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Researcher profile

Max Welling

Max Welling contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningArtificial IntelligenceComputer Visioneess.SPInformation Theorymath.ITComputationcond-mat.stat-mechCryptography and Securityeess.IVHardware Architecturemath.DGMethodologyMultiagent SystemsNeural and Evolutionary Computingphysics.chem-phquant-phQuantitative Methods

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Published work

34 published item(s)

preprint2026arXiv

BLIPs: Bayesian Learned Interatomic Potentials

Machine Learning Interatomic Potentials (MLIPs) are becoming a central tool in simulation-based chemistry. However, like most deep learning models, MLIPs struggle to make accurate predictions on out-of-distribution data or when trained in a data-scarce regime, both common scenarios in simulation-based chemistry. Moreover, MLIPs do not provide uncertainty estimates by construction, which are fundamental to guide active learning pipelines and to ensure the accuracy of simulation results compared to quantum calculations. To address this shortcoming, we propose BLIPs: Bayesian Learned Interatomic Potentials. BLIP is a scalable, architecture-agnostic variational Bayesian framework for training or fine-tuning MLIPs, built on an adaptive version of Variational Dropout. BLIP delivers well-calibrated uncertainty estimates and minimal computational overhead for energy and forces prediction at inference time, while integrating seamlessly with (equivariant) message-passing architectures. Empirical results on simulation-based computational chemistry tasks demonstrate improved predictive accuracy with respect to standard MLIPs, and trustworthy uncertainty estimates, especially in data-scarse or heavy out-of-distribution regimes. Moreover, fine-tuning pretrained MLIPs with BLIP yields consistent performance gains and calibrated uncertainties.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Flowing with Confidence

Generative models can produce nonsensical text, unrealistic images, and unstable materials faster than simulation or human review can absorb; without per-sample confidence, trust erodes. Existing fixes run $k$ ensembles or stochastic trajectories at $k\times$ compute, measuring variability between models, not model confidence. We propose Flow Matching with Confidence (FMwC). FMwC injects input-dependent multiplicative noise at selected layers, propagates its variance through the network in closed form, and integrates it along the ODE trajectory, yielding a per-sample confidence score at standard sampling cost. The score supports multiple uses: filtering improves image quality and thermodynamic stability of crystals; editing rewinds trajectories to the points where the model commits and redirects them; and adaptive stepping concentrates ODE compute where the flow is ambiguous. We find that the confidence score correlates with the magnitude of the divergence of the learned velocity field, which gives us a window to understand the generative process, opening up surgical forms of guidance that target the moments that matter, new sampling algorithms and interpretability of generative models.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Kernel-Gradient Drifting Models

We propose kernel-gradient drifting, a one-step generative modeling framework that replaces the fixed Euclidean displacement direction in drifting models with directions induced by the kernel itself. Standard drifting is attractive because it enables fast, high-quality generation without distilling a large pretrained diffusion model, but its theory is currently understood mainly for Gaussian kernels, where the drift coincides with smoothed score matching and is identifiable. Our gradient-based reformulation exposes this score-based structure for general kernels: the resulting drift is the score difference between kernel-smoothed data and model distributions, yielding identifiability for characteristic kernels and a smoothed-KL descent interpretation of the drifting dynamics. Since kernel gradients are intrinsic tangent vectors, the same construction extends naturally to Riemannian manifolds and to discrete data via the Fisher-Rao geometry of the probability simplex. Across spherical geospatial data, promoter DNA and molecule generation, kernel-gradient drifting enables state-of-the-art one-step generation beyond the Euclidean setting without distillation.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Spontaneous symmetry breaking and Goldstone modes for deep information propagation

