Detection of malicious behavior in a large network is a challenging problem for machine learning in computer security, since it requires a model with high expressive power and scalable inference. Existing solutions struggle to achieve this feat -- current cybersec-tailored approaches are still limited in expressivity, and methods successful in other domains do not scale well for large volumes of data, rendering frequent retraining impossible. This work proposes a new perspective for learning from graph data that is modeling network entity interactions as a large heterogeneous graph. High expressivity of the method is achieved with neural network architecture HMILnet that naturally models this type of data and provides theoretical guarantees. The scalability is achieved by pursuing local graph inference, i.e., classifying individual vertices and their neighborhood as independent samples. Our experiments exhibit improvement over the state-of-the-art Probabilistic Threat Propagation (PTP) algorithm, show a further threefold accuracy improvement when additional data is used, which is not possible with the PTP algorithm, and demonstrate the generalization capabilities of the method to new, previously unseen entities.
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The tolerance of an element of a combinatorial optimization problem with respect to a given optimal solution is the maximum change, i.e., decrease or increase, of its cost, such that this solution remains optimal. The bottleneck path problem, for given an edge-capacitated graph, a source, and a target, is to find the $\max$-$\min$ value of edge capacities on paths between the source and the target. For any given sample of this problem with $n$ vertices and $m$ edges, there is known the Ramaswamy-Orlin-Chakravarty's algorithm to compute an optimal path and all tolerances with respect to it in $O(m+n\log n)$ time. In this paper, for any in advance given $(n,m)$-network with distinct edge capacities and $k$ source-target pairs, we propose an $O\Big(m \alpha(m,n)+\min\big((n+k)\log n,km\big)\Big)$-time preprocessing, where $\alpha(\cdot,\cdot)$ is the inverse Ackermann function, to find in $O(k)$ time all $2k$ tolerances of an arbitrary edge with respect to some $\max\min$ paths between the paired sources and targets. To find both tolerances of all edges with respect to those optimal paths, it asymptotically improves, for some $n,m,k$, the Ramaswamy-Orlin-Chakravarty's complexity $O\big(k(m+n\log n)\big)$ up to $O(m\alpha(n,m)+km)$.
Graph neural networks (GNNs) have gained significant attention in recent years for their ability to process data that may be represented as graphs. This has prompted several studies to explore their representational capability based on the graph isomorphism task. These works inherently assume a countable node feature representation, potentially limiting their applicability. Interestingly, only a few study GNNs with uncountable node feature representation. In the paper, a novel perspective on the representational capability of GNNs is investigated across all levels$\unicode{x2014}$node-level, neighborhood-level, and graph-level$\unicode{x2014}$when the space of node feature representation is uncountable. More specifically, the strict injective and metric requirements are softly relaxed by employing a pseudometric distance on the space of input to create a soft-injective function such that distinct inputs may produce similar outputs if and only if the pseudometric deems the inputs to be sufficiently similar on some representation. As a consequence, a simple and computationally efficient soft-isomorphic relational graph convolution network (SIR-GCN) that emphasizes the contextualized transformation of neighborhood feature representations via anisotropic and dynamic message functions is proposed. A mathematical discussion on the relationship between SIR-GCN and widely used GNNs is then laid out to put the contribution into context, establishing SIR-GCN as a generalization of classical GNN methodologies. Experiments on synthetic and benchmark datasets then demonstrate the relative superiority of SIR-GCN, outperforming comparable models in node and graph property prediction tasks.
Preference-aligned robot navigation in human environments is typically achieved through learning-based approaches, utilizing user feedback or demonstrations for personalization. However, personal preferences are subject to change and might even be context-dependent. Yet traditional reinforcement learning (RL) approaches with static reward functions often fall short in adapting to these varying user preferences, inevitably reflecting demonstrations once training is completed. This paper introduces a framework that combines multi-objective reinforcement learning (MORL) with demonstration-based learning. Our approach allows for dynamic adaptation to changing user preferences without retraining. It fluently modulates between reward-defined preference objectives and the amount of demonstration data reflection. Through rigorous evaluations, including a sim-to-real transfer on two robots, we demonstrate our framework's capability to reflect user preferences accurately while achieving high navigational performance in terms of collision avoidance and goal pursuance.
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We assume no math knowledge beyond what you learned in calculus 1, and provide links to help you refresh the necessary math where needed. Note that you do not need to understand this material before you start learning to train and use deep learning in practice; rather, this material is for those who are already familiar with the basics of neural networks, and wish to deepen their understanding of the underlying math. Don't worry if you get stuck at some point along the way---just go back and reread the previous section, and try writing down and working through some examples. And if you're still stuck, we're happy to answer your questions in the Theory category at forums.fast.ai. Note: There is a reference section at the end of the paper summarizing all the key matrix calculus rules and terminology discussed here. See related articles at //explained.ai
We introduce an approach for deep reinforcement learning (RL) that improves upon the efficiency, generalization capacity, and interpretability of conventional approaches through structured perception and relational reasoning. It uses self-attention to iteratively reason about the relations between entities in a scene and to guide a model-free policy. Our results show that in a novel navigation and planning task called Box-World, our agent finds interpretable solutions that improve upon baselines in terms of sample complexity, ability to generalize to more complex scenes than experienced during training, and overall performance. In the StarCraft II Learning Environment, our agent achieves state-of-the-art performance on six mini-games -- surpassing human grandmaster performance on four. By considering architectural inductive biases, our work opens new directions for overcoming important, but stubborn, challenges in deep RL.
This paper proposes a method to modify traditional convolutional neural networks (CNNs) into interpretable CNNs, in order to clarify knowledge representations in high conv-layers of CNNs. In an interpretable CNN, each filter in a high conv-layer represents a certain object part. We do not need any annotations of object parts or textures to supervise the learning process. Instead, the interpretable CNN automatically assigns each filter in a high conv-layer with an object part during the learning process. Our method can be applied to different types of CNNs with different structures. The clear knowledge representation in an interpretable CNN can help people understand the logics inside a CNN, i.e., based on which patterns the CNN makes the decision. Experiments showed that filters in an interpretable CNN were more semantically meaningful than those in traditional CNNs.
The amount of publicly available biomedical literature has been growing rapidly in recent years, yet question answering systems still struggle to exploit the full potential of this source of data. In a preliminary processing step, many question answering systems rely on retrieval models for identifying relevant documents and passages. This paper proposes a weighted cosine distance retrieval scheme based on neural network word embeddings. Our experiments are based on publicly available data and tasks from the BioASQ biomedical question answering challenge and demonstrate significant performance gains over a wide range of state-of-the-art models.
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