Many real-world networks are directed, sparse and hierarchical, with a mixture of feed-forward an... more Many real-world networks are directed, sparse and hierarchical, with a mixture of feed-forward and feedback connections with respect to the hierarchy. Moreover, a small number of 'master' nodes are often able to drive the whole system. We study the dynamics of pattern presentation and recovery on sparse, directed, Hopfield-like neural networks using Trophic Analysis to characterise their hierarchical structure. This is a recent method which quantifies the local position of each node in a hierarchy (trophic level) as well as the global directionality of the network (trophic coherence). We show that even in a recurrent network, the state of the system can be controlled by a small subset of neurons which can be identified by their low trophic levels. We also find that performance at the pattern recovery task can be significantly improved by tuning the trophic coherence and other topological properties of the network. This may explain the relatively sparse and coherent structures observed in the animal brain, and provide insights for improving the architectures of artificial neural networks. Moreover, we expect that the principles we demonstrate here, through numerical analysis, will be relevant for a broad class of system whose underlying network structure is directed and sparse, such as biological, social or financial networks.
Out-of-Distribution (OoD) detectors based on AutoEncoder (AE) rely on an underlying assumption th... more Out-of-Distribution (OoD) detectors based on AutoEncoder (AE) rely on an underlying assumption that an AE network cannot reconstruct OoD data as good as in-distribution (ID) data when it is constructed based on ID data only. However, this assumption may be violated in practice, resulting in a degradation in detection performance. Therefore, alleviating the factors violating this assumption can potentially improve the robustness of OoD performance. Our empirical studies also show that image complexity can be another factor hindering detection performance for AE-based detectors. To cater for these issues, we propose two OoD detectors LAMAE and LAMAE+. Both can be trained without the availability of any OoD-related data. The key idea is to regularize the AE network architecture with a classifier and a label-assisted memory to confine the reconstruction of OoD data while retaining the reconstruction ability for ID data. We also adjust the reconstruction error by taking image complexity into consideration. Experimental studies show that the proposed OoD detectors can perform well on a wider range of OoD scenarios.
It has recently been shown that gradient descent learning algorithms for recurrent neural network... more It has recently been shown that gradient descent learning algorithms for recurrent neural networks can perform poorly on tasks that involve long-term dependencies. In this paper we explore this problem for a class of architectures called NARX networks, which have powerful representational capabilities. Previous work reported that gradient descent learning is more effective in NARX networks than in recurrent networks with "hidden states". We show that although NARX networks do not circumvent the problem of long-term dependencies, they can greatly improve performance on such problems. We present some experimental 'results that show that NARX networks can often retain information for two to three times as long as conventional recurrent networks.
It has recently been shown that gradient descent learning algorithms for recurrent neural network... more It has recently been shown that gradient descent learning algorithms for recurrent neural networks can perform poorly on tasks that involve long{term dependencies, i.e. those problems for which the desired output depends on inputs presented at times far in the past. In this paper we explore the long{term dependencies problem for a class of architectures called NARX recurrent neural networks, which have powerful representational capabilities. We have previously reported that gradient descent learning is more e ective in NARX networks than in recurrent neural network architectures that have \hidden states" on problems including grammatical inference and nonlinear system identi cation. Typically, the network converges much faster and generalizes better than other networks. The results in this paper are an attempt to explain this phenomenon. We present some experimental results which show that NARX networks can often retain information for two to three times as long as conventional recurrent neural networks. We show that although NARX networks do not circumvent the problem of long{term dependencies, they can greatly improve performance on long-term dependency problems . We also describe in detail some of the assumption regarding what it means to latch information robustly and suggest possible ways to loosen these assumptions.
Knowing which nodes are influential in a complex network and whether the network can be influence... more Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level information without considering the global network architecture. We use the method of Trophic Analysis to study directed networks and show that both 'influence' and 'influenceability' in directed networks depend on the hierarchical structure and the global directionality, as measured by the trophic levels and trophic coherence, respectively. We show that in directed networks trophic hierarchy can explain: the nodes that can reach the most others; where the eigenvector centrality localises; which nodes shape the behaviour in opinion or oscillator dynamics; and which strategies will be successful in generalised rock-paper-scissors games. We show, moreover, that these phenomena are mediated by the global directionality. We also highlight other structural properties of real networks related to influenceability, such as the pseudospectra, which depend on trophic coherence. These results apply to any directed network and the principles highlighted -that node hierarchy is essential for understanding network influence, mediated by global directionality -are applicable to many real-world dynamics.
