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Oct 01, 2026Oct 01, 2026
Designs and analyzes energy-based probabilistic models specified by an energy function—including associative memory models and variants such as DAM and RBM—by deriving their statistical behavior, inference and learning dynamics, and operational regimes. This competence includes computing capacities and memory regimes, classifying modes of fitting data, and constructing analytic mappings between model variants to simplify calculations.
Despite growing interest in Energy-Based Models (EBMs), their theoretical relationships with mainstream generative models—including GANs, VAEs, and normalizing flows—and their formal connections to statistical mechanics (e.g., energy functions, partition functions, MCMC sampling) remain poorly unified and conceptually fragmented. Method: We propose the first cross-paradigm unification framework tailored for physicists, establishing rigorous formal mappings between EBMs and other generative paradigms through an energy-centric lens. Our approach integrates statistical physical modeling, MCMC sampling analysis, EBM optimization theory, and systematic comparative evaluation of generative mechanisms. Contribution/Results: This work bridges the conceptual gap between generative modeling and statistical mechanics, revealing fundamental commonalities and distinctions across models in terms of energy representations, sampling dynamics, and training objectives. It enhances theoretical coherence, interpretability, and principled design of EBMs—while providing a unified foundation for analyzing sampling efficiency, convergence properties, and thermodynamic analogies in deep generative modeling.
This work proposes a brain-inspired neural computing framework designed to unify learning, memory, control, and optimization within a single architecture that is scalable, robust, and energy-efficient. By integrating principles from energy landscapes, gradient flows, control theory, and neuroscience, the study introduces a novel paradigm that transcends conventional feedforward networks and backpropagation. Key mechanisms include continuous-time Hopfield networks, dense associative memory, oscillator-based dynamics, and proximal descent dynamics. The resulting architecture achieves markedly improved computational efficiency and biological plausibility, demonstrating superior performance in data-driven control, constrained reconstruction, and large-scale optimization tasks.
本文通过使用概率模拟内存计算处理器解决了大规模概率能量模型在GPU上执行时面临的可扩展性挑战，实现了超过1000倍的加速。
Traditional empirical risk minimization focuses solely on a single optimal solution, failing to capture the multistability and uncertainty inherent in data-driven learning. This work reframes the empirical loss function as an interaction potential and constructs an energy-based model grounded in Gibbs measures on a Cayley tree, thereby establishing—for the first time—a rigorous connection between loss landscapes and probabilistic inference on tree-structured graphs. By leveraging nonlinear integral fixed-point equations, data-dependent kernels inducing compact operators, and phase transition analysis, the study theoretically proves existence and uniqueness of solutions in the one-dimensional setting. Numerical experiments further demonstrate the coexistence of multiple solution branches under non-separable kernels, revealing that data can induce multiple learning states and associated phase transitions.
Existing dense associative memories (DAMs) operate exclusively on vector representations and lack the capacity to model uncertainty inherent in probabilistic data. Method: This work introduces the first DAM framework operating in the space of probability distributions, specifically the Gaussian family endowed with the Bures–Wasserstein metric. We define an energy function based on the 2-Wasserstein distance, using the Wasserstein barycenter as a fixed point, and perform dynamic retrieval via Gibbs-weighted optimal transport mappings for aggregation. Contribution/Results: We prove that the proposed memory achieves exponential storage capacity. Experiments demonstrate high-accuracy distribution retrieval on both synthetic and real-world distributional tasks, robustness to Wasserstein perturbations, and quantifiable recovery guarantees. By unifying associative memory with generative modeling principles, this work establishes a novel paradigm bridging distributional representation learning and memory-based probabilistic reasoning.
该研究通过生物启发的框架，利用概率内存计算硬件模拟动物学习和决策过程中的贝叶斯推断，以解决不确定性问题。
This work proposes the first compiler framework enabling end-to-end mapping of general stochastic programs to thermodynamic sampling hardware. Addressing the challenge of efficiently compiling stochastic programs—expressed as directed factor graphs or parameterized random circuits—onto native energy-based model (EBM) hardware, the approach integrates context-aware pattern matching with a trajectory-level REINFORCE post-training strategy. This combination substantially reduces compilation error and enhances approximation fidelity. Empirical evaluation demonstrates the framework’s effectiveness and generality across diverse applications, including financial market simulation, ecological probabilistic modeling, Gibbs sampling for non-native EBMs, and Bayesian design of Gaussian random circuits, thereby establishing a viable pathway toward energy-efficient stochastic computing.
本文重构了Hopfield网络，作为记忆的物理理论，通过动态定义内容可寻址记忆、对称循环架构等方法解决了早期神经网络算法的问题。
This work investigates the free energy landscape and memory retrieval mechanisms of high-order dense associative memory models. Leveraging large deviation theory and statistical physics, it constructs a free energy functional tailored to polynomial interactions and Log-Sum-Exponential (LSE) activation, enabling a rigorous analysis of temperature-dependent behavior and ground state energy in the finite pattern regime. The study establishes, for the first time, the exact full-retrieval phase transition threshold for LSE-based models, elucidates the critical role of initial conditions in memory recovery within high-order networks, and develops a general analytical framework extensible to complex associative memory architectures. This framework not only reproduces classical results from the Hopfield model but also systematically extends the theoretical foundations of dense associative memory.
This study addresses the high computational complexity of probabilistic inference and challenges in uncertainty modeling by proposing probabilistic circuits as a novel reasoning framework. By introducing structural constraints, the approach enables exact inference in polynomial time and innovatively integrates deep learning with symbolic paradigms to construct hybrid models supporting Bayesian learning. This research establishes a foundational theoretical system for probabilistic circuits, achieving efficient, exact computation and scalable deployment across diverse inference tasks. Ultimately, this work effectively bridges the gap between neural and symbolic AI, systematically advancing the development of probabilistic circuits at both theoretical and applied levels.
This work addresses the growing challenges of energy consumption and latency in machine learning by proposing a differentiable thermodynamic computing architecture tailored for continuous variables, which deeply integrates energy-based models with physical hardware. Leveraging Langevin dynamics, the approach enables hardware-native probabilistic inference and learning within stochastic superconducting circuits endowed with tunable energy potentials, harnessing thermal noise-driven physical processes to efficiently train probabilistic graphical models. Theoretical analysis and numerical experiments demonstrate that this paradigm substantially reduces both energy expenditure and computational latency. Preliminary hardware validation is achieved through a superconducting circuit prototype, offering a promising new pathway toward low-power, high-efficiency probabilistic machine learning.