Information-theoretic Function Research Articles

Intrinsic Motivation in Dynamical Control Systems

Biological systems often choose actions without an explicit reward signal, a phenomenon known as intrinsic motivation. The computational principles underlying this behavior remain poorly understood. In this study, we investigate an information-theoretic approach to intrinsic motivation, based on maximizing an agent's empowerment (the mutual information between its past actions and future states). We show that this approach generalizes previous attempts to formalize intrinsic motivation, and we provide a computationally efficient algorithm for computing the necessary quantities. We test our approach on several benchmark control problems, and we explain its success in guiding intrinsically motivated behaviors by relating our information-theoretic control function to fundamental properties of the dynamical system representing the combined agent-environment system. This opens the door for designing practical artificial, intrinsically motivated controllers and for linking animal behaviors to their dynamical properties. Published by the American Physical Society 2024

Deep spatial–spectral difference network with heterogeneous feature mutual learning for sea fog detection

Multispectral remote sensing image-based sea fog detection (SFD) is both important and challenging. Deep learning methods for SFD have become mainstream due to their powerful nonlinear learning capabilities and flexibility. However, existing methods have not fully utilized the physical difference priors in multispectral images (MSI) for SFD, making it difficult to skillfully capture the shape and appearance characteristics of sea fog, thus leading to uncertainties in SFD. We propose the spatial–spectral difference network (S2DNet), a deep encoding–decoding framework that merges inter-spectral and intra-spectral heterogeneous difference features. Specifically, inspired by physics-based difference threshold methods, we developed a physics-inspired inter-spectral difference module (PIDM) that combines feature-level difference with deep neural networks to capture the shape characteristics of sea fog. We designed the intra-spectral difference module (ISDM) using difference convolution to represent sea fog’s fine-grained and dynamic appearance information. Furthermore, inspired by multi-view learning, we propose heterogeneous feature mutual learning (HFML) that seeks robust representations by focusing on semantically invariant aspects within heterogeneous difference features, adapting to the dynamic nature of sea fog. HFML is achieved through global feature mutual learning using an adversarial procedure and local feature mutual learning supported by a novel information-theoretic objective function that links maximizing statistical correlation with expectation maximization. Experiments on two SFD datasets show that integrating physical difference priors into deep learning improves SFD. In both continuous temporal and high spatial resolution SFD tasks, S2DNet outperforms existing advanced deep learning methods. Moreover, S2DNet demonstrates stronger robustness under degraded remote sensing image conditions, highlighting its potential usefulness and practicality in real-world applications.

Topological belief space planning for active SLAM with pairwise Gaussian potentials and performance guarantees

Determining a globally optimal solution of belief space planning (BSP) in high-dimensional state spaces directly is computationally expensive, as it involves belief propagation and objective function evaluation for each candidate action. However, many problems of interest, such as active SLAM, exhibit structure that can be harnessed to expedite planning. Also, in order to choose an optimal action, an exact value of the objective function is not required as long as the actions can be sorted in the same way. In this paper we leverage these two key aspects and present the topological belief space planning (t-bsp) concept that uses topological signatures to perform this ranking for information-theoretic cost functions, considering only topologies of factor graphs that correspond to future posterior beliefs. In particular, we propose a highly efficient topological signature based on the von Neumann graph entropy that is a function of graph node degrees and supports an incremental update. We analyze it in the context of active pose SLAM and derive error bounds between the proposed topological signature and the original information-theoretic cost function. These bounds are then used to provide performance guarantees for t-bsp with respect to a given solver of the original information-theoretic BSP problem. Realistic and synthetic simulations demonstrate drastic speed-up of the proposed method with respect to the state-of-the-art methods while retaining the ability to select a near-optimal solution. A proof of concept of t-bsp is given in a small-scale real-world active SLAM experiment.

3D Information-Theoretic Analysis of the Simplest Hydrogen Abstraction Reaction.

