Robustness to distributional shifts remains a critical limitation for deploying deep neural networks (DNNs) in real-world applications. While DNNs excel in standard benchmarks, their performance often deteriorates under unseen or perturbed conditions. Understanding how internal information representations relate to such robustness remains underexplored. In this work, we propose an interpretable framework for robustness assessment based on partial information decomposition (PID), which quantifies how neurons redundantly, uniquely, or synergistically encode task-relevant information. Analysis of PID measures computed from clean inputs reveals that models characterized by higher redundancy rates and lower synergy rates tend to maintain more stable performance under various natural corruptions. Additionally, a higher rate of unique information is positively associated with improved classification accuracy on the data from which the measure is computed. These findings provide new insights for understanding and comparing model behavior through internal information analysis, and highlight the feasibility of lightweight robustness assessment without requiring extensive access to corrupted data.

When training a neural network, the choice of activation function can greatly impact its performance. A function with a larger derivative may cause the coefficients of the latter layers to deviate further from the calculated direction, making deep learning more difficult to train. However, an activation function with a derivative amplitude of less than one can result in the problem of a vanishing gradient. To overcome this drawback, we propose the application of pseudo-normalization to enlarge some gradients by dividing them by the root mean square. This amplification is performed every few layers to ensure that the amplitudes are larger than one, thus avoiding the condition of vanishing gradient and preventing gradient explosion. We successfully applied this approach to several deep learning networks with hyperbolic tangent activation for image classifications. To gain a deeper understanding of the algorithm, we employed interpretability techniques to examine the network’s prediction outcomes. We discovered that, in contrast to popular networks that learn picture characteristics, the networks primarily employ the contour information of images for categorization. This suggests that our technique can be utilized in addition to other widely used algorithms.

We review aspects of entanglement entropy in the quantum mechanics of matrices, i.e., matrix quantum mechanics (MQM), at large N. In doing so, we review standard models of MQM and their relation to string theory, D-brane physics, and emergent non-commutative geometries. We overview, in generality, definitions of subsystems and entanglement entropies in theories with gauge redundancy and discuss the additional structure required for definining subsystems in MQMs possessing a gauge redundancy. In connecting these subsystems to non-commutative geometry, we review several works on ‘target space entanglement,’ and entanglement in non-commutative field theories, highlighting the conditions in which target space entanglement entropy displays an ‘area law’ at large N. We summarize several example calculations of entanglement entropy in non-commutative geometries and MQMs. We review recent work in connecting the area law entanglement of MQM to the Ryu–Takayanagi formula, highlighting the conditions in which invariance implies a minimal area formula for the entanglement entropy at large N. Finally, we make comments on open questions and research directions.

We analyze the effect of varying system conditions on the single-particle entanglement entropy for an arbitrary eigenstate of a complex system that can be described by a multiparametric Gaussian ensemble. Our theoretical analysis leads to the identification of a single functional of the system parameters that governs the entropy dynamics. This reveals a sensitivity of the entropy to collective information content, characterized by the functional, instead of the individual system details. The functional can further be used to identify the universality classes as well as a deep web of connection underlying different quantum states.

We investigate optimizing quantum tree search algorithms by employing a nested Grover Algorithm. This approach seeks to enhance results compared to previous Grover-based methods by expanding the tree of partial assignments to a specific depth and conducting a quantum search within the subset of remaining assignments. The study explores the implications and constraints of this approach, providing a foundation for quantum artificial intelligence applications. Instead of utilizing conventional heuristic functions that are incompatible with quantum tree search, we introduce the partial candidate solution, which indicates a node at a specific depth of the tree. By employing such a function, we define the concatenated oracle, which enables us to decompose the quantum tree search using Grover’s algorithm. With a branching factor of 2 and a depth of m, the costs of Grover’s algorithm are . The concatenated oracle allows us to reduce the cost to for m partial candidate solutions.

