arXiv daily

Machine Learning (cs.LG)

Tue, 09 May 2023

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1.FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance

Authors:Lingjiao Chen, Matei Zaharia, James Zou

Abstract: There is a rapidly growing number of large language models (LLMs) that users can query for a fee. We review the cost associated with querying popular LLM APIs, e.g. GPT-4, ChatGPT, J1-Jumbo, and find that these models have heterogeneous pricing structures, with fees that can differ by two orders of magnitude. In particular, using LLMs on large collections of queries and text can be expensive. Motivated by this, we outline and discuss three types of strategies that users can exploit to reduce the inference cost associated with using LLMs: 1) prompt adaptation, 2) LLM approximation, and 3) LLM cascade. As an example, we propose FrugalGPT, a simple yet flexible instantiation of LLM cascade which learns which combinations of LLMs to use for different queries in order to reduce cost and improve accuracy. Our experiments show that FrugalGPT can match the performance of the best individual LLM (e.g. GPT-4) with up to 98% cost reduction or improve the accuracy over GPT-4 by 4% with the same cost. The ideas and findings presented here lay a foundation for using LLMs sustainably and efficiently.

2.BARA: Efficient Incentive Mechanism with Online Reward Budget Allocation in Cross-Silo Federated Learning

Authors:Yunchao Yang, Yipeng Zhou, Miao Hu, Di Wu, Quan Z. Sheng

Abstract: Federated learning (FL) is a prospective distributed machine learning framework that can preserve data privacy. In particular, cross-silo FL can complete model training by making isolated data islands of different organizations collaborate with a parameter server (PS) via exchanging model parameters for multiple communication rounds. In cross-silo FL, an incentive mechanism is indispensable for motivating data owners to contribute their models to FL training. However, how to allocate the reward budget among different rounds is an essential but complicated problem largely overlooked by existing works. The challenge of this problem lies in the opaque feedback between reward budget allocation and model utility improvement of FL, making the optimal reward budget allocation complicated. To address this problem, we design an online reward budget allocation algorithm using Bayesian optimization named BARA (\underline{B}udget \underline{A}llocation for \underline{R}everse \underline{A}uction). Specifically, BARA can model the complicated relationship between reward budget allocation and final model accuracy in FL based on historical training records so that the reward budget allocated to each communication round is dynamically optimized so as to maximize the final model utility. We further incorporate the BARA algorithm into reverse auction-based incentive mechanisms to illustrate its effectiveness. Extensive experiments are conducted on real datasets to demonstrate that BARA significantly outperforms competitive baselines by improving model utility with the same amount of reward budget.

3.FedNoRo: Towards Noise-Robust Federated Learning by Addressing Class Imbalance and Label Noise Heterogeneity

Authors:Nannan Wu, Li Yu, Xuefeng Jiang, Kwang-Ting Cheng, Zengqiang Yan

Abstract: Federated noisy label learning (FNLL) is emerging as a promising tool for privacy-preserving multi-source decentralized learning. Existing research, relying on the assumption of class-balanced global data, might be incapable to model complicated label noise, especially in medical scenarios. In this paper, we first formulate a new and more realistic federated label noise problem where global data is class-imbalanced and label noise is heterogeneous, and then propose a two-stage framework named FedNoRo for noise-robust federated learning. Specifically, in the first stage of FedNoRo, per-class loss indicators followed by Gaussian Mixture Model are deployed for noisy client identification. In the second stage, knowledge distillation and a distance-aware aggregation function are jointly adopted for noise-robust federated model updating. Experimental results on the widely-used ICH and ISIC2019 datasets demonstrate the superiority of FedNoRo against the state-of-the-art FNLL methods for addressing class imbalance and label noise heterogeneity in real-world FL scenarios.

4.Traffic Forecasting on New Roads Unseen in the Training Data Using Spatial Contrastive Pre-Training