We investigate the course of an elementary chemical reaction from the perspective of information theory in 3D space through the hypersurface of several information-theoretic (IT) functionals such as disequilibrium (D), Shannon entropy (S), Fisher information (I), and the complexity measures of Fisher-Shannon (FS) and López-Mancini-Calbet (LMC). The probe for the study is the hydrogenic identity abstraction reaction. In order to perform the analysis, the reactivity pattern of the reaction is examined by use of the aforementioned functionals of the single-particle density, which is analyzed in position (r) and momentum (p) spaces. The 3D analyses revealed interesting reactivity patterns in the neighborhood of the intrinsic reaction coordinate (IRC) path, which allow to interpret the reaction mechanism for this reaction in a novel manner. In addition, the chemically interesting regions that have been characterized through the information functionals and their complexity measures are depicted and analyzed in the framework of the three-dimensional structure of the information-theoretical data of a chemical reaction, that is, the reactant/product (R/P) complexes, the transition state (TS), and the ones that are only revealed through IT measures such as the bond-cleavage energy region (BCER), the bond-breaking/forming (B-B/F) region, and the spin-coupling (SC) process. Furthermore, focus has been placed on the diagonal part of the hypersurface of the IT functionals, aside from the IRC path itself, with the purpose of analyzing the dissociation process of the triatomic transition-state complex that has revealed other interesting features of the bond-breaking (B-B) process. In other respects, it is shown throughout the combined analyses of the 3D structure of the IT functionals in conjugated spaces that the chemically significant regions occurring at the onset of the TS are completely characterized by information-theoretic aspects of localizability (S), uniformity (D), and disorder. Further, novel regions of low complexity seem to indicate new boundaries for chemically stable complex molecules. Finally, the study reveals that the chemical reaction occurs at low-complexity regions, where the concurrent phenomena take place: bond-breaking/forming (B-B/F), bond-cleavage energy reservoirs (BCER), spin-coupling (SC), and transition state (TS).

Map point selection for visual SLAM

Simultaneous localisation and mapping (SLAM) play a vital role in autonomous robotics. Robotic platforms are often resource-constrained, and this limitation motivates resource-efficient SLAM implementations. While sparse visual SLAM algorithms offer good accuracy for modest hardware requirements, even these more scalable sparse approaches face limitations when applied to large-scale and long-term scenarios. A contributing factor is that the point clouds resulting from SLAM are inefficient to use and contain significant redundancy.This paper proposes the use of subset selection algorithms to reduce the map produced by sparse visual SLAM algorithms. Information-theoretic techniques have been applied to simpler related problems before, but they do not scale if applied to the full visual SLAM problem. This paper proposes a number of novel information-theoretic utility functions for map point selection and optimises these functions using greedy algorithms. The reduced maps are evaluated using practical data alongside an existing visual SLAM implementation (ORB-SLAM 2). Approximate selection techniques proposed in this paper achieve trajectory accuracy comparable to an offline baseline while being suitable for online use. These techniques enable the practical reduction of maps for visual SLAM with competitive trajectory accuracy.Results also demonstrate that SLAM front-end performance can significantly impact the performance of map point selection. This shows the importance of testing map point selection with a front-end implementation. To exploit this, this paper proposes an approach that includes a model of the front-end in the utility function when additional information is available. This approach outperforms alternatives on applicable datasets and highlights future research directions.

Entanglement dynamics of multi-parametric random states: a single parametric formulation

A non-ergodic quantum state of a complex system is in general random as well as multi-parametric, former due to a lack of exact information due to complexity and latter reflecting its varied behavior in different parts of the Hilbert space. An appropriate representation for the reduced density matrix of such a state is a generalized, multi-parametric Wishart ensemble with unit trace. Our theoretical analysis of these ensembles not only resolves the controversy about the growth rates of the average information entropies of the generic states but also leads to new insights in their entanglement dynamics. While the state itself is multi-parametric, we find that the growth of the average measures can be described in terms of an information-theoretic function, referred as the complexity parameter. The latter in turn leads to a common mathematical formulation of the measures for a wide range of states; it could also act as a possible tool for hierarchical arrangement of the entangled states of different systems.

Hölder Divergence-Based Reward Function for Poisson RFSs and Application to Multitarget Sensor Management

In this study, we propose a novel information theoretic reward function based on the statistical Hölder divergence. The Hölder divergence is the generalization of Cauchy-Schwarz divergence. We extend the Hölder divergence to the FISST densities, thus making it possible to use in the multi-object applications based on the RFS theory. We derive the analytic expressions for the extended Hölder divergence (EHD) for the case when the multi-target densities have the form of Poisson RFSs and apply it to the PHD filter in a sequential Monte Carlo implementation. We evaluated the performance of the proposed reward function in a multi-target sensor management problem where the next position of a moving observer is decided according to the value of the EHD-based reward function. The performance of the algorithm is compared against, in terms of OSPA metric, and it is shown that the proposed reward function is superior to other similar reward functions in multi-target sensor management literature. We also show that it is possible to adapt the management algorithm to different situations, such as static and dynamic environments.