In physical systems, whenever a continuous symmetry is spontaneously broken, the system possesses excitations called Goldstone modes, which allow coherent information propagation over long distances and times. In this work, we study deep neural networks whose internal layers are equivariant under a continuous symmetry and may therefore support analogous Goldstone-like degrees of freedom. We demonstrate, both analytically and empirically, that these degrees of freedom enable coherent signal propagation across depth and recurrent iterations, providing a mechanism for stable information flow without relying on architectural stabilizers such as residual connections or normalization. In feedforward networks, this results in improved trainability and representational diversity across layers. In recurrent settings, we demonstrate the same mechanism is valuable for long-term memory by propagating information over recurrent iterations, thereby improving performance of RNNs and GRUs on long-sequence modeling tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Adversarial Defense via Image Denoising with Chaotic Encryption

In the literature on adversarial examples, white box and black box attacks have received the most attention. The adversary is assumed to have either full (white) or no (black) access to the defender's model. In this work, we focus on the equally practical gray box setting, assuming an attacker has partial information. We propose a novel defense that assumes everything but a private key will be made available to the attacker. Our framework uses an image denoising procedure coupled with encryption via a discretized Baker map. Extensive testing against adversarial images (e.g. FGSM, PGD) crafted using various gradients shows that our defense achieves significantly better results on CIFAR-10 and CIFAR-100 than the state-of-the-art gray box defenses in both natural and adversarial accuracy.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data

On time-series data, most causal discovery methods fit a new model whenever they encounter samples from a new underlying causal graph. However, these samples often share relevant information which is lost when following this approach. Specifically, different samples may share the dynamics which describe the effects of their causal relations. We propose Amortized Causal Discovery, a novel framework that leverages such shared dynamics to learn to infer causal relations from time-series data. This enables us to train a single, amortized model that infers causal relations across samples with different underlying causal graphs, and thus leverages the shared dynamics information. We demonstrate experimentally that this approach, implemented as a variational model, leads to significant improvements in causal discovery performance, and show how it can be extended to perform well under added noise and hidden confounding.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Bayesian Optimization for Macro Placement

Macro placement is the problem of placing memory blocks on a chip canvas. It can be formulated as a combinatorial optimization problem over sequence pairs, a representation which describes the relative positions of macros. Solving this problem is particularly challenging since the objective function is expensive to evaluate. In this paper, we develop a novel approach to macro placement using Bayesian optimization (BO) over sequence pairs. BO is a machine learning technique that uses a probabilistic surrogate model and an acquisition function that balances exploration and exploitation to efficiently optimize a black-box objective function. BO is more sample-efficient than reinforcement learning and therefore can be used with more realistic objectives. Additionally, the ability to learn from data and adapt the algorithm to the objective function makes BO an appealing alternative to other black-box optimization methods such as simulated annealing, which relies on problem-dependent heuristics and parameter-tuning. We benchmark our algorithm on the fixed-outline macro placement problem with the half-perimeter wire length objective and demonstrate competitive performance.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

E(n) Equivariant Graph Neural Networks

This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does not require computationally expensive higher-order representations in intermediate layers while it still achieves competitive or better performance. In addition, whereas existing methods are limited to equivariance on 3 dimensional spaces, our model is easily scaled to higher-dimensional spaces. We demonstrate the effectiveness of our method on dynamical systems modelling, representation learning in graph autoencoders and predicting molecular properties.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

E(n) Equivariant Normalizing Flows

This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential equation to obtain an invertible equivariant function: a continuous-time normalizing flow. We demonstrate that E-NFs considerably outperform baselines and existing methods from the literature on particle systems such as DW4 and LJ13, and on molecules from QM9 in terms of log-likelihood. To the best of our knowledge, this is the first flow that jointly generates molecule features and positions in 3D.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Equivariant Diffusion for Molecule Generation in 3D

This work introduces a diffusion model for molecule generation in 3D that is equivariant to Euclidean transformations. Our E(3) Equivariant Diffusion Model (EDM) learns to denoise a diffusion process with an equivariant network that jointly operates on both continuous (atom coordinates) and categorical features (atom types). In addition, we provide a probabilistic analysis which admits likelihood computation of molecules using our model. Experimentally, the proposed method significantly outperforms previous 3D molecular generative methods regarding the quality of generated samples and efficiency at training time.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Geometric and Physical Quantities Improve E(3) Equivariant Message Passing

