Jiang Zhang

The pursuit of self-evolving AI raises a critical question: when is autonomous self-improvement sustainable rather than degenerative? Drawing an analogy to von Neumann’s complexity threshold for self-reproducing automata, we argue that sustainable recursive self-improvement in large language models (LLMs) requires a functional analogue: introspection—the system’s capacity to simulate its own operations and target modifications. Grounded in Kleene’s Second Recursion Theorem, we construct such introspective self-improvement programs and prove their key properties: completeness of self-modification, necessity of the reflective architecture, undecidability of improvement in general, and equivalence with Schmidhuber’s Gödel machine under a rewrite-equivalence notion, which transfers the global optimality guarantee. An empirical review, organized around these functional criteria, suggests that current LLMs exhibit only quasi-introspection.The available evidence does not establish complete introspection in the formal sense developed here, while pointing to several candidate structural bottlenecks, including incomplete self-access, feedforward processing, and limited computational depth. We outline architectural paths toward the threshold and discuss the safety implications of crossing it.

Causal emergence (CE) based on effective information (EI) demonstrates that macrostates can exhibit stronger causal effects than microstates in dynamics. However, the identification of CE and the maximization of EI both rely on coarse-graining strategies, which is a key challenge. A recently proposed CE framework based on approximate dynamical reversibility, utilizing singular-value decomposition (SVD), is independent of coarse-graining. Still, it is limited to transition probability matrices in discrete states. To address this, this article proposes a CE quantification framework for Gaussian iterative systems, based on approximate dynamical reversibility derived from the SVD of inverse covariance matrices in forward and backward dynamics. The positive correlation between SVD-based and EI-based CE, along with the equivalence condition, is given analytically. After that, we provide precise coarse-graining strategies directly from singular-value spectra and orthogonal matrices. This new framework can be applied to any dynamical system with continuous states and Gaussian noise, such as autoregressive growth models, Markov-Gaussian systems, and even SIR modeling using neural networks. Numerical simulations on typical cases validate our theory and offer a new approach to studying the CE phenomenon, emphasizing noise and covariance over dynamical functions in both known models and machine learning.

High-resolution mapping of fine particulate matter (PM2.5) is a cornerstone of sustainable urbanism but remains critically hindered by the spatial sparsity of ground monitoring networks. While traditional data-driven methods attempt to bridge this gap using satellite Aerosol Optical Depth (AOD), they often suffer from severe, non-random data missingness (e.g., due to cloud cover or nighttime) and inversion biases. To overcome these limitations, this study proposes the Spatiotemporal Physics-Guided Inference Network (SPIN), a novel framework designed for inductive spatiotemporal kriging. Unlike conventional approaches, SPIN synergistically integrates domain knowledge into deep learning by explicitly modeling physical advection and diffusion processes via parallel graph kernels. Crucially, we introduce a paradigm-shifting training strategy: rather than using error-prone AOD as a direct input, we repurpose it as a spatial gradient constraint within the loss function. This allows the model to learn structural pollution patterns from satellite data while remaining robust to data voids. Validated in the highly polluted Beijing-Tianjin-Hebei and Surrounding Areas (BTHSA), SPIN achieves a new state-of-the-art with a Mean Absolute Error (MAE) of 9.52 ug/m^3, effectively generating continuous, physically plausible pollution fields even in unmonitored areas. This work provides a robust, low-cost, and all-weather solution for fine-grained environmental management.

Living systems maintain structural and functional stability while adapting to environmental changes, a capability independent of specific system‑environment states. Existing frameworks, such as self‑organization theory and free energy principles, cannot measure system‑environment interaction at the causal level. In this article, we propose a new causal indicator, Flexibility, to measure a system’s ability to respond to its environment. We construct this indicator based on information theory and interventional operations from causal inference, which implies the indicator depends only on the dynamical causal mechanism. We show this indicator satisfies the axiom system of the partial information decomposition (PID) framework and decomposes into two components, Expansiveness and Introversion, which correspond to different strategic tendencies for environmental adaptation. This decomposition reveals that Flexibility depends on the entanglement between system‑environment variables and noise magnitude. Through experiments on cellular automata (CA), random Boolean networks, and real gene regulatory networks (GRNs), we validate that the indicator identifies the most complex and computationally capable CA (Langton’s parameter at 0.5), while demonstrating that feedback loops carrying important biological functions in GRNs exhibit the highest flexibility. We also find that flexibility peaks at a moderate level of dynamical noise. Furthermore, we combine this framework with machine learning techniques to demonstrate its applicability when the underlying dynamics are unknown.

Consciousness spans macroscopic experience and microscopic neuronal activity, yet linking these scales remains challenging. Prevailing theories, such as Integrated Information Theory, focus on a single scale, overlooking how causal power and its dynamics unfold across scales. Progress is constrained by scarce cross-scale data and difficulties in quantifying multiscale causality and dynamics. Here, we present a machine learning framework that infers multiscale causal variables and their dynamics from near-cellular-resolution calcium imaging in the mouse dorsal cortex. At lower levels, variables primarily aggregate input-driven information, whereas at higher levels they realize causality through metastable or saddle-point dynamics during wakefulness, collapsing into localized, stochastic dynamics under anesthesia. A one-dimensional top-level conscious variable captures the majority of causal power, yet variables across other scales also contribute substantially, giving rise to high emergent complexity in the conscious state. Together, these findings provide a multiscale causal framework that links neural activity to conscious states.

Air quality forecasting (AQF) is critical for public health and environmental management, yet remains challenging due to the complex interplay of emissions, meteorology, and chemical transformations. Traditional numerical models, such as CMAQ and WRF-Chem, provide physically grounded simulations but are computationally expensive and rely on uncertain emission inventories. Deep learning models, while computationally efficient, often struggle with generalization due to their lack of physical constraints. To bridge this gap, we propose PCDCNet, a surrogate model that integrates numerical modeling principles with deep learning. PCDCNet explicitly incorporates emissions, meteorological influences, and domain-informed constraints to model pollutant formation, transport, and dissipation. By combining graph-based spatial transport modeling, recurrent structures for temporal accumulation, and representation enhancement for local interactions, PCDCNet achieves state-of-the-art (SOTA) performance in 72-hour station-level PM2.5 and O3 forecasting while significantly reducing computational costs. Furthermore, our model is deployed in an online platform, providing free, real-time air quality forecasts, demonstrating its scalability and societal impact. By aligning deep learning with physical consistency, PCDCNet offers a practical and interpretable solution for AQF, enabling informed decision-making for both personal and regulatory applications.

Information dynamics plays a crucial role in complex systems, from cells to societies. Recent advances in statistical physics have made it possible to capture key network properties, such as flow diversity and signal speed, using entropy and free energy. However, large system sizes pose computational challenges. We use graph neural networks to identify suitable groups of components for coarse-graining a network and achieve a low computational complexity, suitable for practical application. Our approach preserves information flow even under significant compression, as shown through theoretical analysis and experiments on synthetic and empirical networks. We find that the model merges nodes with similar structural properties, suggesting they perform redundant roles in information transmission. This method enables low-complexity compression for extremely large networks, offering a multiscale perspective that preserves information flow in biological, social, and technological networks better than existing methods mostly focused on network structure.