Epistemic uncertainty aware semantic localization and mapping for inference and belief space planning

We investigate the problem of autonomous object classification and semantic SLAM, which generally exhibits a tight coupling between classification, metric SLAM, and planning under uncertainty. We contribute a unified framework for inference and belief space planning (BSP) that addresses prominent sources of uncertainty in this context: classification aliasing (classifier cannot distinguish between candidate classes from certain viewpoints), classifier epistemic uncertainty (classifier receives data “far” from its training set), and localization uncertainty (camera and object poses are uncertain). Specifically, two methods are developed for maintaining a joint distribution over robot and object poses, and over a posterior class probability vector that considers epistemic uncertainty in a Bayesian fashion. The first approach is Multi-Hybrid (MH), where multiple hybrid beliefs over poses and classes are maintained to approximate the joint belief over poses and posterior class probability. The second approach is Joint Lambda Pose (JLP), where the joint belief is maintained directly using a novel JLP factor. Furthermore, we extend both methods to BSP, while reasoning about future posterior epistemic uncertainty indirectly or directly via a novel information-theoretic reward function. Both inference methods utilize a novel viewpoint-dependent classifier uncertainty model that leverages the coupling between poses and classification scores and predicts the epistemic uncertainty from certain viewpoints. In addition, this model is used to generate predicted measurements during planning. To the best of our knowledge, this is the first work that reasons about classifier epistemic uncertainty within semantic SLAM and BSP. We extensively evaluate our inference and BSP approaches in simulation using real image data from the Active Vision Dataset. Results clearly indicate superior classification performance of our methods compared to an approach that is not epistemic uncertainty aware.

Filtering ASVs/OTUs via mutual information-based microbiome network analysis

Microbial communities are widely studied using high-throughput sequencing techniques, such as 16S rRNA gene sequencing. These techniques have attracted biologists as they offer powerful tools to explore microbial communities and investigate their patterns of diversity in biological and biomedical samples at remarkable resolution. However, the accuracy of these methods can negatively affected by the presence of contamination. Several studies have recognized that contamination is a common problem in microbial studies and have offered promising computational and laboratory-based approaches to assess and remove contaminants. Here we propose a novel strategy, MI-based (mutual information based) filtering method, which uses information theoretic functionals and graph theory to identify and remove contaminants. We applied MI-based filtering method to a mock community data set and evaluated the amount of information loss due to filtering taxa. We also compared our method to commonly practice traditional filtering methods. In a mock community data set, MI-based filtering approach maintained the true bacteria in the community without significant loss of information. Our results indicate that MI-based filtering method effectively identifies and removes contaminants in microbial communities and hence it can be beneficial as a filtering method to microbiome studies. We believe our filtering method has two advantages over traditional filtering methods. First, it does not required an arbitrary choice of threshold and second, it is able to detect true taxa with low abundance.

A discrepant information selection mechanism for cooperative sensors

Aiming at the discrepancy of information raised by different fields of view of cooperative sensors, this paper proposes a fusion rule based on a new information-theoretic cost function. Specifically, the optimal function is proposed based on the principle of Minimum Discrimination Information (MDI), where the fusion weights are the functions of the label set. The solution of the optimal function exhibits the information selection mechanism, i.e., the GLMB components of the global multitarget density are selected among the local GLMB components based on their weights. Besides, to evaluate the performance of the proposed method, we also propose the overlapping indicator which assesses the similarity among the FoVs of cooperative sensors. The simulation results demonstrate that the proposed method achieves robust performance under different values of the overlapping indicator.

CONCERTS: Coverage Competency-Based Target Search for Heterogeneous Robot Teams

This paper proposes CONCERTS: Coverage competency-based target search, a failure-resilient path-planning algorithm for heterogeneous robot teams performing target searches for static targets in indoor and outdoor environments. This work aims to improve search completion time for realistic scenarios such as search and rescue or surveillance, while maintaining the computational speed required to perform online re-planning in scenarios when teammates fail. To provide high-quality candidate paths to an information-theoretic utility function, we split the sample generation process into two steps, namely Heterogeneous Clustering (H-Clustering) and multiple Traveling Salesman Problems (TSP). The H-Clustering step generates plans that maximize the coverage potential of each team member, while the TSP step creates optimal sample paths. In situations without prior target information, we compare our method against a state-of-the-art algorithm for multi-robot Coverage Path Planning and show a 9% advantage in total mission time. Additionally, we perform experiments to demonstrate that our algorithm can take advantage of prior target information when it is available. The proposed method provides resilience in the event of single or multiple teammate failure by recomputing global team plans online. Finally, we present simulations and deploy real hardware for search to show that the generated plans are sufficient for executing realistic missions.

