arXiv subjects

Jakub M. Tomczak

Publications and source records attributed to Jakub M. Tomczak.

At least 37 records · Page 2Linked to original sources

arXiv2022

CKConv: Continuous Kernel Convolution For Sequential Data

Conventional neural architectures for sequential data present important limitations. Recurrent networks suffer from exploding and vanishing gradients, small effective memory horizons, and must be trained sequentially. Convolutional networks are unable to handle sequences of unknown size and their memory horizon must be defined a priori. In this work, we show that all these problems can be solved by formulating convolutional kernels in CNNs as continuous functions. The resulting Continuous Kernel Convolution (CKConv) allows us to model arbitrarily long sequences in a parallel manner, within a single operation, and without relying on any form of recurrence. We show that Continuous Kernel Convolutional Networks (CKCNNs) obtain state-of-the-art results in multiple datasets, e.g., permuted MNIST, and, thanks to their continuous nature, are able to handle non-uniformly sampled datasets and irregularly-sampled data natively. CKCNNs match or perform better than neural ODEs designed for these purposes in a faster and simpler manner.

cs.LG↗

arXiv2022

FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizes

When designing Convolutional Neural Networks (CNNs), one must select the size\break of the convolutional kernels before training. Recent works show CNNs benefit from different kernel sizes at different layers, but exploring all possible combinations is unfeasible in practice. A more efficient approach is to learn the kernel size during training. However, existing works that learn the kernel size have a limited bandwidth. These approaches scale kernels by dilation, and thus the detail they can describe is limited. In this work, we propose FlexConv, a novel convolutional operation with which high bandwidth convolutional kernels of learnable kernel size can be learned at a fixed parameter cost. FlexNets model long-term dependencies without the use of pooling, achieve state-of-the-art performance on several sequential datasets, outperform recent works with learned kernel sizes, and are competitive with much deeper ResNets on image benchmark datasets. Additionally, FlexNets can be deployed at higher resolutions than those seen during training. To avoid aliasing, we propose a novel kernel parameterization with which the frequency of the kernels can be analytically controlled. Our novel kernel parameterization shows higher descriptive power and faster convergence speed than existing parameterizations. This leads to important improvements in classification accuracy.

cs.CV↗

arXiv2021

The Effects of Learning in Morphologically Evolving Robot Systems

Simultaneously evolving morphologies (bodies) and controllers (brains) of robots can cause a mismatch between the inherited body and brain in the offspring. To mitigate this problem, the addition of an infant learning period by the so-called Triangle of Life framework has been proposed relatively long ago. However, an empirical assessment is still lacking to-date. In this paper we investigate the effects of such a learning mechanism from different perspectives. Using extensive simulations we show that learning can greatly increase task performance and reduce the number of generations required to reach a certain fitness level compared to the purely evolutionary approach. Furthermore, although learning only directly affects the controllers, we demonstrate that the evolved morphologies will be also different. This provides a quantitative demonstration that changes in the brain can induce changes in the body. Finally, we examine the concept of morphological intelligence quantified by the ability of a given body to learn. We observe that the learning delta, the performance difference between the inherited and the learned brain, is growing throughout the evolutionary process. This shows that evolution is producing robots with an increasing plasticity, that is, consecutive generations are becoming better and better learners which in turn makes them better and better at the given task. All in all, our results demonstrate that the Triangle of Life is not only a concept of theoretical interest, but a system architecture with practical benefits.

cs.RO↗

arXiv2021

Storchastic: A Framework for General Stochastic Automatic Differentiation

Modelers use automatic differentiation (AD) of computation graphs to implement complex Deep Learning models without defining gradient computations. Stochastic AD extends AD to stochastic computation graphs with sampling steps, which arise when modelers handle the intractable expectations common in Reinforcement Learning and Variational Inference. However, current methods for stochastic AD are limited: They are either only applicable to continuous random variables and differentiable functions, or can only use simple but high variance score-function estimators. To overcome these limitations, we introduce Storchastic, a new framework for AD of stochastic computation graphs. Storchastic allows the modeler to choose from a wide variety of gradient estimation methods at each sampling step, to optimally reduce the variance of the gradient estimates. Furthermore, Storchastic is provably unbiased for estimation of any-order gradients, and generalizes variance reduction techniques to higher-order gradient estimates. Finally, we implement Storchastic as a PyTorch library at https://github.com/HEmile/storchastic.

