Temporal networks are widely used as abstract graph representations for real-world dynamic systems. Indeed, recognizing the network evolution states is crucial in understanding and analyzing temporal networks. For instance, social networks will generate the clustering and formation of tightly-knit groups or communities over time, relying on the triadic closure theory. However, the existing methods often struggle to account for the time-varying nature of these network structures, hindering their performance when applied to networks with complex evolution states. To mitigate this problem, we propose a novel framework called ESSEN, an Evolution StateS awarE Network, to measure temporal network evolution using von Neumann entropy and thermodynamic temperature. The developed framework utilizes a von Neumann entropy aware attention mechanism and network evolution state contrastive learning in the graph encoding. In addition, it employs a unique decoder the so-called Mixture of Thermodynamic Experts (MoTE) for decoding. ESSEN extracts local and global network evolution information using thermodynamic features and adaptively recognizes the network evolution states. Moreover, the proposed method is evaluated on link prediction tasks under both transductive and inductive settings, with the corresponding results demonstrating its effectiveness compared to various state-of-the-art baselines.

As Large Language Models (LLMs) are increasingly integrated in diverse applications, obtaining reliable measures of their predictive uncertainty has become critically important. A precise distinction between aleatoric uncertainty, arising from inherent ambiguities within input data, and epistemic uncertainty, originating exclusively from model limitations, is essential to effectively address each uncertainty source. In this paper, we introduce Spectral Uncertainty, a novel approach to quantifying and decomposing uncertainties in LLMs. Leveraging the V on Neumann entropy from quantum information theory, Spectral Uncertainty provides a rigorous theoretical foundation for separating total uncertainty into distinct aleatoric and epistemic components. Unlike existing baseline methods, our approach incorporates a fine-grained representation of semantic similarity, enabling nuanced differentiation among various semantic interpretations in model responses. Empirical evaluations demonstrate that Spectral Uncertainty outperforms state-of-the-art methods in estimating both aleatoric and total uncertainty across diverse models and benchmark datasets.

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

Indeed, recognizing the network evolution states is crucial in understanding and analyzing temporal networks.

We search for efficient disentanglers on random Clifford circuits of two-qubit gates arranged in a brick-wall pattern, using the proximal policy optimization (PPO) algorithm \cite{schulman2017proximalpolicyoptimizationalgorithms}. Disentanglers are defined as a set of projective measurements inserted between consecutive entangling layers. An efficient disentangler is a set of projective measurements that minimize the averaged von Neumann entropy of the final state with the least number of total projections possible. The problem is naturally amenable to reinforcement learning techniques by taking the binary matrix representing the projective measurements along the circuit as our state, and actions as bit flipping operations on this binary matrix that add or delete measurements at specified locations. We give rewards to our agent dependent on the averaged von Neumann entropy of the final state and the configuration of measurements, such that the agent learns the optimal policy that will take him from the initial state of no measurements to the optimal measurement state that minimizes the entanglement entropy. Our results indicate that the number of measurements required to disentangle a random quantum circuit is drastically less than the numerical results of measurement-induced phase transition papers. Additionally, the reinforcement learning procedure enables us to characterize the pattern of optimal disentanglers, which is not possible in the works of measurement-induced phase transitions.

Entropy measures quantify the amount of information and correlations present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy measures. Here we propose a variational quantum algorithm for estimating the von Neumann and R\'enyi entropies, as well as the measured relative entropy and measured R\'enyi relative entropy. Our approach first parameterizes a variational formula for the measure of interest by a quantum circuit and a classical neural network, and then optimizes the resulting objective over parameter space. Numerical simulations of our quantum algorithm are provided, using a noiseless quantum simulator. The algorithm provides accurate estimates of the various entropy measures for the examples tested, which renders it as a promising approach for usage in downstream tasks.

There are important algorithms built upon a mixture of basic techniques described; for example, the Fast Fourier Transform (FFT) employs both Divide - and - Conquer and Transform - and - Conquer techniques. In this article, the evolution of a quantum algorithm (QA) is examined from a n information theory viewpoint. The complex vector entering the quantum algorithmic gate - QAG is considered as an information source both from the classical and the quantum level. The analysis of the classical and quantum information flow in Deutsch - Jozsa, Shor and Grover algorithm s is used. It is shown that QAG, based on superposition of states, quantum entanglement and interference, when acting on the input vector, stores information into the system state, minimizing the gap between classical Shannon ent ropy and quantum von Neumann entropy. Minimizing of the gap between Shannon and von Neumann entropies is considered as a termination criterion of QA computational intelligence measure. Let us discuss the main properties of classical and quantum information that in dynamic analysis of quantum algorithms are used. Additional necessary detail description of general properties of information amounts in Appendix 1 to this article is given. Any c omputation (both classical and quantum) is formally identical to a communication in time. By considering quantum computation as a communication process, it is possible to relate its efficiency to its classical communication capacity. At time, the programmer sets the computer to accomplish any one of several possible tasks. Each of these tasks can be regarded as embodying a different message. Another programmer can obtain this message by looking at the output of the computer when th e computation is finished at time . Computation based on quantum principles allows for more efficient algorithms for solving certain problems than algorithms based on pure classical principles [ 1 ]. The sender conveys the maximum information when all the message states have equal a priori probability (which also maximizes the channel capacity). In that case the mutual information (channel capacity) at the end of the computation is . Let us consider any peculiarities of information axioms and information capability of quantum computing as the dynamic evolution of QAs. If one breaks down the general unitary transformation of a QA into a number of successive unitary blocks, then the maximum capacity may be achieved only after the number of applications of the blocks. When its total value reaches the maximum possible value consistent with a given initial state o f the quantum computing, the computation is regarded as being complete (see, in details [ 2,3 ]). The classical capacity of a quantum communication channel is connected with the efficiency of quantum computing using entropic arguments [ 1 - 9 ]. This formalism allows us to derive lower bounds on the computational complexity of QA's in the most general context.

Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy~(VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.

Inspired by foundational studies in classical and quantum physics, and by information retrieval studies in quantum information theory, we prove that the notions of 'energy' and 'entropy' can be consistently introduced in human language and, more generally, in human culture. More explicitly, if energy is attributed to words according to their frequency of appearance in a text, then the ensuing energy levels are distributed non-classically, namely, they obey Bose-Einstein, rather than Maxwell-Boltzmann, statistics, as a consequence of the genuinely 'quantum indistinguishability' of the words that appear in the text. Secondly, the 'quantum entanglement' due to the way meaning is carried by a text reduces the (von Neumann) entropy of the words that appear in the text, a behaviour which cannot be explained within classical (thermodynamic or information) entropy. We claim here that this 'quantum-type behaviour is valid in general in human language', namely, any text is conceptually more concrete than the words composing it, which entails that the entropy of the overall text decreases. In addition, we provide examples taken from cognition, where quantization of energy appears in categorical perception, and from culture, where entities collaborate, thus 'entangle', to decrease overall entropy. We use these findings to propose the development of a new 'non-classical thermodynamic theory' for human cognition, which also covers broad parts of human culture and its artefacts and bridges concepts with quantum physics entities.