Autonomous Cave Surveying With an Aerial Robot

This paper presents a method for cave surveying in total darkness using an autonomous aerial vehicle equipped with a depth camera for mapping, downward-facing camera for state estimation, and forward and downward lights. Traditional methods of cave surveying are labor-intensive and dangerous due to the risk of hypothermia when collecting data over extended periods of time in cold and damp environments, the risk of injury when operating in darkness in rocky or muddy environments, and the potential structural instability of the subterranean environment. Although these dangers can be mitigated by deploying robots to map dangerous passages and voids, real-time feedback is often needed to operate robots safely and efficiently. Few state-of-the-art, high-resolution perceptual modeling techniques attempt to reduce their high bandwidth requirements to work well with low bandwidth communication channels. To bridge this gap in the state of the art, this work compactly represents sensor observations as Gaussian mixture models and maintains a local occupancy grid map for a motion planner that greedily maximizes an information-theoretic objective function. The approach accommodates both limited field of view depth cameras and larger field of view LiDAR sensors and is extensively evaluated in long duration simulations on an embedded PC. An aerial system is leveraged to demonstrate the repeatability of the approach in a flight arena as well as the effects of communication dropouts. Finally, the system is deployed in Laurel Caverns, a commercially owned and operated cave in southwestern Pennsylvania, USA, and a wild cave in West Virginia, USA.

A Deep Reinforcement Learning Approach to Sensor Placement under Uncertainty

Optimal sensor placement is critical for enhancing the effectiveness of monitoring dynamical systems. Deterministic solutions do not reflect the effects of input and parameter uncertainty on the sensor placement. Using a Markov decision process (MDP) and a sensor placement agent, this study proposes a stochastic approach to maximize the gain from placing a fixed number of sensors within the system. Utilizing Deep Reinforcement Learning (DRL), the agent is trained by collecting interactive samples within the environment, which uses an information-theoretic reward function that is a measure, based on Shannon entropy, of the identifiability of the model parameters. The goal of the agent is to maximize its expected future reward by selecting, at each step, the action (placing a sensor) that provides the most information. This framework is validated using a synthetic model of a base-isolated structure. To consider the existing uncertainty in the parameters, a prior probability distribution is chosen (e.g., based on expert judgement or preliminary study) for each model parameter. Further, a probabilistic model for the input is used to reflect input variability. In a Deep Q-network, a type of DRL algorithm, the agent learns a mapping from states (i.e., sensor configurations) to the ”quality” of each action at that state, called ”Q-values”. This network is trained using samples of state, action, and reward by interacting with the environment. The modular property of the framework and the function approximation used in this study makes it scalable to complex real-world applications of sensor placement problems in the presence of uncertainties.

Mining sequences with exceptional transition behaviour of varying order using quality measures based on information-theoretic scoring functions

Discrete Markov chains are frequently used to analyse transition behaviour in sequential data. Here, the transition probabilities can be estimated using varying order Markov chains, where order k specifies the length of the sequence history that is used to model these probabilities. Generally, such a model is fitted to the entire dataset, but in practice it is likely that some heterogeneity in the data exists and that some sequences would be better modelled with alternative parameter values, or with a Markov chain of a different order. We use the framework of Exceptional Model Mining (EMM) to discover these exceptionally behaving sequences. In particular, we propose an EMM model class that allows for discovering subgroups with transition behaviour of varying order. To that end, we propose three new quality measures based on information-theoretic scoring functions. Our findings from controlled experiments show that all three quality measures find exceptional transition behaviour of varying order and are reasonably sensitive. The quality measure based on Akaike’s Information Criterion is most robust for the number of observations. We furthermore add to existing work by seeking for subgroups of sequences, as opposite to subgroups of transitions. Since we use sequence-level descriptive attributes, we form subgroups of entire sequences, which is practically relevant in situations where you want to identify the originators of exceptional sequences, such as patients. We show this relevance by analysing sequences of blood glucose values of adult persons with diabetes type 2. In the experiments, we find subgroups of patients based on age and glycated haemoglobin (HbA1c), a measure known to correlate with average blood glucose values. Clinicians and domain experts confirmed the transition behaviour as estimated by the fitted Markov chain models.