Including covariant information, such as position, force, velocity or spin is important in many tasks in computational physics and chemistry. We introduce Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that generalise equivariant graph networks, such that node and edge attributes are not restricted to invariant scalars, but can contain covariant information, such as vectors or tensors. This model, composed of steerable MLPs, is able to incorporate geometric and physical information in both the message and update functions. Through the definition of steerable node attributes, the MLPs provide a new class of activation functions for general use with steerable feature fields. We discuss ours and related work through the lens of equivariant non-linear convolutions, which further allows us to pin-point the successful components of SEGNNs: non-linear message aggregation improves upon classic linear (steerable) point convolutions; steerable messages improve upon recent equivariant graph networks that send invariant messages. We demonstrate the effectiveness of our method on several tasks in computational physics and chemistry and provide extensive ablation studies.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Lie Point Symmetry Data Augmentation for Neural PDE Solvers

Neural networks are increasingly being used to solve partial differential equations (PDEs), replacing slower numerical solvers. However, a critical issue is that neural PDE solvers require high-quality ground truth data, which usually must come from the very solvers they are designed to replace. Thus, we are presented with a proverbial chicken-and-egg problem. In this paper, we present a method, which can partially alleviate this problem, by improving neural PDE solver sample complexity -- Lie point symmetry data augmentation (LPSDA). In the context of PDEs, it turns out that we are able to quantitatively derive an exhaustive list of data transformations, based on the Lie point symmetry group of the PDEs in question, something not possible in other application areas. We present this framework and demonstrate how it can easily be deployed to improve neural PDE solver sample complexity by an order of magnitude.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Mixed Variable Bayesian Optimization with Frequency Modulated Kernels

The sample efficiency of Bayesian optimization(BO) is often boosted by Gaussian Process(GP) surrogate models. However, on mixed variable spaces, surrogate models other than GPs are prevalent, mainly due to the lack of kernels which can model complex dependencies across different types of variables. In this paper, we propose the frequency modulated (FM) kernel flexibly modeling dependencies among different types of variables, so that BO can enjoy the further improved sample efficiency. The FM kernel uses distances on continuous variables to modulate the graph Fourier spectrum derived from discrete variables. However, the frequency modulation does not always define a kernel with the similarity measure behavior which returns higher values for pairs of more similar points. Therefore, we specify and prove conditions for FM kernels to be positive definite and to exhibit the similarity measure behavior. In experiments, we demonstrate the improved sample efficiency of GP BO using FM kernels (BO-FM).On synthetic problems and hyperparameter optimization problems, BO-FM outperforms competitors consistently. Also, the importance of the frequency modulation principle is empirically demonstrated on the same problems. On joint optimization of neural architectures and SGD hyperparameters, BO-FM outperforms competitors including Regularized evolution(RE) and BOHB. Remarkably, BO-FM performs better even than RE and BOHB using three times as many evaluations.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Multi-Agent MDP Homomorphic Networks

This paper introduces Multi-Agent MDP Homomorphic Networks, a class of networks that allows distributed execution using only local information, yet is able to share experience between global symmetries in the joint state-action space of cooperative multi-agent systems. In cooperative multi-agent systems, complex symmetries arise between different configurations of the agents and their local observations. For example, consider a group of agents navigating: rotating the state globally results in a permutation of the optimal joint policy. Existing work on symmetries in single agent reinforcement learning can only be generalized to the fully centralized setting, because such approaches rely on the global symmetry in the full state-action spaces, and these can result in correspondences across agents. To encode such symmetries while still allowing distributed execution we propose a factorization that decomposes global symmetries into local transformations. Our proposed factorization allows for distributing the computation that enforces global symmetries over local agents and local interactions. We introduce a multi-agent equivariant policy network based on this factorization. We show empirically on symmetric multi-agent problems that globally symmetric distributable policies improve data efficiency compared to non-equivariant baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Neural RF SLAM for unsupervised positioning and mapping with channel state information