In many real, directed networks, the strongly connected component of nodes which are mutually rea... more In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean degree and degree-degree correlations. And it has important implications for other properties of real networks and the dynamical behaviour of many complex systems. We find that strong connectivity depends crucially on the extent to which the network has an overall direction or hierarchical ordering -a property measured by trophic coherence. Using percolation theory, we find the critical point separating weakly and strongly connected regimes, and confirm our results on many real-world networks, including ecological, neural, trade and social networks. We show that the connectivity structure can be disrupted with minimal effort by a targeted attack on edges which run counter to the overall direction. And we illustrate with example dynamics -the SIS model, majority vote, Kuramoto oscillators and the voter model -how a small number of edge deletions can utterly change dynamical processes in a wide range of systems.
This paper aims to describe the geometrical structure and explicit expressions of family of finit... more This paper aims to describe the geometrical structure and explicit expressions of family of finitely parametrized probability densities over smooth manifold M. The geometry of family of probability densities on M are inherited from probability densities on Euclidean spaces {U α } via bundle morphisms, induced by an orientation-preserving diffeomorphisms ρ α : U α → M. Current literature inherits densities on M from tangent spaces via Riemannian exponential map exp : T x M → M; densities on M are defined locally on region where the exponential map is a diffeomorphism. We generalize this approach with an arbitrary orientation-preserving bundle morphism; we show that the dualistic geometry of family of densities on U α can be inherited to family of densities on M. Furthermore, we provide explicit expressions for parametrized probability densities on ρ α (U α ) ⊂ M. Finally, using the component densities on ρ α (U α ), we construct parametrized mixture densities on totally bounded subsets of M. We provide a description of inherited mixture product dualistic geometry of the family of mixture densities.
cs.bham.ac.uk † ,ontariotechu.ca ‡ ,glasgow.ac.uk § Abstract-Self-awareness is a crucial capabili... more cs.bham.ac.uk † ,ontariotechu.ca ‡ ,glasgow.ac.uk § Abstract-Self-awareness is a crucial capability of autonomous service-based systems that enables them to self-adapt. There are different types of self-awareness whereby certain types of knowledge are captured at various levels. We argue that effective management of the trade-offs of dependability requirements can be achieved through "seamless" switching between different levels of awareness. However, the assessment of the quality of knowledge to enable dynamic switching between self-awareness levels has not been tackled yet. We propose a general architecture that exploits symbiotic simulation in order to tackle the complexity of assessing the quality of knowledge and attaining the metaself-awareness property, wherein the system can reflect on its different levels of awareness. We conduct a thorough real-world study in the context of volunteer services. We conclude that a system made meta-self-aware using our approach achieves optimal performance by activating the most suitable awareness level. This comes at the cost of a modest computational overhead.
Galaxy groups play a significant role in explaining the evolution of the universe. Given the amou... more Galaxy groups play a significant role in explaining the evolution of the universe. Given the amounts of available survey data, automated discovery of galaxy groups is of utmost interest. We introduce a novel methodology, based on probabilistic Hough transform, for finding galaxy groups embedded in a rich background. The model takes advantage of a typical signature pattern of galaxy groups known as “fingers-of-God”. It also allows us to include prior astrophysical knowledge as an inherent part of the method. The proposed method is first tested in large scale controlled experiments with 2-D patterns and then verified on 3-D realistic mock data (comparing with the well-known friends-of-friends method used in astrophysics). The experiments suggest that our methodology is a promising new candidate for galaxy group finders developed within a machine learning framework.
Along with the great success of deep neural networks, there is also growing concern about their b... more Along with the great success of deep neural networks, there is also growing concern about their black-box nature. The interpretability issue affects people's trust on deep learning systems. It is also related to many ethical problems, e.g., algorithmic discrimination. Moreover, interpretability is a desired property for deep networks to become powerful tools in other research fields, e.g., drug discovery and genomics. In this survey, we conduct a comprehensive review of the neural network interpretability research. We first clarify the definition of interpretability as it has been used in many different contexts. Then we elaborate on the importance of interpretability and propose a novel taxonomy organized along three dimensions: type of engagement (passive vs. active interpretation approaches), the type of explanation, and the focus (from local to global interpretability). This taxonomy provides a meaningful 3D view of distribution of papers from the relevant literature as two of the dimensions are not simply categorical but allow ordinal subcategories. Finally, we summarize the existing interpretability evaluation methods and suggest possible research directions inspired by our new taxonomy.
