Guangyu wang (79 resultados)

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Taschenbuch. Condición: Neu. Neuware - How should we think geometrically about the parameters of a modern learning system When is the Fisher matrix a genuine metric, what does natural gradient really make invariant, and what replaces smooth Riemannian geometry when parameterizations become redundant or singular Geometric Foundations of AI (I) develops a rigorous, graduate-level framework for answering these questions. Beginning with statistical manifolds and information geometry, it moves through Fisher-Rao geometry, natural-gradient methods, variational inference, Legendre and Bregman duality, high-dimensional convex geometry, symmetry and quotient structure, loss-landscape geometry, singular learning theory, parameter-space topology, and spectral questions at modern scale. Throughout, the emphasis is not only on what a theorem says, but on the hypotheses that make it true and on what survives when the theorem is transferred to neural networks. Designed for graduate students and researchers in machine learning, statistics, applied mathematics, and optimization, the book combines classical geometric ideas with contemporary AI questions. Worked examples, carefully separated levels of evidence, and tiered exercises help readers distinguish intrinsic structure from coordinate artifacts-and develop a more reliable geometric understanding of optimization and learning.…

Taschenbuch. Condición: Neu. Neuware - What geometry does a learning system discover in data-and what does it impose through architecture, objectives, and representation How should we compare representations across models or modalities, and when do claims about manifolds, symmetry, topology, or emergent structure have mathematical content rather than visual appeal Geometric Foundations of AI (II) develops the object-side geometry of modern machine learning. It begins with group actions, representation theory, and equivariant architectures, then builds toward information bottlenecks, contrastive and self-supervised representation geometry, non-Euclidean and hyperbolic embeddings, manifold hypotheses and intrinsic dimension, representation diagnostics, alignment and transfer, topological data analysis, and the geometry of foundation-model representations. A recurring theme is that a geometric claim becomes meaningful only after the object, metric, symmetry, scale, and estimator have been specified. Written for advanced undergraduates, graduate students, and researchers in machine learning, statistics, geometry, and applied mathematics, the book combines exact mathematics with carefully delimited model-dependent and empirical claims. It is both a technical foundation for geometric and representation learning and a guide to deciding which geometric interpretations are justified by the evidence.…

Taschenbuch. Condición: Neu. Neuware - Continuous-time mathematics has become a common language across modern artificial intelligence. Yet the same words-gradient flow, diffusion, entropy, sampling, control, and equilibrium-often refer to different mathematical objects, metrics, and regimes. This book is built around making those distinctions precise. Stochastic Dynamics for AI develops deterministic and stochastic dynamics from first principles and then uses them to connect Fokker-Planck equations and Wasserstein gradient flows; diffusion and flow-based generative models; Langevin, Hamiltonian, and non-reversible sampling; particle and variational inference; stochastic-gradient dynamics and the edge of stability; entropy-regularized control and continuous-time reinforcement learning; mean-field limits and games; and path-space relative entropy and Schrödinger bridges. Rather than presenting these subjects as isolated toolkits, the book asks a harder question: when does an idea transfer from one domain to another Each major connection is separated into what is exact, what requires a limiting argument or a change of representation, and what fails outside its stated assumptions. Scope boxes, counterexamples, comparison tables, and four tiers of exercises make the hypotheses-and the boundaries of the conclusions-part of the mathematics. Designed for advanced undergraduates, graduate students, and researchers in mathematics, statistics, machine learning, and related fields, this volume offers a rigorous guide to the continuous-time structures that underlie learning, generation, sampling, optimization, control, and interacting AI systems.…

Taschenbuch. Condición: Neu. Neuware - What changes when a learning system does more than predict-when it acts, changes what it will observe next, remembers a history, and must control a process over time Sequential Decision Making for AI develops the mathematical language for that setting. Beginning with decision theory, Markov decision processes, bandits, and dynamic programming, it builds toward reinforcement learning under exploration, function approximation, offline data, partial observability, planning, constraints, and multi-agent interaction. The unifying theme is interaction: once actions influence future data, the objects that govern learning change. The book separates familiar ideas from the assumptions that make them valid. Representability is distinguished from learnability; Bellman closure from mere function-class membership; offline sample size from policy coverage; belief-state sufficiency from minimal memory; and statistical information from computational access. Upper bounds, lower bounds, and algorithmic guarantees are tied to the observation model, interaction protocol, horizon, and resource being counted. The same framework is connected to modern foundation-model post-training and agent design: behavioural cloning, preference and reward modelling, KL-regularised optimisation, offline evaluation, context and recurrent memory, test-time planning, tool use, constrained control, and multi-agent interaction. These are interpreted through theorem-native quantities such as interaction rounds, independent samples, effective horizon, coverage, planning depth, memory bits, and computation. Written for graduate students and researchers in machine learning, statistics, applied mathematics, control, and AI, this volume is not an algorithm catalogue. It is a resource-aware guide to what sequential-learning theorems establish, what they leave open, and what additional assumptions are required before they become claims about real AI agents. …

Taschenbuch. Condición: Neu. Neuware - When AI acts through a physical system, an error is no longer only an incorrect output. It becomes a force, a trajectory, a collision risk, or a decision whose consequences may arrive before a human can intervene. Safety of Embodied AI and Autonomous Systems develops the mathematical and engineering foundations needed to reason about those consequences. The book moves from hybrid safety contracts, hazard sets, physical loss, reachability, and viability to Lyapunov methods, control barrier functions, constrained action selection, stochastic reach-avoid analysis, chance constraints, and risk measures. It then extends the framework to learning-enabled systems through belief-space safety, safe exploration under uncertainty, and learned components operating off distribution. A unifying theme is the intervention margin: the time or state-space room available before a hazard becomes unavoidable, measured against sensing, computation, communication, actuation, and human-response delays. This perspective carries through runtime assurance and backup controllers, shared autonomy, fault-tolerant operation, degraded modes, and the final verification and safety-case framework. Designed for graduate students, researchers, and engineers in AI safety, robotics, control, and autonomous systems, the text combines formal results with engineering interpretation, computational labs, structured evidence, and safety-case templates-showing how control, learning, verification, and runtime assurance must fit together when AI decisions have physical consequences.…