This work explores a geometric description of black holes in which spacetime terminates on a curvature-triggered hypersurface rather than extending to an interior singularity. We study the implications of a scenario in which, upon reaching a critical curvature threshold, the three-dimensional spatial geometry compresses into a thin, closed boundary identified here as the wafold. Beyond this, the manifold would no longer continue, and all mass–energy and information would be confined to the hypersurface itself. This framework combines two well-explored paths: (1) curvature-driven geometric compression, in which extreme curvature forces the bulk degrees of freedom to become supported on a thin hypersurface (without altering the underlying dimensionality of spacetime), and (2) the motivation underlying the holographic principle, namely that black-hole entropy scales with surface area rather than volume, suggesting that information is governed by a boundary geometry rather than a bulk volume. We elaborate a dimensional conversion law that would be required to describe the collapse of spatial volume into surface area as a conserved flux of geometric capacity across the wafold, and we analyze the resulting consequences of treating this hypersurface as the terminal boundary of the manifold.

As an in-depth integration of green capital chains and technological innovation chains, green fintech provides strong support for enterprises in promoting green and low-carbon development and achieving carbon neutrality. Based on relevant data from Chinese listed companies between 2014 and 2023, this study constructs indices for green fintech development and corporate carbon neutrality to empirically examine the impact of green fintech on corporate carbon neutrality. Benchmark regression results show that green fintech exerts a significantly positive effect on corporate carbon neutrality. A mediation analysis of financing incentives indicates that alleviating corporate financing constraints and reducing financial distress are effective pathways through which green fintech facilitates carbon neutrality. Furthermore, a moderating effect analysis reveals that green fintech plays a more pronounced role in enhancing carbon neutrality for enterprises with higher audit quality and larger operational scales. Accordingly, policy recommendations are proposed, focusing on establishing a green fintech service-sharing platform, providing targeted policy support, and improving carbon information disclosure mechanisms.

In continuous-variable quantum key distribution (CV-QKD) systems, information reconciliation (IR) is a crucial step that significantly affects the secret key rate (SKR). The fixed-rate error-correcting codes used in IR are highly sensitive to changes in the signal-to-noise ratio (SNR) and cannot maintain a high reconciliation efficiency in practical CV-QKD systems. To address this issue, we first propose a rate-adaptive IR protocol, namely Threshold-based IR (TIR), which changes the code rate of low-density parity-check (LDPC) codes by selectively revealing bits with lower reliability and adjusting their log-likelihood ratios (LLRs). Then, we propose a rate-adaptive IR protocol, namely Sorting-based IR (SIR), which not only adjusts the code rate according to variations in SNR, but also enables the CV-QKD systems to achieve high reconciliation efficiency over a wide range of SNRs. Furthermore, we perform an analysis of the protocols in terms of code rate, reconciliation efficiency, and complexity. The simulation results demonstrate that the proposed protocols outperform other rate-adaptive IR protocols, achieving a reconciliation efficiency higher than 98.5% in the SNR range below −20 dB and maintaining a certain SKR in long-distance transmission.

Entropic Dynamics (ED) is a framework that allows one to derive quantum theory as a Hamilton–Killing flow on the cotangent bundle of a statistical manifold. These flows are such that they preserve the symplectic and the metric geometries; they explain the linearity of quantum mechanics and the appearance of complex numbers. In this paper the ED framework is extended to deal with local gauge symmetries. More specifically, on the basis of maximum entropy methods and information geometry, for an appropriate choice of ontic variables and constraints, we derive the quantum dynamics of radiation fields interacting with charged particles.

Controllable Image Captioning (CIC) aims to generate coherent and semantically faithful textual descriptions of images while adhering to user-specified constraints. Existing methods have achieved promising results under individual constraints such as sentimental style or sentence length. However, they typically fail to handle and satisfy multiple constraints simultaneously, as the controls often interact and interfere with one another. To overcome these challenges, we propose Internal–External Multi-Agent Steering (IE-MAS) for CIC. IE-MAS introduces an internal multimodal steering (IMS) strategy to control affective coherence within the caption, and an external multi-agent collaboration system (EMCS) to guide visual grounding and contextual alignment. From an information-theoretic view, IMS reduces uncertainty in the generation process, while EMCS strengthens the dependency between captions and visual inputs, converting the length and sentiment constraints into information gains. Together, they produce a stable balance among semantic consistency, affective expression, and length control through an adaptive steering process that dynamically balances internal linguistic control and external perceptual grounding. Experimental results demonstrate that IE-MAS effectively coordinates multiple constraints, producing captions that satisfy the length constraint and are sentimental expressive and visually faithful.