Proceedings of the Genetic and Evolutionary Computation Conference Companion
In this work we study the generalization of Stochastic Derivative-Free Optimization (SDFO) algori... more In this work we study the generalization of Stochastic Derivative-Free Optimization (SDFO) algorithms from Euclidean spaces to Riemannian manifolds. In the literature, Riemannian adaptations of SDFO relies on the Riemannian exponential map, which imposes local restrictions. We aim to address this restriction using only the intrinsic geometry of the Riemannian manifold. We first propose Riemannian SDFO (RSDFO), a generalized framework for adapting SDFO algorithms on Euclidean spaces to Riemannian manifolds. We then propose a novel algorithm --- Extended RSDFO, and discuss its convergence behaviour on finite volume Riemann manifolds.
2021 13th International Conference on Measurement, 2021
During multi-lead ECG recording, some electrodes can be identified as broken and thus information... more During multi-lead ECG recording, some electrodes can be identified as broken and thus information from those electrodes cannot be used for the inverse problem of electrocardiography. The objective of this study is to explore the significance of individual ECG electrodes derived from the patient-specific transfer matrix for homogeneous volume conductor. Four multi-lead ECG measurement datasets with corresponding geometries were used for this study. The transfer matrices were computed using the boundary element method. The significance of individual torso electrodes for a given position of the dipole as the equivalent heart generator was assessed by the singular value decomposition of the transfer matrices for the forward and inverse problem of electrocardiography, respectively. The study showed that the position of the most significant electrodes depends on the position of the heart within the chest and the position of the dipole as an equivalent heart generator. The positions of the first 20% of the most significant electrodes for the forward and inverse problem differ from 0% to 16%.
Neural Networks (NNs) with random weights represent nowadays a topic of consolidated use in the M... more Neural Networks (NNs) with random weights represent nowadays a topic of consolidated use in the Machine Learning research community. In this contribution we focus in particular on recurrent NN models, which in a randomized setting represent a case of particular interest per se, entailing a number of intriguing research challenges primarily related to the control of the developed dynamics for the learning purposes. Framed in the Reservoir Computing paradigm, this paper aims at providing the basic elements and summarizing the recent advances on the topic of randomized recurrent NNs (divided in theoretical, architectural, deep learning and structured domain aspects), and introducing the papers accepted for the ESANN special session.
Many real-world networks are directed, sparse and hierarchical, with a mixture of feed-forward an... more Many real-world networks are directed, sparse and hierarchical, with a mixture of feed-forward and feedback connections with respect to the hierarchy. Moreover, a small number of 'master' nodes are often able to drive the whole system. We study the dynamics of pattern presentation and recovery on sparse, directed, Hopfield-like neural networks using Trophic Analysis to characterise their hierarchical structure. This is a recent method which quantifies the local position of each node in a hierarchy (trophic level) as well as the global directionality of the network (trophic coherence). We show that even in a recurrent network, the state of the system can be controlled by a small subset of neurons which can be identified by their low trophic levels. We also find that performance at the pattern recovery task can be significantly improved by tuning the trophic coherence and other topological properties of the network. This may explain the relatively sparse and coherent structures observed in the animal brain, and provide insights for improving the architectures of artificial neural networks. Moreover, we expect that the principles we demonstrate here, through numerical analysis, will be relevant for a broad class of system whose underlying network structure is directed and sparse, such as biological, social or financial networks.
Out-of-Distribution (OoD) detectors based on AutoEncoder (AE) rely on an underlying assumption th... more Out-of-Distribution (OoD) detectors based on AutoEncoder (AE) rely on an underlying assumption that an AE network cannot reconstruct OoD data as good as in-distribution (ID) data when it is constructed based on ID data only. However, this assumption may be violated in practice, resulting in a degradation in detection performance. Therefore, alleviating the factors violating this assumption can potentially improve the robustness of OoD performance. Our empirical studies also show that image complexity can be another factor hindering detection performance for AE-based detectors. To cater for these issues, we propose two OoD detectors LAMAE and LAMAE+. Both can be trained without the availability of any OoD-related data. The key idea is to regularize the AE network architecture with a classifier and a label-assisted memory to confine the reconstruction of OoD data while retaining the reconstruction ability for ID data. We also adjust the reconstruction error by taking image complexity into consideration. Experimental studies show that the proposed OoD detectors can perform well on a wider range of OoD scenarios.