Authors:Arian Prabowo, Wei Shao, Hao Xue, Piotr Koniusz, Flora D. Salim

Abstract: New roads are being constructed all the time. However, the capabilities of previous deep forecasting models to generalize to new roads not seen in the training data (unseen roads) are rarely explored. In this paper, we introduce a novel setup called a spatio-temporal (ST) split to evaluate the models' capabilities to generalize to unseen roads. In this setup, the models are trained on data from a sample of roads, but tested on roads not seen in the training data. Moreover, we also present a novel framework called Spatial Contrastive Pre-Training (SCPT) where we introduce a spatial encoder module to extract latent features from unseen roads during inference time. This spatial encoder is pre-trained using contrastive learning. During inference, the spatial encoder only requires two days of traffic data on the new roads and does not require any re-training. We also show that the output from the spatial encoder can be used effectively to infer latent node embeddings on unseen roads during inference time. The SCPT framework also incorporates a new layer, named the spatially gated addition (SGA) layer, to effectively combine the latent features from the output of the spatial encoder to existing backbones. Additionally, since there is limited data on the unseen roads, we argue that it is better to decouple traffic signals to trivial-to-capture periodic signals and difficult-to-capture Markovian signals, and for the spatial encoder to only learn the Markovian signals. Finally, we empirically evaluated SCPT using the ST split setup on four real-world datasets. The results showed that adding SCPT to a backbone consistently improves forecasting performance on unseen roads. More importantly, the improvements are greater when forecasting further into the future.

5.Learnable Behavior Control: Breaking Atari Human World Records via Sample-Efficient Behavior Selection

Authors:Jiajun Fan, Yuzheng Zhuang, Yuecheng Liu, Jianye Hao, Bin Wang, Jiangcheng Zhu, Hao Wang, Shu-Tao Xia

Abstract: The exploration problem is one of the main challenges in deep reinforcement learning (RL). Recent promising works tried to handle the problem with population-based methods, which collect samples with diverse behaviors derived from a population of different exploratory policies. Adaptive policy selection has been adopted for behavior control. However, the behavior selection space is largely limited by the predefined policy population, which further limits behavior diversity. In this paper, we propose a general framework called Learnable Behavioral Control (LBC) to address the limitation, which a) enables a significantly enlarged behavior selection space via formulating a hybrid behavior mapping from all policies; b) constructs a unified learnable process for behavior selection. We introduce LBC into distributed off-policy actor-critic methods and achieve behavior control via optimizing the selection of the behavior mappings with bandit-based meta-controllers. Our agents have achieved 10077.52% mean human normalized score and surpassed 24 human world records within 1B training frames in the Arcade Learning Environment, which demonstrates our significant state-of-the-art (SOTA) performance without degrading the sample efficiency.

6.Leveraging Generative AI Models for Synthetic Data Generation in Healthcare: Balancing Research and Privacy

Authors:Aryan Jadon, Shashank Kumar

Abstract: The widespread adoption of electronic health records and digital healthcare data has created a demand for data-driven insights to enhance patient outcomes, diagnostics, and treatments. However, using real patient data presents privacy and regulatory challenges, including compliance with HIPAA and GDPR. Synthetic data generation, using generative AI models like GANs and VAEs offers a promising solution to balance valuable data access and patient privacy protection. In this paper, we examine generative AI models for creating realistic, anonymized patient data for research and training, explore synthetic data applications in healthcare, and discuss its benefits, challenges, and future research directions. Synthetic data has the potential to revolutionize healthcare by providing anonymized patient data while preserving privacy and enabling versatile applications.

7.Towards Understanding Generalization of Macro-AUC in Multi-label Learning

Authors:Guoqiang Wu, Chongxuan Li, Yilong Yin

Abstract: Macro-AUC is the arithmetic mean of the class-wise AUCs in multi-label learning and is commonly used in practice. However, its theoretical understanding is far lacking. Toward solving it, we characterize the generalization properties of various learning algorithms based on the corresponding surrogate losses w.r.t. Macro-AUC. We theoretically identify a critical factor of the dataset affecting the generalization bounds: \emph{the label-wise class imbalance}. Our results on the imbalance-aware error bounds show that the widely-used univariate loss-based algorithm is more sensitive to the label-wise class imbalance than the proposed pairwise and reweighted loss-based ones, which probably implies its worse performance. Moreover, empirical results on various datasets corroborate our theory findings. To establish it, technically, we propose a new (and more general) McDiarmid-type concentration inequality, which may be of independent interest.