We present a neural network architecture for jointly learning user locations and environment mapping up to isometry, in an unsupervised way, from channel state information (CSI) values with no location information. The model is based on an encoder-decoder architecture. The encoder network maps CSI values to the user location. The decoder network models the physics of propagation by parametrizing the environment using virtual anchors. It aims at reconstructing, from the encoder output and virtual anchor location, the set of time of flights (ToFs) that are extracted from CSI using super-resolution methods. The neural network task is set prediction and is accordingly trained end-to-end. The proposed model learns an interpretable latent, i.e., user location, by just enforcing a physics-based decoder. It is shown that the proposed model achieves sub-meter accuracy on synthetic ray tracing based datasets with single anchor SISO setup while recovering the environment map up to 4cm median error in a 2D environment and 15cm in a 3D environment

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Supervised Uncertainty Quantification for Segmentation with Multiple Annotations

The accurate estimation of predictive uncertainty carries importance in medical scenarios such as lung node segmentation. Unfortunately, most existing works on predictive uncertainty do not return calibrated uncertainty estimates, which could be used in practice. In this work we exploit multi-grader annotation variability as a source of 'groundtruth' aleatoric uncertainty, which can be treated as a target in a supervised learning problem. We combine this groundtruth uncertainty with a Probabilistic U-Net and test on the LIDC-IDRI lung nodule CT dataset and MICCAI2012 prostate MRI dataset. We find that we are able to improve predictive uncertainty estimates. We also find that we can improve sample accuracy and sample diversity. In real-world applications, our method could inform doctors about the confidence of the segmentation results.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Topographic VAEs learn Equivariant Capsules

In this work we seek to bridge the concepts of topographic organization and equivariance in neural networks. To accomplish this, we introduce the Topographic VAE: a novel method for efficiently training deep generative models with topographically organized latent variables. We show that such a model indeed learns to organize its activations according to salient characteristics such as digit class, width, and style on MNIST. Furthermore, through topographic organization over time (i.e. temporal coherence), we demonstrate how predefined latent space transformation operators can be encouraged for observed transformed input sequences -- a primitive form of unsupervised learned equivariance. We demonstrate that this model successfully learns sets of approximately equivariant features (i.e. "capsules") directly from sequences and achieves higher likelihood on correspondingly transforming test sequences. Equivariance is verified quantitatively by measuring the approximate commutativity of the inference network and the sequence transformations. Finally, we demonstrate approximate equivariance to complex transformations, expanding upon the capabilities of existing group equivariant neural networks.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning

This paper introduces MDP homomorphic networks for deep reinforcement learning. MDP homomorphic networks are neural networks that are equivariant under symmetries in the joint state-action space of an MDP. Current approaches to deep reinforcement learning do not usually exploit knowledge about such structure. By building this prior knowledge into policy and value networks using an equivariance constraint, we can reduce the size of the solution space. We specifically focus on group-structured symmetries (invertible transformations). Additionally, we introduce an easy method for constructing equivariant network layers numerically, so the system designer need not solve the constraints by hand, as is typically done. We construct MDP homomorphic MLPs and CNNs that are equivariant under either a group of reflections or rotations. We show that such networks converge faster than unstructured baselines on CartPole, a grid world and Pong.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Neural Augmentation of Kalman Filter with Hypernetwork for Channel Tracking

We propose Hypernetwork Kalman Filter (HKF) for tracking applications with multiple different dynamics. The HKF combines generalization power of Kalman filters with expressive power of neural networks. Instead of keeping a bank of Kalman filters and choosing one based on approximating the actual dynamics, HKF adapts itself to each dynamics based on the observed sequence. Through extensive experiments on CDL-B channel model, we show that the HKF can be used for tracking the channel over a wide range of Doppler values, matching Kalman filter performance with genie Doppler information. At high Doppler values, it achieves around 2dB gain over genie Kalman filter. The HKF generalizes well to unseen Doppler, SNR values and pilot patterns unlike LSTM, which suffers from severe performance degradation.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