It has recently been shown that gradient descent learning algorithms for recurrent neural network... more It has recently been shown that gradient descent learning algorithms for recurrent neural networks can perform poorly on tasks that involve long-term dependencies. In this paper we explore this problem for a class of architectures called NARX networks, which have powerful representational capabilities. Previous work reported that gradient descent learning is more effective in NARX networks than in recurrent networks with "hidden states". We show that although NARX networks do not circumvent the problem of long-term dependencies, they can greatly improve performance on such problems. We present some experimental 'results that show that NARX networks can often retain information for two to three times as long as conventional recurrent networks.
It has recently been shown that gradient descent learning algorithms for recurrent neural network... more It has recently been shown that gradient descent learning algorithms for recurrent neural networks can perform poorly on tasks that involve long{term dependencies, i.e. those problems for which the desired output depends on inputs presented at times far in the past. In this paper we explore the long{term dependencies problem for a class of architectures called NARX recurrent neural networks, which have powerful representational capabilities. We have previously reported that gradient descent learning is more e ective in NARX networks than in recurrent neural network architectures that have \hidden states" on problems including grammatical inference and nonlinear system identi cation. Typically, the network converges much faster and generalizes better than other networks. The results in this paper are an attempt to explain this phenomenon. We present some experimental results which show that NARX networks can often retain information for two to three times as long as conventional recurrent neural networks. We show that although NARX networks do not circumvent the problem of long{term dependencies, they can greatly improve performance on long-term dependency problems . We also describe in detail some of the assumption regarding what it means to latch information robustly and suggest possible ways to loosen these assumptions.
Knowing which nodes are influential in a complex network and whether the network can be influence... more Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level information without considering the global network architecture. We use the method of Trophic Analysis to study directed networks and show that both 'influence' and 'influenceability' in directed networks depend on the hierarchical structure and the global directionality, as measured by the trophic levels and trophic coherence, respectively. We show that in directed networks trophic hierarchy can explain: the nodes that can reach the most others; where the eigenvector centrality localises; which nodes shape the behaviour in opinion or oscillator dynamics; and which strategies will be successful in generalised rock-paper-scissors games. We show, moreover, that these phenomena are mediated by the global directionality. We also highlight other structural properties of real networks related to influenceability, such as the pseudospectra, which depend on trophic coherence. These results apply to any directed network and the principles highlighted -that node hierarchy is essential for understanding network influence, mediated by global directionality -are applicable to many real-world dynamics.
In many real, directed networks, the strongly connected component of nodes which are mutually rea... more In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean degree and degree-degree correlations. And it has important implications for other properties of real networks and the dynamical behaviour of many complex systems. We find that strong connectivity depends crucially on the extent to which the network has an overall direction or hierarchical ordering -a property measured by trophic coherence. Using percolation theory, we find the critical point separating weakly and strongly connected regimes, and confirm our results on many real-world networks, including ecological, neural, trade and social networks. We show that the connectivity structure can be disrupted with minimal effort by a targeted attack on edges which run counter to the overall direction. And we illustrate with example dynamics -the SIS model, majority vote, Kuramoto oscillators and the voter model -how a small number of edge deletions can utterly change dynamical processes in a wide range of systems.
This paper aims to describe the geometrical structure and explicit expressions of family of finit... more This paper aims to describe the geometrical structure and explicit expressions of family of finitely parametrized probability densities over smooth manifold M. The geometry of family of probability densities on M are inherited from probability densities on Euclidean spaces {U α } via bundle morphisms, induced by an orientation-preserving diffeomorphisms ρ α : U α → M. Current literature inherits densities on M from tangent spaces via Riemannian exponential map exp : T x M → M; densities on M are defined locally on region where the exponential map is a diffeomorphism. We generalize this approach with an arbitrary orientation-preserving bundle morphism; we show that the dualistic geometry of family of densities on U α can be inherited to family of densities on M. Furthermore, we provide explicit expressions for parametrized probability densities on ρ α (U α ) ⊂ M. Finally, using the component densities on ρ α (U α ), we construct parametrized mixture densities on totally bounded subsets of M. We provide a description of inherited mixture product dualistic geometry of the family of mixture densities.
cs.bham.ac.uk † ,ontariotechu.ca ‡ ,glasgow.ac.uk § Abstract-Self-awareness is a crucial capabili... more cs.bham.ac.uk † ,ontariotechu.ca ‡ ,glasgow.ac.uk § Abstract-Self-awareness is a crucial capability of autonomous service-based systems that enables them to self-adapt. There are different types of self-awareness whereby certain types of knowledge are captured at various levels. We argue that effective management of the trade-offs of dependability requirements can be achieved through "seamless" switching between different levels of awareness. However, the assessment of the quality of knowledge to enable dynamic switching between self-awareness levels has not been tackled yet. We propose a general architecture that exploits symbiotic simulation in order to tackle the complexity of assessing the quality of knowledge and attaining the metaself-awareness property, wherein the system can reflect on its different levels of awareness. We conduct a thorough real-world study in the context of volunteer services. We conclude that a system made meta-self-aware using our approach achieves optimal performance by activating the most suitable awareness level. This comes at the cost of a modest computational overhead.