8.Survey of Federated Learning Models for Spatial-Temporal Mobility Applications

Authors:Yacine Belal, Sonia Ben Mokhtar, Hamed Haddadi, Jaron Wang, Afra Mashhadi

Abstract: Federated learning involves training statistical models over edge devices such as mobile phones such that the training data is kept local. Federated Learning (FL) can serve as an ideal candidate for training spatial temporal models that rely on heterogeneous and potentially massive numbers of participants while preserving the privacy of highly sensitive location data. However, there are unique challenges involved with transitioning existing spatial temporal models to decentralized learning. In this survey paper, we review the existing literature that has proposed FL-based models for predicting human mobility, traffic prediction, community detection, location-based recommendation systems, and other spatial-temporal tasks. We describe the metrics and datasets these works have been using and create a baseline of these approaches in comparison to the centralized settings. Finally, we discuss the challenges of applying spatial-temporal models in a decentralized setting and by highlighting the gaps in the literature we provide a road map and opportunities for the research community.

9.Causal Discovery from Subsampled Time Series with Proxy Variables

Authors:Mingzhou Liu, Xinwei Sun, Lingjing Hu, Yizhou Wang

Abstract: Inferring causal structures from time series data is the central interest of many scientific inquiries. A major barrier to such inference is the problem of subsampling, i.e., the frequency of measurements is much lower than that of causal influence. To overcome this problem, numerous model-based and model-free methods have been proposed, yet either limited to the linear case or failed to establish identifiability. In this work, we propose a model-free algorithm that can identify the entire causal structure from subsampled time series, without any parametric constraint. The idea is that the challenge of subsampling arises mainly from \emph{unobserved} time steps and therefore should be handled with tools designed for unobserved variables. Among these tools, we find the proxy variable approach particularly fits, in the sense that the proxy of an unobserved variable is naturally itself at the observed time step. Following this intuition, we establish comprehensive structural identifiability results. Our method is constraint-based and requires no more regularities than common continuity and differentiability. Theoretical advantages are reflected in experimental results.

10.On the Limitations of Model Stealing with Uncertainty Quantification Models

Authors:David Pape, Sina Däubener, Thorsten Eisenhofer, Antonio Emanuele Cinà, Lea Schönherr

Abstract: Model stealing aims at inferring a victim model's functionality at a fraction of the original training cost. While the goal is clear, in practice the model's architecture, weight dimension, and original training data can not be determined exactly, leading to mutual uncertainty during stealing. In this work, we explicitly tackle this uncertainty by generating multiple possible networks and combining their predictions to improve the quality of the stolen model. For this, we compare five popular uncertainty quantification models in a model stealing task. Surprisingly, our results indicate that the considered models only lead to marginal improvements in terms of label agreement (i.e., fidelity) to the stolen model. To find the cause of this, we inspect the diversity of the model's prediction by looking at the prediction variance as a function of training iterations. We realize that during training, the models tend to have similar predictions, indicating that the network diversity we wanted to leverage using uncertainty quantification models is not (high) enough for improvements on the model stealing task.

11.How Informative is the Approximation Error from Tensor Decomposition for Neural Network Compression?

Authors:Jetze T. Schuurmans, Kim Batselier, Julian F. P. Kooij

Abstract: Tensor decompositions have been successfully applied to compress neural networks. The compression algorithms using tensor decompositions commonly minimize the approximation error on the weights. Recent work assumes the approximation error on the weights is a proxy for the performance of the model to compress multiple layers and fine-tune the compressed model. Surprisingly, little research has systematically evaluated which approximation errors can be used to make choices regarding the layer, tensor decomposition method, and level of compression. To close this gap, we perform an experimental study to test if this assumption holds across different layers and types of decompositions, and what the effect of fine-tuning is. We include the approximation error on the features resulting from a compressed layer in our analysis to test if this provides a better proxy, as it explicitly takes the data into account. We find the approximation error on the weights has a positive correlation with the performance error, before as well as after fine-tuning. Basing the approximation error on the features does not improve the correlation significantly. While scaling the approximation error commonly is used to account for the different sizes of layers, the average correlation across layers is smaller than across all choices (i.e. layers, decompositions, and level of compression) before fine-tuning. When calculating the correlation across the different decompositions, the average rank correlation is larger than across all choices. This means multiple decompositions can be considered for compression and the approximation error can be used to choose between them.

12.Towards the Characterization of Representations Learned via Capsule-based Network Architectures

Authors:Saja AL-Tawalbeh, José Oramas

Abstract: Capsule Networks (CapsNets) have been re-introduced as a more compact and interpretable alternative to standard deep neural networks. While recent efforts have proved their compression capabilities, to date, their interpretability properties have not been fully assessed. Here, we conduct a systematic and principled study towards assessing the interpretability of these types of networks. Moreover, we pay special attention towards analyzing the level to which part-whole relationships are indeed encoded within the learned representation. Our analysis in the MNIST, SVHN, PASCAL-part and CelebA datasets suggest that the representations encoded in CapsNets might not be as disentangled nor strictly related to parts-whole relationships as is commonly stated in the literature.

