ansatz design

This work addresses the fundamental trade-off in parametrized quantum circuits (PQCs) between expressibility and trainability: highly expressive circuits are prone to barren plateaus, while trainable architectures may be classically simulable. The authors derive a finite-sample, dimension-independent concentration bound on the variance of the cost function, establishing the first rigorous theoretical guarantee for trainability and revealing an inverse relationship between trainability and expressibility. Leveraging this insight, they propose a property-driven variational circuit search framework that jointly optimizes both criteria. Experimental validation on real quantum hardware demonstrates that the discovered circuits achieve over sixfold reduction in parameter count while exhibiting higher effective dimensionality. In the VQE task for the H₂ molecule, these circuits attain accuracy comparable to UCCSD with significantly lower computational complexity.

Function-parameterized neural networks are highly sensitive to initialization, and conventional data-agnostic initialization schemes often fail to capture the structural characteristics of target signals, leading to slow convergence and unstable performance. This work proposes a prior-guided initialization strategy that, for the first time, integrates data-driven spectral priors into both network initialization and architecture design. Specifically, fast Fourier transform (FFT) is employed to extract seasonal priors that inform model depth and initial state, while residual regression is used to parameterize trend components. Without altering the training procedure, the proposed method significantly accelerates convergence, reduces performance variance, and improves computational efficiency across both synthetic and real-world datasets. Notably, it maintains reconstruction accuracy even when using a lower-dimensional encoder, consistently outperforming standard initialization approaches.

This work investigates how task-relevant symmetries—exact or approximate equivariance—affect the generalization of deep learning models, particularly under symmetry mismatch between model and data. Method: We develop the first generalization bound that does not assume group structure, rigorously quantifying the interplay between model equivariance error and data equivariance error. Our approach integrates probabilistic generalization theory, function approximation theory, and symmetry metrics, accommodating non-group, non-exact, and non-global equivariance settings. Contributions/Results: We establish that precise modeling of task symmetries significantly improves generalization. We formally characterize the optimal error trade-off under approximate or local equivariance when model and data symmetries are misaligned. Furthermore, we derive an “error alignment” principle—a concrete, actionable theoretical guideline for designing robust equivariant models—thereby bridging abstract symmetry considerations with practical architectural design.

In deep learning, model initialization and learning rate tuning are often guided by empirical rules or heuristics due to prohibitive computational costs of systematic hyperparameter search. Method: This work conducts the first large-scale empirical validation of μ-Parameterization (μP) for learning rate transfer across model sizes in Transformer architectures—specifically at unprecedented scale (10B parameters, 190B tokens)—to enable zero-shot inference of near-optimal learning rates for large models from small ones. Using massive distributed training and ablation studies, we evaluate μP’s efficacy across diverse configurations. Contribution/Results: μP achieves near-optimal convergence in most settings: <5% accuracy degradation on a 1.2B model and 2–3× faster training on a 10B model compared to baselines. The study confirms μP’s practical universality while identifying its failure modes and proposing targeted refinements. These advances substantially reduce hyperparameter optimization cost for large language models, bridging theory and practice in scalable neural network training.

This work addresses the “circuit discovery” problem in neural network interpretability, formally characterizing its intrinsic computational complexity. Method: We introduce the first unified formal query framework for description, explanation, prediction, and control; model mechanistic explanation queries on multilayer perceptrons; and systematically apply classical and parameterized complexity theory to intrinsic interpretability. Results: We rigorously prove that core explanation queries are NP-hard, W[1]-hard, and inapproximable; identify precise boundaries of tractable subproblems—those solvable in polynomial time or fixed-parameter tractable (FPT); and propose two novel paradigms: “tractable subproblem transformation” and “lightweight query design.” These yield a complexity map guiding heuristic algorithm development, establishing both theoretical foundations and practical pathways for interpretable AI.

This work addresses the challenges of parameterizing convex sets in shape optimization and inverse design by proposing an implicit representation based on sublinear neural networks. The method flexibly characterizes arbitrary convex bodies by learning positively homogeneous and convex support and gauge functions. It enjoys theoretical universal approximation capabilities for convex sets and demonstrates strong empirical performance, accurately reconstructing target shapes in experiments, thereby validating its expressiveness and effectiveness. The key innovation lies in integrating convex analysis with neural networks to establish a convex set parameterization framework that simultaneously offers rigorous theoretical guarantees and practical performance.

This work addresses the lack of systematic methodologies in model optimization, which often relies on heuristic choices and struggles to accommodate diverse deployment constraints. It formalizes model compression and acceleration as a constraint-aware multi-objective engineering decision problem, establishing a unified and actionable framework grounded in five key dimensions: data availability, latency, memory footprint, accuracy tolerance, and retraining budget. By integrating techniques such as quantization, pruning, knowledge distillation, parameter-efficient fine-tuning (PEFT), and inference optimization, the study proposes tailored optimization pipelines for four representative industrial scenarios, delivering a reproducible and quantifiable guide for technology selection.

This work addresses the lack of a unified modular framework for analyzing adaptive optimizers, which hinders a precise characterization of their behavior under constraints on directional reachability, information budgets, and update rules. We propose a geometric–non-geometric decoupled calculus for optimizers: the geometric module, constituted by a family of positive-definite cometrics, captures realizable descent directions, while the non-geometric module governs mechanisms such as information processing, memory, and control. Within this framework, we establish a direction expressivity theorem and a residual theory for constrained cometric families, disentangling directional expressiveness from condition-number complexity and recasting optimizer design as a Pareto optimization problem under modular budgets. Theoretically, we prove that fully positive-definite geometry exactly spans all strictly descending directions; experiments demonstrate that high-information full-metric probes attain numerical precision on deterministic quadratic problems, and a Muon-style implementation preliminarily validates the auditability of matrix-operator updates.

This work addresses the barren plateau problem in quantum neural network training caused by poor parameter initialization by proposing a first-moment–based analytical framework. Combining operator concentration theory with numerical experiments, the study systematically evaluates and compares the efficacy of various initialization strategies—including identity, Gaussian, and several shifted or asymmetric distributions. For the first time, it establishes an operator-level criterion for initialization validity, demonstrating that viable initializations avoiding barren plateaus are highly non-unique and form exponentially many inequivalent families. Moreover, the research reveals that initializations with distinct first moments can converge to different local minima, indicating that intelligent initialization effectively transforms the exponential concentration challenge into a selection problem among numerous trainable regions.