RE-MIMO: Recurrent and Permutation Equivariant Neural MIMO Detection

In this paper, we present a novel neural network for MIMO symbol detection. It is motivated by several important considerations in wireless communication systems; permutation equivariance and a variable number of users. The neural detector learns an iterative decoding algorithm that is implemented as a stack of iterative units. Each iterative unit is a neural computation module comprising of 3 sub-modules: the likelihood module, the encoder module, and the predictor module. The likelihood module injects information about the generative (forward) process into the neural network. The encoder-predictor modules together update the state vector and symbol estimates. The encoder module updates the state vector and employs a transformer based attention network to handle the interactions among the users in a permutation equivariant manner. The predictor module refines the symbol estimates. The modular and permutation equivariant architecture allows for dealing with a varying number of users. The resulting neural detector architecture is unique and exhibits several desirable properties unseen in any of the previously proposed neural detectors. We compare its performance against existing methods and the results show the ability of our network to efficiently handle a variable number of transmitters with high accuracy.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC

Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. However, a major limitation of HMC is its inability to be applied to discrete domains due to the lack of gradient signal. In this work, we introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions using a combination of neural transport methods like normalizing flows and variational dequantization, and the Metropolis-Hastings rule. Our method first learns a continuous embedding of the discrete space using a surjective map and subsequently learns a bijective transformation from the continuous space to an approximately Gaussian distributed latent variable. Sampling proceeds by simulating MCMC chains in the latent space and mapping these samples to the target discrete space via the learned transformations. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning

In this work we develop a quantum field theory formalism for deep learning, where input signals are encoded in Gaussian states, a generalization of Gaussian processes which encode the agent's uncertainty about the input signal. We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles, dubbed ``Hintons''. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing, and provides quantum deformations of neural networks that can be run efficiently on those devices. Finally, we discuss a semi-classical limit of the quantum deformed models which is amenable to classical simulation.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A Data and Compute Efficient Design for Limited-Resources Deep Learning

Thanks to their improved data efficiency, equivariant neural networks have gained increased interest in the deep learning community. They have been successfully applied in the medical domain where symmetries in the data can be effectively exploited to build more accurate and robust models. To be able to reach a much larger body of patients, mobile, on-device implementations of deep learning solutions have been developed for medical applications. However, equivariant models are commonly implemented using large and computationally expensive architectures, not suitable to run on mobile devices. In this work, we design and test an equivariant version of MobileNetV2 and further optimize it with model quantization to enable more efficient inference. We achieve close-to state of the art performance on the Patch Camelyon (PCam) medical dataset while being more computationally efficient.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Batch-Shaping for Learning Conditional Channel Gated Networks

We present a method that trains large capacity neural networks with significantly improved accuracy and lower dynamic computational cost. We achieve this by gating the deep-learning architecture on a fine-grained-level. Individual convolutional maps are turned on/off conditionally on features in the network. To achieve this, we introduce a new residual block architecture that gates convolutional channels in a fine-grained manner. We also introduce a generally applicable tool $batch$-$shaping$ that matches the marginal aggregate posteriors of features in a neural network to a pre-specified prior distribution. We use this novel technique to force gates to be more conditional on the data. We present results on CIFAR-10 and ImageNet datasets for image classification, and Cityscapes for semantic segmentation. Our results show that our method can slim down large architectures conditionally, such that the average computational cost on the data is on par with a smaller architecture, but with higher accuracy. In particular, on ImageNet, our ResNet50 and ResNet34 gated networks obtain 74.60% and 72.55% top-1 accuracy compared to the 69.76% accuracy of the baseline ResNet18 model, for similar complexity. We also show that the resulting networks automatically learn to use more features for difficult examples and fewer features for simple examples.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Contrastive Learning of Structured World Models