stat.ML↗

arXiv2021

Invertible DenseNets with Concatenated LipSwish

We introduce Invertible Dense Networks (i-DenseNets), a more parameter efficient extension of Residual Flows. The method relies on an analysis of the Lipschitz continuity of the concatenation in DenseNets, where we enforce invertibility of the network by satisfying the Lipschitz constant. Furthermore, we propose a learnable weighted concatenation, which not only improves the model performance but also indicates the importance of the concatenated weighted representation. Additionally, we introduce the Concatenated LipSwish as activation function, for which we show how to enforce the Lipschitz condition and which boosts performance. The new architecture, i-DenseNet, out-performs Residual Flow and other flow-based models on density estimation evaluated in bits per dimension, where we utilize an equal parameter budget. Moreover, we show that the proposed model out-performs Residual Flows when trained as a hybrid model where the model is both a generative and a discriminative model.

stat.ML↗

arXiv2021

Training Deep Spiking Auto-encoders without Bursting or Dying Neurons through Regularization

Spiking neural networks are a promising approach towards next-generation models of the brain in computational neuroscience. Moreover, compared to classic artificial neural networks, they could serve as an energy-efficient deployment of AI by enabling fast computation in specialized neuromorphic hardware. However, training deep spiking neural networks, especially in an unsupervised manner, is challenging and the performance of a spiking model is significantly hindered by dead or bursting neurons. Here, we apply end-to-end learning with membrane potential-based backpropagation to a spiking convolutional auto-encoder with multiple trainable layers of leaky integrate-and-fire neurons. We propose bio-inspired regularization methods to control the spike density in latent representations. In the experiments, we show that applying regularization on membrane potential and spiking output successfully avoids both dead and bursting neurons and significantly decreases the reconstruction error of the spiking auto-encoder. Training regularized networks on the MNIST dataset yields image reconstruction quality comparable to non-spiking baseline models (deterministic and variational auto-encoder) and indicates improvement upon earlier approaches. Importantly, we show that, unlike the variational auto-encoder, the spiking latent representations display structure associated with the image class.

cs.NE↗

arXiv2021

General Invertible Transformations for Flow-based Generative Modeling

In this paper, we present a new class of invertible transformations with an application to flow-based generative models. We indicate that many well-known invertible transformations in reversible logic and reversible neural networks could be derived from our proposition. Next, we propose two new coupling layers that are important building blocks of flow-based generative models. In the experiments on digit data, we present how these new coupling layers could be used in Integer Discrete Flows (IDF), and that they achieve better results than standard coupling layers used in IDF and RealNVP.

cs.LG↗

arXiv2021

Diagnosing Vulnerability of Variational Auto-Encoders to Adversarial Attacks

In this work, we explore adversarial attacks on the Variational Autoencoders (VAE). We show how to modify data point to obtain a prescribed latent code (supervised attack) or just get a drastically different code (unsupervised attack). We examine the influence of model modifications ($β$-VAE, NVAE) on the robustness of VAEs and suggest metrics to quantify it.

cs.CR↗

arXiv2021

Invertible DenseNets

We introduce Invertible Dense Networks (i-DenseNets), a more parameter efficient alternative to Residual Flows. The method relies on an analysis of the Lipschitz continuity of the concatenation in DenseNets, where we enforce the invertibility of the network by satisfying the Lipschitz constraint. Additionally, we extend this method by proposing a learnable concatenation, which not only improves the model performance but also indicates the importance of the concatenated representation. We demonstrate the performance of i-DenseNets and Residual Flows on toy, MNIST, and CIFAR10 data. Both i-DenseNets outperform Residual Flows evaluated in negative log-likelihood, on all considered datasets under an equal parameter budget.