13.Turning Privacy-preserving Mechanisms against Federated Learning

Authors:Marco Arazzi, Mauro Conti, Antonino Nocera, Stjepan Picek

Abstract: Recently, researchers have successfully employed Graph Neural Networks (GNNs) to build enhanced recommender systems due to their capability to learn patterns from the interaction between involved entities. In addition, previous studies have investigated federated learning as the main solution to enable a native privacy-preserving mechanism for the construction of global GNN models without collecting sensitive data into a single computation unit. Still, privacy issues may arise as the analysis of local model updates produced by the federated clients can return information related to sensitive local data. For this reason, experts proposed solutions that combine federated learning with Differential Privacy strategies and community-driven approaches, which involve combining data from neighbor clients to make the individual local updates less dependent on local sensitive data. In this paper, we identify a crucial security flaw in such a configuration, and we design an attack capable of deceiving state-of-the-art defenses for federated learning. The proposed attack includes two operating modes, the first one focusing on convergence inhibition (Adversarial Mode), and the second one aiming at building a deceptive rating injection on the global federated model (Backdoor Mode). The experimental results show the effectiveness of our attack in both its modes, returning on average 60% performance detriment in all the tests on Adversarial Mode and fully effective backdoors in 93% of cases for the tests performed on Backdoor Mode.

14.Large Language Model Programs

Authors:Imanol Schlag, Sainbayar Sukhbaatar, Asli Celikyilmaz, Wen-tau Yih, Jason Weston, Jürgen Schmidhuber, Xian Li

Abstract: In recent years, large pre-trained language models (LLMs) have demonstrated the ability to follow instructions and perform novel tasks from a few examples. The possibility to parameterise an LLM through such in-context examples widens their capability at a much lower cost than finetuning. We extend this line of reasoning and present a method which further expands the capabilities of an LLM by embedding it within an algorithm or program. To demonstrate the benefits of this approach, we present an illustrative example of evidence-supported question-answering. We obtain a 6.4\% improvement over the chain of thought baseline through a more algorithmic approach without any finetuning. Furthermore, we highlight recent work from this perspective and discuss the advantages and disadvantages in comparison to the standard approaches.

15.GNNs,You can be Stronger,Deeper and Faster

Authors:Jingbo Zhou, Yixuan Du, Ruqiong Zhang, Rui Zhang, Di Jin, Carl Yang

Abstract: Graph neural networks (GNNs), a type of neural network that can learn from graph-structured data and learn the representation of nodes by aggregating their neighbors, have shown excellent performance in downstream tasks.However, it is known that the performance of graph neural networks (GNNs) degrades gradually as the number of layers increases. Based on k-hop subgraph aggregation, which is a new concept, we propose a new perspective to understand the expressive power of GNN.From this perspective, we reveal the potential causes of the performance degradation of the deep traditional GNN - aggregated subgraph overlap, and the fact that the residual-based graph neural networks in fact exploit the aggregation results of 1 to k hop subgraphs to improve the effectiveness.Further, we propose a new sampling-based node-level residual module named SDF, which is shown by theoretical derivation to obtain a superior expressive power compared to previous residual methods by using information from 1 to k hop subgraphs more flexibly. Extensive experiments show that the performance and efficiency of GNN with the SDF module outperform other methods.

16.On the Relation between Sharpness-Aware Minimization and Adversarial Robustness

Authors:Zeming Wei, Jingyu Zhu, Yihao Zhang

Abstract: We propose a novel understanding of Sharpness-Aware Minimization (SAM) in the context of adversarial robustness. In this paper, we point out that both SAM and adversarial training (AT) can be viewed as specific feature perturbations, which improve adversarial robustness. However, we note that SAM and AT are distinct in terms of perturbation strength, leading to different accuracy and robustness trade-offs. We provide theoretical evidence for these claims in a simplified model with rigorous mathematical proofs. Furthermore, we conduct experiment to demonstrate that only utilizing SAM can achieve superior adversarial robustness compared to standard training, which is an unexpected benefit. As adversarial training can suffer from a decrease in clean accuracy, we show that using SAM alone can improve robustness without sacrificing clean accuracy. Code is available at https://github.com/weizeming/SAM_AT.

