On Certifying Non-Uniform Bounds against Adversarial Attacks

This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded uniformly along all input features, we consider non-uniform bounds and use it to study the decision boundary of neural network models. We formulate our target as an optimization problem with nonlinear constraints. Then, a framework applicable for general feedforward neural networks is proposed to bound the output logits so that the relaxed problem can be solved by the augmented Lagrangian method. Our experiments show the non-uniform bounds have larger volumes than uniform ones and the geometric similarity of the non-uniform bounds gives a quantitative, dataagnostic metric of input features’ robustness. Further, compared with normal models, the robust models have even larger non-uniform bounds and better interpretability.

Towards Verifiable, Generalizable and Efficient Robust Deep Neural Networks.

Chen Liu

In the last decade, deep neural networks have achieved tremendous success in many fields of machine learning.However, they are shown vulnerable against adversarial attacks: well-designed, yet imperceptible, perturbations can make the state-of-the-art deep neural networks output incorrect results.Understanding adversarial attacks and designing algorithms to make deep neural networks robust against these attacks are key steps to building reliable artificial intelligence in real-life applications.In this thesis, we will first formulate the robust learning problem.Based on the notations of empirical robustness and verified robustness, we design new algorithms to achieve both of these types of robustness.Specifically, we investigate the robust learning problem from the optimization perspectives.Compared with classic empirical risk minimization, we show the slow convergence and large generalization gap in robust learning.Our theoretical and numerical analysis indicates that these challenges arise, respectively, from non-smooth loss landscapes and model's fitting hard adversarial instances.Our insights shed some light on designing algorithms for mitigating these challenges.Robust learning has other challenges, such as large model capacity requirements and high computational complexity.To solve the model capacity issue, we combine robust learning with model compression.We design an algorithm to obtain sparse and binary neural networks and make it robust.To decrease the computational complexity, we accelerate the existing adversarial training algorithm and preserve its performance stability.In addition to making models robust, our research provides other benefits.Our methods demonstrate that robust models, compared with non-robust ones, usually utilize input features in a way more similar to the way human beings use them, hence the robust models are more interpretable.To obtain verified robustness, our methods indicate the geometric similarity of the decision boundaries near data points.Our approaches towards reliable artificial intelligence can not only render deep neural networks more robust in safety-critical applications but also make us better aware of how they work.

EPFL2022

Viability evolutionary algorithms and applications to neuroscience and biology

Andrea Maesani

Evolutionary algorithms are heuristic methods that operate on a population of individuals, which represent candidate solutions to optimization problems. Individuals with better quality, or fitness, are reproduced at a higher rate than less fit individuals by recombination and mutation. This process of selection and reproduction, based on fitness, models competition between individuals and leads to survival-of-the-fittest. Although this process lays at the foundation of evolutionary algorithms, the simplistic assumption that a single criterion can describe the quality of individuals is often unmet in real world problems, where multiple objectives or constraints have to be combined in the same fitness function. Furthermore, in nature, survival-of-the-fittest does not derive uniquely from competition, but is better seen as the outcome of an ongoing process of competition in parallel to a process of elimination of non-fit individuals. To resolve this mismatch and model different criteria for individuals separately, the Viability Evolution paradigm has been proposed in the literature. While the idea was previously introduced at a conceptual level, it had not yet been put to the test and lacks experimental validation. Here, we bridged this gap and tested whether viability-inspired evolutionary algorithms could confer advantages over the traditional evolutionary computation paradigm based on fitness. We started by investigating the evolutionary dynamics of a simple viability evolutionary method, and we analyzed the diversity of evolving populations. We also showed that the additional information available to a viability-based algorithm, such as the number of non-viable individuals for each viability criteria, can be exploited during the search for achieving better performance on optimization problems. In particular, we devised viability algorithms for constrained optimization, which outperformed current state-of-the-art methods on a well-known set of constrained optimization benchmarks. Furthermore, we embedded one of our algorithms into a novel framework for predicting structures of protein assemblies at atomic resolution. Finally, we used evolutionary methods to optimize neural networks in the context of a neuroscience investigation on the role of noise in animal behaviors. Noise is a ubiquitous feature of neural systems, but how it affects behaviors is far from being fully understood. After collecting large-scale measurements of Drosophila walking, we used evolutionary algorithms to search for neural networks that could match observed patterns of Drosophila spontaneous and odor-induced walking. By combining dynamical systems analysis and simulations, we showed how a noise-mediated memory of odor exposure accounts for the observed responses. In conclusion, this thesis contributes to evolutionary computation by testing the Viability Evolution paradigm and by proposing efficient viability evolutionary algorithms for constrained optimization. Furthermore, this thesis contributes to biology, by providing a new viability-based framework for predicting protein assemblies and by elucidating a mechanism through which neural noise may shape animal behaviors.

EPFL2015

Theory of representation learning in cortical neural networks

Carlos Stein Naves de Brito

Our brain continuously self-organizes to construct and maintain an internal representation of the world based on the information arriving through sensory stimuli. Remarkably, cortical areas related to different sensory modalities appear to share the same functional unit, the neuron, and develop through the same learning mechanism, synaptic plasticity. It motivates the conjecture of a unifying theory to explain cortical representational learning across sensory modalities. In this thesis we present theories and computational models of learning and optimization in neural networks, postulating functional properties of synaptic plasticity that support the apparent universal learning capacity of cortical networks. In the past decades, a variety of theories and models have been proposed to describe receptive field formation in sensory areas. They include normative models such as sparse coding, and bottom-up models such as spike-timing dependent plasticity. We bring together candidate explanations by demonstrating that in fact a single principle is sufficient to explain receptive field development. First, we show that many representative models of sensory development are in fact implementing variations of a common principle: nonlinear Hebbian learning. Second, we reveal that nonlinear Hebbian learning is sufficient for receptive field formation through sensory inputs. A surprising result is that our findings are independent of specific details, and allow for robust predictions of the learned receptive fields. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities. The Hebbian learning theory substantiates that synaptic plasticity can be interpreted as an optimization procedure, implementing stochastic gradient descent. In stochastic gradient descent inputs arrive sequentially, as in sensory streams. However, individual data samples have very little information about the correct learning signal, and it becomes a fundamental problem to know how many samples are required for reliable synaptic changes. Through estimation theory, we develop a novel adaptive learning rate model, that adapts the magnitude of synaptic changes based on the statistics of the learning signal, enabling an optimal use of data samples. Our model has a simple implementation and demonstrates improved learning speed, making this a promising candidate for large artificial neural network applications. The model also makes predictions on how cortical plasticity may modulate synaptic plasticity for optimal learning. The optimal sampling size for reliable learning allows us to estimate optimal learning times for a given model. We apply this theory to derive analytical bounds on times for the optimization of synaptic connections. First, we show this optimization problem to have exponentially many saddle-nodes, which lead to small gradients and slow learning. Second, we show that the number of input synapses to a neuron modulates the magnitude of the initial gradient, determining the duration of learning. Our final result reveals that the learning duration increases supra-linearly with the number of synapses, suggesting an effective limit on synaptic connections and receptive field sizes in developing neural networks.

EPFL2016