Focus and Intensification in the Semantics of Brow Raise

We argue that in American Sign Language (ASL), Brow Raise has two sorts of functions that can be distinguished by timing: it may serve well-known information-theoretic functions that can, among others, realize focus; but it may also intensify gradable constructions – a far less well-known observation. While Brow Raise on an expression can fulfill both functions, Brow Raise right before an expression preferentially has an information-theoretic function. The main findings are replicated on some examples from LSF (French Sign Language). Strikingly, these two functions mirror those found for 'stress' (= emphasis) by Bergen 2016, who argued for a unified analysis of information-theoretic effects and of intensificational effects. We sketch a unified analysis within Alternative Semantics, and discuss a further possibility within a simplified version of Bergen's own theory of 'noise-reduction' (Bergen 2016). An extension of our ASL data shows that related generalizations hold when Brow Raise is applied to a highly iconic construction (here involving a helicopter path): depending on timing, Brow Raise may serve to evoke alternatives or to intensify part of the construction.

An Entropic Gradient Structure in the Network Dynamics of a Slime Mold

The approach to equilibrium in certain dynamical systems can be usefully described in terms of information-theoretic functionals. Well-studied models of this kind are Markov processes, chemical reaction networks, and replicator dynamics, for all of which it can be proven, under suitable assumptions, that the relative entropy (informational divergence) of the state of the system with respect to an equilibrium is nonincreasing over time. This work reviews another recent result of this type, which emerged in the study of the network optimization dynamics of an acellular slime mold, Physarum polycephalum. In this setting, not only the relative entropy of the state is nonincreasing, but its evolution over time is crucial to the stability of the entire system, and the equilibrium towards which the dynamics is attracted proves to be a global minimizer of the cost of the network.

A free-energy principle for representation learning

This paper employs a formal connection of machine learning with thermodynamics to characterize the quality of learned representations for transfer learning. We discuss how information-theoretic functionals such as rate, distortion and classification loss of a model lie on a convex, so-called, equilibrium surface. We prescribe dynamical processes to traverse this surface under specific constraints; in particular we develop an iso-classification process that trades off rate and distortion to keep the classification loss unchanged. We demonstrate how this process can be used for transferring representations from a source task to a target task while keeping the classification loss constant. Experimental validation of the theoretical results is provided on image-classification datasets.

An Information-Theoretic Framework for Unifying Active Learning Problems

This paper presents an information-theoretic framework for unifying active learning problems: level set estimation (LSE), Bayesian optimization (BO), and their generalized variant. We first introduce a novel active learning criterion that subsumes an existing LSE algorithm and achieves state-of-the-art performance in LSE problems with a continuous input domain. Then, by exploiting the relationship between LSE and BO, we design a competitive information-theoretic acquisition function for BO that has interesting connections to upper confidence bound and max-value entropy search (MES). The latter connection reveals a drawback of MES which has important implications on not only MES but also on other MES-based acquisition functions. Finally, our unifying information-theoretic framework can be applied to solve a generalized problem of LSE and BO involving multiple level sets in a data-efficient manner. We empirically evaluate the performance of our proposed algorithms using synthetic benchmark functions, a real-world dataset, and in hyperparameter tuning of machine learning models.

Top-k Ranking Bayesian Optimization

This paper presents a novel approach to top-k ranking Bayesian optimization (top-k ranking BO) which is a practical and significant generalization of preferential BO to handle top-k ranking and tie/indifference observations. We first design a surrogate model that is not only capable of catering to the above observations, but is also supported by a classic random utility model. Another equally important contribution is the introduction of the first information-theoretic acquisition function in BO with preferential observation called multinomial predictive entropy search (MPES) which is flexible in handling these observations and optimized for all inputs of a query jointly. MPES possesses superior performance compared with existing acquisition functions that select the inputs of a query one at a time greedily. We empirically evaluate the performance of MPES using several synthetic benchmark functions, CIFAR-10 dataset, and SUSHI preference dataset.

Hash Bit Selection via Collaborative Neurodynamic Optimization With Discrete Hopfield Networks.

Hash bit selection (HBS) aims to find the most discriminative and informative hash bits from a hash pool generated by using different hashing algorithms. It is usually formulated as a binary quadratic programming problem with an information-theoretic objective function and a string-length constraint. In this article, it is equivalently reformulated in the form of a quadratic unconstrained binary optimization problem by augmenting the objective function with a penalty function. The reformulated problem is solved via collaborative neurodynamic optimization (CNO) with a population of classic discrete Hopfield networks. The two most important hyperparameters of the CNO approach are determined based on Monte Carlo test results. Experimental results on three benchmark data sets are elaborated to substantiate the superiority of the collaborative neurodynamic approach to several existing methods for HBS.