17.Investigating the Corruption Robustness of Image Classifiers with Random Lp-norm Corruptions

Authors:Georg Siedel, Silvia Vock, Andrey Morozov

Abstract: Robustness is a fundamental property of machine learning classifiers to achieve safety and reliability. In the fields of adversarial robustness and formal robustness verification of image classification models, robustness is commonly defined as the stability to all input variations within an Lp-norm distance. However, robustness to random corruptions is usually improved and evaluated using variations observed in the real-world, while mathematically defined Lp-norm corruptions are rarely considered. This study investigates the use of random Lp-norm corruptions to augment the training and test data of image classifiers. We adapt an approach from the field of adversarial robustness to assess the model robustness to imperceptible random corruptions. We empirically and theoretically investigate whether robustness is transferable across different Lp-norms and derive conclusions on which Lp-norm corruptions a model should be trained and evaluated on. We find that training data augmentation with L0-norm corruptions improves corruption robustness while maintaining accuracy compared to standard training and when applied on top of selected state-of-the-art data augmentation techniques.

18.Consistent Text Categorization using Data Augmentation in e-Commerce

Authors:Guy Horowitz, Stav Yanovsky Daye, Noa Avigdor-Elgrabli, Ariel Raviv

Abstract: The categorization of massive e-Commerce data is a crucial, well-studied task, which is prevalent in industrial settings. In this work, we aim to improve an existing product categorization model that is already in use by a major web company, serving multiple applications. At its core, the product categorization model is a text classification model that takes a product title as an input and outputs the most suitable category out of thousands of available candidates. Upon a closer inspection, we found inconsistencies in the labeling of similar items. For example, minor modifications of the product title pertaining to colors or measurements majorly impacted the model's output. This phenomenon can negatively affect downstream recommendation or search applications, leading to a sub-optimal user experience. To address this issue, we propose a new framework for consistent text categorization. Our goal is to improve the model's consistency while maintaining its production-level performance. We use a semi-supervised approach for data augmentation and presents two different methods for utilizing unlabeled samples. One method relies directly on existing catalogs, while the other uses a generative model. We compare the pros and cons of each approach and present our experimental results.

19.Robust Implicit Regularization via Weight Normalization

Authors:Hung-Hsu Chou, Holger Rauhut, Rachel Ward

Abstract: Overparameterized models may have many interpolating solutions; implicit regularization refers to the hidden preference of a particular optimization method towards a certain interpolating solution among the many. A by now established line of work has shown that (stochastic) gradient descent tends to have an implicit bias towards low rank and/or sparse solutions when used to train deep linear networks, explaining to some extent why overparameterized neural network models trained by gradient descent tend to have good generalization performance in practice. However, existing theory for square-loss objectives often requires very small initialization of the trainable weights, which is at odds with the larger scale at which weights are initialized in practice for faster convergence and better generalization performance. In this paper, we aim to close this gap by incorporating and analyzing gradient descent with weight normalization, where the weight vector is reparamterized in terms of polar coordinates, and gradient descent is applied to the polar coordinates. By analyzing key invariants of the gradient flow and using Lojasiewicz's Theorem, we show that weight normalization also has an implicit bias towards sparse solutions in the diagonal linear model, but that in contrast to plain gradient descent, weight normalization enables a robust bias that persists even if the weights are initialized at practically large scale. Experiments suggest that the gains in both convergence speed and robustness of the implicit bias are improved dramatically by using weight normalization in overparameterized diagonal linear network models.

20.The emergence of clusters in self-attention dynamics

Authors:Borjan Geshkovski, Cyril Letrouit, Yury Polyanskiy, Philippe Rigollet

Abstract: Viewing Transformers as interacting particle systems, we describe the geometry of learned representations when the weights are not time dependent. We show that particles, representing tokens, tend to cluster toward particular limiting objects as time tends to infinity. The type of limiting object that emerges depends on the spectrum of the value matrix. Additionally, in the one-dimensional case we prove that the self-attention matrix converges to a low-rank Boolean matrix. The combination of these results mathematically confirms the empirical observation made by Vaswani et al. \cite{vaswani2017attention} that \emph{leaders} appear in a sequence of tokens when processed by Transformers.