cs.LG↗

arXiv2020

Selecting Data Augmentation for Simulating Interventions

Machine learning models trained with purely observational data and the principle of empirical risk minimization \citep{vapnik_principles_1992} can fail to generalize to unseen domains. In this paper, we focus on the case where the problem arises through spurious correlation between the observed domains and the actual task labels. We find that many domain generalization methods do not explicitly take this spurious correlation into account. Instead, especially in more application-oriented research areas like medical imaging or robotics, data augmentation techniques that are based on heuristics are used to learn domain invariant features. To bridge the gap between theory and practice, we develop a causal perspective on the problem of domain generalization. We argue that causal concepts can be used to explain the success of data augmentation by describing how they can weaken the spurious correlation between the observed domains and the task labels. We demonstrate that data augmentation can serve as a tool for simulating interventional data. We use these theoretical insights to derive a simple algorithm that is able to select data augmentation techniques that will lead to better domain generalization.

stat.ML↗

arXiv2020

The Convolution Exponential and Generalized Sylvester Flows

This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it is guaranteed to be invertible, its inverse is straightforward to compute and the log Jacobian determinant is equal to the trace of the linear transformation. An important insight is that the exponential can be computed implicitly, which allows the use of convolutional layers. Using this insight, we develop new invertible transformations named convolution exponentials and graph convolution exponentials, which retain the equivariance of their underlying transformations. In addition, we generalize Sylvester Flows and propose Convolutional Sylvester Flows which are based on the generalization and the convolution exponential as basis change. Empirically, we show that the convolution exponential outperforms other linear transformations in generative flows on CIFAR10 and the graph convolution exponential improves the performance of graph normalizing flows. In addition, we show that Convolutional Sylvester Flows improve performance over residual flows as a generative flow model measured in log-likelihood.

cs.LG↗

arXiv2020

Learning Locomotion Skills in Evolvable Robots

The challenge of robotic reproduction -- making of new robots by recombining two existing ones -- has been recently cracked and physically evolving robot systems have come within reach. Here we address the next big hurdle: producing an adequate brain for a newborn robot. In particular, we address the task of targeted locomotion which is arguably a fundamental skill in any practical implementation. We introduce a controller architecture and a generic learning method to allow a modular robot with an arbitrary shape to learn to walk towards a target and follow this target if it moves. Our approach is validated on three robots, a spider, a gecko, and their offspring, in three real-world scenarios.

cs.AI↗

arXiv2020

ABC-Di: Approximate Bayesian Computation for Discrete Data

Many real-life problems are represented as a black-box, i.e., the internal workings are inaccessible or a closed-form mathematical expression of the likelihood function cannot be defined. For continuous random variables likelihood-free inference problems can be solved by a group of methods under the name of Approximate Bayesian Computation (ABC). However, a similar approach for discrete random variables is yet to be formulated. Here, we aim to fill this research gap. We propose to use a population-based MCMC ABC framework. Further, we present a valid Markov kernel, and propose a new kernel that is inspired by Differential Evolution. We assess the proposed approach on a problem with the known likelihood function, namely, discovering the underlying diseases based on a QMR-DT Network, and three likelihood-free inference problems: (i) the QMR-DT Network with the unknown likelihood function, (ii) learning binary neural network, and (iii) Neural Architecture Search. The obtained results indicate the high potential of the proposed framework and the superiority of the new Markov kernel.

stat.ML↗

arXiv2020

Self-Supervised Variational Auto-Encoders

Density estimation, compression and data generation are crucial tasks in artificial intelligence. Variational Auto-Encoders (VAEs) constitute a single framework to achieve these goals. Here, we present a novel class of generative models, called self-supervised Variational Auto-Encoder (selfVAE), that utilizes deterministic and discrete variational posteriors. This class of models allows to perform both conditional and unconditional sampling, while simplifying the objective function. First, we use a single self-supervised transformation as a latent variable, where a transformation is either downscaling or edge detection. Next, we consider a hierarchical architecture, i.e., multiple transformations, and we show its benefits compared to the VAE. The flexibility of selfVAE in data reconstruction finds a particularly interesting use case in data compression tasks, where we can trade-off memory for better data quality, and vice-versa. We present performance of our approach on three benchmark image data (Cifar10, Imagenette64, and CelebA).

