中国人民银行

Klindt, LeCun, and Balestriero (arXiv:2605.26379) proved that Joint-Embedding Predictive Architectures (JEPAs) achieve linear identifiability, the linear recovery of the world's true latent variables, if and only if the world's latent dynamics follow a Gaussian, stationary process. This Gaussian boundary implies a fundamental limit on temporal consistency: for any non-Gaussian physical system, the representation error of a statistical World Model grows monotonically with time. We prove that this limit is an artifact of the statistical alignment mechanism, not a property of World Models in general. We introduce the Physics-Grounded Symbolic Architecture (PGSA) and prove three results: (1) a PGSA achieves exact linear identifiability for all physical regimes, regardless of the latent distribution; (2) the per-step error of a PGSA is bounded by numerical precision alone; and (3) as a direct consequence, a PGSA maintains temporal consistency for an unbounded number of transitions, a property we term near-infinite temporal consistency. We further prove that statistical World Models cannot achieve this property for any non-Gaussian system, regardless of model capacity or the volume of training data. The algebraic cores of four of the theorems are formalized in Lean 4 with Mathlib4 v4.31.0 (zero sorry placeholders); the Klindt et al. converse is taken as an external premise. The contrast establishes that symbolic grounding in the causal generator of the world's dynamics is the sufficient condition and, in non-Gaussian regimes, the only condition for near-infinite temporal consistency.

Residual connections are central to modern deep neural networks, enabling stable optimization and efficient information flow across depth. In this work, we propose SCORE (Skip-Connection ODE Recurrent Embedding), a discrete recurrent alternative to classical layer stacking. Instead of composing multiple independent layers, SCORE iteratively applies a single shared neural block using an ODE (Ordinary Differential Equation)-inspired contractive update: ht+1 = (1 - dt) * ht + dt * F(ht) This formulation can be interpreted as a depth-by-iteration refinement process, where the step size dt explicitly controls stability and update magnitude. Unlike continuous Neural ODE approaches, SCORE uses a fixed number of discrete iterations and standard backpropagation without requiring ODE solvers or adjoint methods. We evaluate SCORE across graph neural networks (ESOL molecular solubility), multilayer perceptrons, and Transformer-based language models (nanoGPT). Across architectures, SCORE generally improves convergence speed and often accelerates training. SCORE is reducing parameter count through shared weights. In practice, simple Euler integration provides the best trade-off between computational cost and performance, while higher-order integrators yield marginal gains at increased compute. These results suggest that controlled recurrent depth with contractive residual updates offers a lightweight and effective alternative to classical stacking in deep neural networks.

In this article, I trace the evolution of the tidyverse, a cohesive ecosystem of R packages for data science. Beginning with early packages I created during my PhD at Iowa State University, I explain how they coalesced into a unified collection with consistent principles. I detail key innovations including tidy data, tibbles, the pipe operator, tidy evaluation and the role of hex stickers in community building. I describe the transition from my individual efforts to a collaborative enterprise supported by a team at Posit and a vibrant global community. I highlight the importance of human-centred design, consistency, composability and inclusivity as our guiding principles. I discuss how our recent priorities have shifted from innovation to maintenance as the ecosystem has matured. Looking to the future, I discuss our current areas of focus including Positron (a new data science IDE), R in production environments and integrating large language models into data science workflows.

The security and reliability of blockchain systems are critically dependent on their consensus mechanisms; however, a significant gap exists between theoretical design and engineering implementation in terms of security transformation and environmental adaptability. This research proposes a simulation testing methodology and implementation platform, ChaosConsensus, based on chaos engineering principles, for systematically verifying the robustness and fault tolerance of blockchain consensus protocols in complex production environments. Through proactive fault injection and abnormal behavior simulation, ChaosConsensus constructs a multilayered, cross-protocol verification environment that overcomes the limitations of traditional testing approaches, which are typically confined to unit-level testing and simplistic fault simulation. The platform is capable of providing simulation support for diverse failure scenarios that may occur across various blockchain system environments. The primary innovations of this research encompass four key aspects. First, we propose a universal hierarchical and domain-partitioned consensus fault test case framework that integrates multiple fault-tolerance model use cases. This framework exhibits two distinctive features: (1) it integrates both BFT-type and CFT-type fault tolerance models within a unified test case structure, and (2) drawing upon the upper-lower tester methodology from the international standard ISO 9646 for protocol conformance testing, it introduces a three-layer tester architecture consisting of “upper tester - inner tester - lower tester” to enhance the mapping and correspondence of test cases. This framework achievement has been further refined and incorporated into the ITU-T international standard for blockchain stability testing entitled “Stability assessment methods for distributed ledger technology platforms” (Document No. ITU-T T22-SG16–240415-TD-WP1–0258). Second, we propose a high-precision fault injection mechanism based on the message constructor and HOOK methods, which enables precise intervention in the fine-grained behaviors of consensus protocols. Third, we propose a universal multichain multiconsensus adaptation scheme decoupled from the business layer, thereby enhancing the platform’s portability and practical deployment capabilities. Fourth, we design a multidimensional simulation evaluation system incorporating both primary and secondary metrics, providing a unified benchmark for comprehensive quantitative assessment of consensus protocol fault simulation. In terms of practical applications, this solution has been tested and validated across multiple national-level financial blockchain payment systems and electricity trading blockchain systems that deploy various consensus protocols, including Dasheng, Dino, Raft, Tendermint, and HotStuff. The testing and verification were conducted in testing environments, preproduction environments (with configurations identical to production systems), and production environments. The results demonstrate that the platform is capable of discovering deep-seated issues that are difficult to detect using traditional testing methods, significantly enhancing the security and reliability of critical infrastructure and providing a valuable complement to existing blockchain system testing methodologies.