Galaxy groups play a significant role in explaining the evolution of the universe. Given the amou... more Galaxy groups play a significant role in explaining the evolution of the universe. Given the amounts of available survey data, automated discovery of galaxy groups is of utmost interest. We introduce a novel methodology, based on probabilistic Hough transform, for finding galaxy groups embedded in a rich background. The model takes advantage of a typical signature pattern of galaxy groups known as “fingers-of-God”. It also allows us to include prior astrophysical knowledge as an inherent part of the method. The proposed method is first tested in large scale controlled experiments with 2-D patterns and then verified on 3-D realistic mock data (comparing with the well-known friends-of-friends method used in astrophysics). The experiments suggest that our methodology is a promising new candidate for galaxy group finders developed within a machine learning framework.
Along with the great success of deep neural networks, there is also growing concern about their b... more Along with the great success of deep neural networks, there is also growing concern about their black-box nature. The interpretability issue affects people's trust on deep learning systems. It is also related to many ethical problems, e.g., algorithmic discrimination. Moreover, interpretability is a desired property for deep networks to become powerful tools in other research fields, e.g., drug discovery and genomics. In this survey, we conduct a comprehensive review of the neural network interpretability research. We first clarify the definition of interpretability as it has been used in many different contexts. Then we elaborate on the importance of interpretability and propose a novel taxonomy organized along three dimensions: type of engagement (passive vs. active interpretation approaches), the type of explanation, and the focus (from local to global interpretability). This taxonomy provides a meaningful 3D view of distribution of papers from the relevant literature as two of the dimensions are not simply categorical but allow ordinal subcategories. Finally, we summarize the existing interpretability evaluation methods and suggest possible research directions inspired by our new taxonomy.
Proceedings of the Genetic and Evolutionary Computation Conference Companion
In this work we study the generalization of Stochastic Derivative-Free Optimization (SDFO) algori... more In this work we study the generalization of Stochastic Derivative-Free Optimization (SDFO) algorithms from Euclidean spaces to Riemannian manifolds. In the literature, Riemannian adaptations of SDFO relies on the Riemannian exponential map, which imposes local restrictions. We aim to address this restriction using only the intrinsic geometry of the Riemannian manifold. We first propose Riemannian SDFO (RSDFO), a generalized framework for adapting SDFO algorithms on Euclidean spaces to Riemannian manifolds. We then propose a novel algorithm --- Extended RSDFO, and discuss its convergence behaviour on finite volume Riemann manifolds.
2021 13th International Conference on Measurement, 2021
During multi-lead ECG recording, some electrodes can be identified as broken and thus information... more During multi-lead ECG recording, some electrodes can be identified as broken and thus information from those electrodes cannot be used for the inverse problem of electrocardiography. The objective of this study is to explore the significance of individual ECG electrodes derived from the patient-specific transfer matrix for homogeneous volume conductor. Four multi-lead ECG measurement datasets with corresponding geometries were used for this study. The transfer matrices were computed using the boundary element method. The significance of individual torso electrodes for a given position of the dipole as the equivalent heart generator was assessed by the singular value decomposition of the transfer matrices for the forward and inverse problem of electrocardiography, respectively. The study showed that the position of the most significant electrodes depends on the position of the heart within the chest and the position of the dipole as an equivalent heart generator. The positions of the first 20% of the most significant electrodes for the forward and inverse problem differ from 0% to 16%.
Neural Networks (NNs) with random weights represent nowadays a topic of consolidated use in the M... more Neural Networks (NNs) with random weights represent nowadays a topic of consolidated use in the Machine Learning research community. In this contribution we focus in particular on recurrent NN models, which in a randomized setting represent a case of particular interest per se, entailing a number of intriguing research challenges primarily related to the control of the developed dynamics for the learning purposes. Framed in the Reservoir Computing paradigm, this paper aims at providing the basic elements and summarizing the recent advances on the topic of randomized recurrent NNs (divided in theoretical, architectural, deep learning and structured domain aspects), and introducing the papers accepted for the ESANN special session.
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Papers by Peter Tino