stat.ML↗

arXiv2020

Population-based Optimization for Kinetic Parameter Identification in Glycolytic Pathway in Saccharomyces cerevisiae

Models in systems biology are mathematical descriptions of biological processes that are used to answer questions and gain a better understanding of biological phenomena. Dynamic models represent the network through rates of the production and consumption for the individual species. The ordinary differential equations that describe rates of the reactions in the model include a set of parameters. The parameters are important quantities to understand and analyze biological systems. Moreover, the perturbation of the kinetic parameters are correlated with upregulation of the system by cell-intrinsic and cell-extrinsic factors, including mutations and the environment changes. Here, we aim at using well-established models of biological pathways to identify parameter values and point their potential perturbation/deviation. We present our population-based optimization framework that is able to identify kinetic parameters in the dynamic model based on only input and output data (i.e., timecourses of selected metabolites). Our approach can deal with the identification of the non-measurable parameters as well as with discovering deviation of the parameters. We present our proposed optimization framework on the example of the well-studied glycolytic pathway in Saccharomyces cerevisiae.

q-bio.BM↗

arXiv2020

Attentive Group Equivariant Convolutional Networks

Although group convolutional networks are able to learn powerful representations based on symmetry patterns, they lack explicit means to learn meaningful relationships among them (e.g., relative positions and poses). In this paper, we present attentive group equivariant convolutions, a generalization of the group convolution, in which attention is applied during the course of convolution to accentuate meaningful symmetry combinations and suppress non-plausible, misleading ones. We indicate that prior work on visual attention can be described as special cases of our proposed framework and show empirically that our attentive group equivariant convolutional networks consistently outperform conventional group convolutional networks on benchmark image datasets. Simultaneously, we provide interpretability to the learned concepts through the visualization of equivariant attention maps.

cs.CV↗

arXiv2020

Super-resolution Variational Auto-Encoders

The framework of variational autoencoders (VAEs) provides a principled method for jointly learning latent-variable models and corresponding inference models. However, the main drawback of this approach is the blurriness of the generated images. Some studies link this effect to the objective function, namely, the (negative) log-likelihood. Here, we propose to enhance VAEs by adding a random variable that is a downscaled version of the original image and still use the log-likelihood function as the learning objective. Further, by providing the downscaled image as an input to the decoder, it can be used in a manner similar to the super-resolution. We present empirically that the proposed approach performs comparably to VAEs in terms of the negative log-likelihood, but it obtains a better FID score in data synthesis.

cs.LG↗

arXiv2020

Time Efficiency in Optimization with a Bayesian-Evolutionary Algorithm

Not all generate-and-test search algorithms are created equal. Bayesian Optimization (BO) invests a lot of computation time to generate the candidate solution that best balances the predicted value and the uncertainty given all previous data, taking increasingly more time as the number of evaluations performed grows. Evolutionary Algorithms (EA) on the other hand rely on search heuristics that typically do not depend on all previous data and can be done in constant time. Both the BO and EA community typically assess their performance as a function of the number of evaluations. However, this is unfair once we start to compare the efficiency of these classes of algorithms, as the overhead times to generate candidate solutions are significantly different. We suggest to measure the efficiency of generate-and-test search algorithms as the expected gain in the objective value per unit of computation time spent. We observe that the preference of an algorithm to be used can change after a number of function evaluations. We therefore propose a new algorithm, a combination of Bayesian optimization and an Evolutionary Algorithm, BEA for short, that starts with BO, then transfers knowledge to an EA, and subsequently runs the EA. We compare the BEA with BO and the EA. The results show that BEA outperforms both BO and the EA in terms of time efficiency, and ultimately leads to better performance on well-known benchmark objective functions with many local optima. Moreover, we test the three algorithms on nine test cases of robot learning problems and here again we find that BEA outperforms the other algorithms.

cs.NE↗