A structured understanding of our world in terms of objects, relations, and hierarchies is an important component of human cognition. Learning such a structured world model from raw sensory data remains a challenge. As a step towards this goal, we introduce Contrastively-trained Structured World Models (C-SWMs). C-SWMs utilize a contrastive approach for representation learning in environments with compositional structure. We structure each state embedding as a set of object representations and their relations, modeled by a graph neural network. This allows objects to be discovered from raw pixel observations without direct supervision as part of the learning process. We evaluate C-SWMs on compositional environments involving multiple interacting objects that can be manipulated independently by an agent, simple Atari games, and a multi-object physics simulation. Our experiments demonstrate that C-SWMs can overcome limitations of models based on pixel reconstruction and outperform typical representatives of this model class in highly structured environments, while learning interpretable object-based representations.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Estimating Gradients for Discrete Random Variables by Sampling without Replacement

We derive an unbiased estimator for expectations over discrete random variables based on sampling without replacement, which reduces variance as it avoids duplicate samples. We show that our estimator can be derived as the Rao-Blackwellization of three different estimators. Combining our estimator with REINFORCE, we obtain a policy gradient estimator and we reduce its variance using a built-in control variate which is obtained without additional model evaluations. The resulting estimator is closely related to other gradient estimators. Experiments with a toy problem, a categorical Variational Auto-Encoder and a structured prediction problem show that our estimator is the only estimator that is consistently among the best estimators in both high and low entropy settings.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Federated Learning of User Authentication Models

Machine learning-based User Authentication (UA) models have been widely deployed in smart devices. UA models are trained to map input data of different users to highly separable embedding vectors, which are then used to accept or reject new inputs at test time. Training UA models requires having direct access to the raw inputs and embedding vectors of users, both of which are privacy-sensitive information. In this paper, we propose Federated User Authentication (FedUA), a framework for privacy-preserving training of UA models. FedUA adopts federated learning framework to enable a group of users to jointly train a model without sharing the raw inputs. It also allows users to generate their embeddings as random binary vectors, so that, unlike the existing approach of constructing the spread out embeddings by the server, the embedding vectors are kept private as well. We show our method is privacy-preserving, scalable with number of users, and allows new users to be added to training without changing the output layer. Our experimental results on the VoxCeleb dataset for speaker verification shows our method reliably rejects data of unseen users at very high true positive rates.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Gradient $\ell_1$ Regularization for Quantization Robustness

We analyze the effect of quantizing weights and activations of neural networks on their loss and derive a simple regularization scheme that improves robustness against post-training quantization. By training quantization-ready networks, our approach enables storing a single set of weights that can be quantized on-demand to different bit-widths as energy and memory requirements of the application change. Unlike quantization-aware training using the straight-through estimator that only targets a specific bit-width and requires access to training data and pipeline, our regularization-based method paves the way for "on the fly'' post-training quantization to various bit-widths. We show that by modeling quantization as a $\ell_\infty$-bounded perturbation, the first-order term in the loss expansion can be regularized using the $\ell_1$-norm of gradients. We experimentally validate the effectiveness of our regularization scheme on different architectures on CIFAR-10 and ImageNet datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Graph Refinement based Airway Extraction using Mean-Field Networks and Graph Neural Networks

Graph refinement, or the task of obtaining subgraphs of interest from over-complete graphs, can have many varied applications. In this work, we extract trees or collection of sub-trees from image data by, first deriving a graph-based representation of the volumetric data and then, posing the tree extraction as a graph refinement task. We present two methods to perform graph refinement. First, we use mean-field approximation (MFA) to approximate the posterior density over the subgraphs from which the optimal subgraph of interest can be estimated. Mean field networks (MFNs) are used for inference based on the interpretation that iterations of MFA can be seen as feed-forward operations in a neural network. This allows us to learn the model parameters using gradient descent. Second, we present a supervised learning approach using graph neural networks (GNNs) which can be seen as generalisations of MFNs. Subgraphs are obtained by training a GNN-based graph refinement model to directly predict edge probabilities. We discuss connections between the two classes of methods and compare them for the task of extracting airways from 3D, low-dose, chest CT data. We show that both the MFN and GNN models show significant improvement when compared to one baseline method, that is similar to a top performing method in the EXACT'09 Challenge, and a 3D U-Net based airway segmentation model, in detecting more branches with fewer false positives.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Guided Variational Autoencoder for Disentanglement Learning