21.Graph Neural Networks for Airfoil Design

Authors:Florent Bonnet

Abstract: The study of partial differential equations (PDE) through the framework of deep learning emerged a few years ago leading to the impressive approximations of simple dynamics. Graph neural networks (GNN) turned out to be very useful in those tasks by allowing the treatment of unstructured data often encountered in the field of numerical resolutions of PDE. However, the resolutions of harder PDE such as Navier-Stokes equations are still a challenging task and most of the work done on the latter concentrate either on simulating the flow around simple geometries or on qualitative results that looks physical for design purpose. In this study, we try to leverage the work done on deep learning for PDE and GNN by proposing an adaptation of a known architecture in order to tackle the task of approximating the solution of the two-dimensional steady-state incompressible Navier-Stokes equations over different airfoil geometries. In addition to that, we test our model not only on its performance over the volume but also on its performance to approximate surface quantities such as the wall shear stress or the isostatic pressure leading to the inference of global coefficients such as the lift and the drag of our airfoil in order to allow design exploration. This work takes place in a longer project that aims to approximate three dimensional steady-state solutions over industrial geometries.

22.Self-Supervised Anomaly Detection of Rogue Soil Moisture Sensors

Authors:Boje Deforce, Bart Baesens, Jan Diels, Estefanía Serral Asensio

Abstract: IoT data is a central element in the successful digital transformation of agriculture. However, IoT data comes with its own set of challenges. E.g., the risk of data contamination due to rogue sensors. A sensor is considered rogue when it provides incorrect measurements over time. To ensure correct analytical results, an essential preprocessing step when working with IoT data is the detection of such rogue sensors. Existing methods assume that well-behaving sensors are known or that a large majority of the sensors is well-behaving. However, real-world data is often completely unlabeled and voluminous, calling for self-supervised methods that can detect rogue sensors without prior information. We present a self-supervised anomalous sensor detector based on a neural network with a contrastive loss, followed by DBSCAN. A core contribution of our paper is the use of Dynamic Time Warping in the negative sampling for the triplet loss. This novelty makes the use of triplet networks feasible for anomalous sensor detection. Our method shows promising results on a challenging dataset of soil moisture sensors deployed in multiple pear orchards.

23.Balancing Privacy and Security in Federated Learning with FedGT: A Group Testing Framework

Authors:Marvin Xhemrishi, Johan Östman, Antonia Wachter-Zeh, Alexandre Graell i Amat

Abstract: We propose FedGT, a novel framework for identifying malicious clients in federated learning with secure aggregation. Inspired by group testing, the framework leverages overlapping groups of clients to detect the presence of malicious clients in the groups and to identify them via a decoding operation. The identified clients are then removed from the training of the model, which is performed over the remaining clients. FedGT strikes a balance between privacy and security, allowing for improved identification capabilities while still preserving data privacy. Specifically, the server learns the aggregated model of the clients in each group. The effectiveness of FedGT is demonstrated through extensive experiments on the MNIST and CIFAR-10 datasets, showing its ability to identify malicious clients with low misdetection and false alarm probabilities, resulting in high model utility.

24.Minimal Learning Machine for Multi-Label Learning

Authors:Joonas Hämäläinen, Amauri Souza, César L. C. Mattos, João P. P. Gomes, Tommi Kärkkäinen

Abstract: Distance-based supervised method, the minimal learning machine, constructs a predictive model from data by learning a mapping between input and output distance matrices. In this paper, we propose methods and evaluate how this technique and its core component, the distance mapping, can be adapted to multi-label learning. The proposed approach is based on combining the distance mapping with an inverse distance weighting. Although the proposal is one of the simplest methods in the multi-label learning literature, it achieves state-of-the-art performance for small to moderate-sized multi-label learning problems. Besides its simplicity, the proposed method is fully deterministic and its hyper-parameter can be selected via ranking loss-based statistic which has a closed form, thus avoiding conventional cross-validation-based hyper-parameter tuning. In addition, due to its simple linear distance mapping-based construction, we demonstrate that the proposed method can assess predictions' uncertainty for multi-label classification, which is a valuable capability for data-centric machine learning pipelines.

25.SkelEx and BoundEx: Natural Visualization of ReLU Neural Networks

Authors:Pawel Pukowski, Haiping Lu

Abstract: Despite their limited interpretability, weights and biases are still the most popular encoding of the functions learned by ReLU Neural Networks (ReLU NNs). That is why we introduce SkelEx, an algorithm to extract a skeleton of the membership functions learned by ReLU NNs, making those functions easier to interpret and analyze. To the best of our knowledge, this is the first work that considers linear regions from the perspective of critical points. As a natural follow-up, we also introduce BoundEx, which is the first analytical method known to us to extract the decision boundary from the realization of a ReLU NN. Both of those methods introduce very natural visualization tool for ReLU NNs trained on low-dimensional data.

