role of Self Attention for Efficient Speech Recognition

Kyuhong Shim, Jungwook Choi, Wonyong Sung

展开摘要

Self-attention (SA) is a critical component of Transformer neural networks that have succeeded in automatic speech recognition (ASR). In this paper, we analyze the role of SA in Transformer-based ASR models for not only understanding the mechanism of improved recognition accuracy but also lowering the computational complexity. We reveal that SA performs two distinct roles: phonetic and linguistic localization. Especially, we show by experiments that phonetic localization in the lower layers extracts phonologically meaningful features from speech and reduces the phonetic variance in the utterance for proper linguistic localization in the upper layers. From this understanding, we discover that attention maps can be reused as long as their localization capability is preserved. To evaluate this idea, we implement the layer-wise attention map reuse on real GPU platforms and achieve up to 1.96 times speedup in inference and 33% savings in training time with noticeably improved ASR performance for the challenging benchmark on LibriSpeech dev/test-other dataset.

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Emergent Communication at Scale

Rahma Chaabouni, Florian Strub, Florent Altché, Eugene Tarassov, Corentin Tallec, Elnaz Davoodi, Kory Wallace Mathewson, Olivier Tieleman, Angeliki Lazaridou, Bilal Piot

展开摘要

Emergent communication aims for a better understanding of human language evolution and building more efficient representations. We posit that reaching these goals will require scaling up, in contrast to a significant amount of literature that focuses on setting up small-scale problems to tease out desired properties of the emergent languages. We focus on three independent aspects to scale up, namely the dataset, task complexity, and population size. We provide a first set of results for large populations solving complex tasks on realistic large-scale datasets, as well as an easy-to-use codebase to enable further experimentation. In more complex tasks and datasets, we find that RL training can become unstable, but responds well to established stabilization techniques. We also identify the need for a different metric than topographic similarity, which does not correlate with the generalization performances when working with natural images. In this context, we probe ease-of-learnability and transfer methods to assess emergent languages. Finally, we observe that larger populations do not induce robust emergent protocols with high generalization performance, leading us to explore different ways to leverage population, through voting and imitation learning.

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POETREE: Interpretable Policy Learning with Adaptive Decision Trees

Alizée Pace, Alex Chan, Mihaela van der Schaar

展开摘要

Building models of human decision-making from observed behaviour is critical to better understand, diagnose and support real-world policies such as clinical care. As established policy learning approaches remain focused on imitation performance, they fall short of explaining the demonstrated decision-making process. Policy Extraction through decision Trees (POETREE) is a novel framework for interpretable policy learning, compatible with fully-offline and partially-observable clinical decision environments -- and builds probabilistic tree policies determining physician actions based on patients' observations and medical history. Fully-differentiable tree architectures are grown incrementally during optimization to adapt their complexity to the modelling task, and learn a representation of patient history through recurrence, resulting in decision tree policies that adapt over time with patient information. This policy learning method outperforms the state-of-the-art on real and synthetic medical datasets, both in terms of understanding, quantifying and evaluating observed behaviour as well as in accurately replicating it -- with potential to improve future decision support systems.

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