We propose an algorithm, guided variational autoencoder (Guided-VAE), that is able to learn a controllable generative model by performing latent representation disentanglement learning. The learning objective is achieved by providing signals to the latent encoding/embedding in VAE without changing its main backbone architecture, hence retaining the desirable properties of the VAE. We design an unsupervised strategy and a supervised strategy in Guided-VAE and observe enhanced modeling and controlling capability over the vanilla VAE. In the unsupervised strategy, we guide the VAE learning by introducing a lightweight decoder that learns latent geometric transformation and principal components; in the supervised strategy, we use an adversarial excitation and inhibition mechanism to encourage the disentanglement of the latent variables. Guided-VAE enjoys its transparency and simplicity for the general representation learning task, as well as disentanglement learning. On a number of experiments for representation learning, improved synthesis/sampling, better disentanglement for classification, and reduced classification errors in meta-learning have been observed.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Involutive MCMC: a Unifying Framework

Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. The field has developed a broad spectrum of algorithms, varying in the way they are motivated, the way they are applied and how efficiently they sample. Despite all the differences, many of them share the same core principle, which we unify as the Involutive MCMC (iMCMC) framework. Building upon this, we describe a wide range of MCMC algorithms in terms of iMCMC, and formulate a number of "tricks" which one can use as design principles for developing new MCMC algorithms. Thus, iMCMC provides a unified view of many known MCMC algorithms, which facilitates the derivation of powerful extensions. We demonstrate the latter with two examples where we transform known reversible MCMC algorithms into more efficient irreversible ones.

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preprint2020arXiv

Plannable Approximations to MDP Homomorphisms: Equivariance under Actions

This work exploits action equivariance for representation learning in reinforcement learning. Equivariance under actions states that transitions in the input space are mirrored by equivalent transitions in latent space, while the map and transition functions should also commute. We introduce a contrastive loss function that enforces action equivariance on the learned representations. We prove that when our loss is zero, we have a homomorphism of a deterministic Markov Decision Process (MDP). Learning equivariant maps leads to structured latent spaces, allowing us to build a model on which we plan through value iteration. We show experimentally that for deterministic MDPs, the optimal policy in the abstract MDP can be successfully lifted to the original MDP. Moreover, the approach easily adapts to changes in the goal states. Empirically, we show that in such MDPs, we obtain better representations in fewer epochs compared to representation learning approaches using reconstructions, while generalizing better to new goals than model-free approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Relational Generalized Few-Shot Learning

Transferring learned models to novel tasks is a challenging problem, particularly if only very few labeled examples are available. Although this few-shot learning setup has received a lot of attention recently, most proposed methods focus on discriminating novel classes only. Instead, we consider the extended setup of generalized few-shot learning (GFSL), where the model is required to perform classification on the joint label space consisting of both previously seen and novel classes. We propose a graph-based framework that explicitly models relationships between all seen and novel classes in the joint label space. Our model Graph-convolutional Global Prototypical Networks (GcGPN) incorporates these inter-class relations using graph-convolution in order to embed novel class representations into the existing space of previously seen classes in a globally consistent manner. Our approach ensures both fast adaptation and global discrimination, which is the major challenge in GFSL. We demonstrate the benefits of our model on two challenging benchmark datasets.

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preprint2020arXiv

To Relieve Your Headache of Training an MRF, Take AdVIL

We propose a black-box algorithm called {\it Adversarial Variational Inference and Learning} (AdVIL) to perform inference and learning on a general Markov random field (MRF). AdVIL employs two variational distributions to approximately infer the latent variables and estimate the partition function of an MRF, respectively. The two variational distributions provide an estimate of the negative log-likelihood of the MRF as a minimax optimization problem, which is solved by stochastic gradient descent. AdVIL is proven convergent under certain conditions. On one hand, compared with contrastive divergence, AdVIL requires a minimal assumption about the model structure and can deal with a broader family of MRFs. On the other hand, compared with existing black-box methods, AdVIL provides a tighter estimate of the log partition function and achieves much better empirical results.

0 citations0 reviewsNo code linkedOpen access