26.SMAClite: A Lightweight Environment for Multi-Agent Reinforcement Learning

Authors:Adam Michalski, Filippos Christianos, Stefano V. Albrecht

Abstract: There is a lack of standard benchmarks for Multi-Agent Reinforcement Learning (MARL) algorithms. The Starcraft Multi-Agent Challenge (SMAC) has been widely used in MARL research, but is built on top of a heavy, closed-source computer game, StarCraft II. Thus, SMAC is computationally expensive and requires knowledge and the use of proprietary tools specific to the game for any meaningful alteration or contribution to the environment. We introduce SMAClite -- a challenge based on SMAC that is both decoupled from Starcraft II and open-source, along with a framework which makes it possible to create new content for SMAClite without any special knowledge. We conduct experiments to show that SMAClite is equivalent to SMAC, by training MARL algorithms on SMAClite and reproducing SMAC results. We then show that SMAClite outperforms SMAC in both runtime speed and memory.

27.An Algorithm For Adversary Aware Decentralized Networked MARL

Authors:Soumajyoti Sarkar

Abstract: Decentralized multi-agent reinforcement learning (MARL) algorithms have become popular in the literature since it allows heterogeneous agents to have their own reward functions as opposed to canonical multi-agent Markov Decision Process (MDP) settings which assume common reward functions over all agents. In this work, we follow the existing work on collaborative MARL where agents in a connected time varying network can exchange information among each other in order to reach a consensus. We introduce vulnerabilities in the consensus updates of existing MARL algorithms where agents can deviate from their usual consensus update, who we term as adversarial agents. We then proceed to provide an algorithm that allows non-adversarial agents to reach a consensus in the presence of adversaries under a constrained setting.

28.Deep Learning and Geometric Deep Learning: an introduction for mathematicians and physicists

Authors:R. Fioresi, F. Zanchetta

Abstract: In this expository paper we want to give a brief introduction, with few key references for further reading, to the inner functioning of the new and successfull algorithms of Deep Learning and Geometric Deep Learning with a focus on Graph Neural Networks. We go over the key ingredients for these algorithms: the score and loss function and we explain the main steps for the training of a model. We do not aim to give a complete and exhaustive treatment, but we isolate few concepts to give a fast introduction to the subject. We provide some appendices to complement our treatment discussing Kullback-Leibler divergence, regression, Multi-layer Perceptrons and the Universal Approximation Theorem.

29.Metric Space Magnitude and Generalisation in Neural Networks

Authors:Rayna Andreeva, Katharina Limbeck, Bastian Rieck, Rik Sarkar

Abstract: Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive. The purpose of this work is to quantify the learning process of deep neural networks through the lens of a novel topological invariant called magnitude. Magnitude is an isometry invariant; its properties are an active area of research as it encodes many known invariants of a metric space. We use magnitude to study the internal representations of neural networks and propose a new method for determining their generalisation capabilities. Moreover, we theoretically connect magnitude dimension and the generalisation error, and demonstrate experimentally that the proposed framework can be a good indicator of the latter.

30.Policy Gradient Methods in the Presence of Symmetries and State Abstractions

Authors:Prakash Panangaden, Sahand Rezaei-Shoshtari, Rosie Zhao, David Meger, Doina Precup

Abstract: Reinforcement learning on high-dimensional and complex problems relies on abstraction for improved efficiency and generalization. In this paper, we study abstraction in the continuous-control setting, and extend the definition of MDP homomorphisms to the setting of continuous state and action spaces. We derive a policy gradient theorem on the abstract MDP for both stochastic and deterministic policies. Our policy gradient results allow for leveraging approximate symmetries of the environment for policy optimization. Based on these theorems, we propose a family of actor-critic algorithms that are able to learn the policy and the MDP homomorphism map simultaneously, using the lax bisimulation metric. Finally, we introduce a series of environments with continuous symmetries to further demonstrate the ability of our algorithm for action abstraction in the presence of such symmetries. We demonstrate the effectiveness of our method on our environments, as well as on challenging visual control tasks from the DeepMind Control Suite. Our method's ability to utilize MDP homomorphisms for representation learning leads to improved performance, and the visualizations of the latent space clearly demonstrate the structure of the learned abstraction.