电网优化

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a few steps. When the student underperforms, the usual explanation is insufficient capacity. We argue the opposite: the trajectory is the bottleneck, not the student. Each training trajectory is built through a chain of blind stochastic jumps with no evaluation of sequence quality; a single bad decision at an early midpoint propagates through subsequent steps, yet the student must imitate the result. Trajectory-Shaped Discrete Flow Matching (TS-DFM) replaces these blind jumps with guided navigation: a lightweight energy compass evaluates candidate continuations at each midpoint, selecting the most coherent. All shaping is training-only; inference cost is unchanged. On 170M-parameter language modeling, the shaped student at 8 steps achieves 32% lower perplexity than the 1 024-step teacher while being 128×faster, with gains consistent across source distributions and three evaluators of increasing scale. TS-DFM achieves the best perplexity of any discrete-generation baseline we compare against, including methods trained on 6×more data or using 5×larger models.

Energy efficiency in LLM inference is often treated as a property of the model, the hardware, or the serving software. We show that, for decode-dominated serving, a simpler systems variable dominates: the serving context window. Because KV-cache memory is finite, increasing the context window reduces the number of concurrent sequences a GPU can hold. Under continuous batching, this concurrency limit directly sets decode throughput, while GPU power remains nearly flat over most of the operating range. The result is a simple $1/\mathcal{W}$ law: tokens per watt scale inversely with the serving context window $\mathcal{W}$. We derive this law from KV-cache capacity and a logistic GPU power model, and empirically verify it for Llama-3.1-70B inference over the 2K--128K context range. On identical H100 hardware and software, tok/W varies by nearly $40\times$ across this range. We then show that the same mechanism determines GPU fleet-level energy efficiency. Context-length routing keeps short requests on high-concurrency short-window pools, while newer hardware shifts the power and memory curve upward. These two operator-controllable levers are approximately multiplicative: on the short-context-dominant Azure trace, two-pool context-length routing improves tok/W by $2.5\times$ over a homogeneous NVIDIA H100 fleet, a calibrated NVIDIA B200 deployment improves tok/W by $2.0\times$ at fixed topology, and combining them reaches $5.76\times$. Finally, we analyze active-parameter weight streaming in MoE models as a third, architecture-level lever, giving an upper-bound gain of up to $5.1\times$. Together, these results suggest a deployment order for energy-efficient LLM serving: route by context length first, upgrade hardware second, and exploit sparse architectures where dispatch costs are controlled. We release code, data, and simulator in anonymous [repository](https://anonymous.4open.science/r/gpu-fleet-sim-1BEB) to facilitate reproduction and further research.

We consider the scheduling problem of online speed scaling where the goal is to minimize the energy consumption of a machine that controls the speed at which jobs are processed. Recent work has leveraged the learning-augmented framework, where the algorithm is provided with predictions about jobs that will arrive in the future, to manage power usage more efficiently. This paper proposes a novel prediction model for speed scaling where the predictions are about the machine speed (the output), instead of the jobs (the input). Machine speed predictions have multiple advantages: they are succinct, admit strong PAC-learnability guarantees, can be provided dynamically, and lead to a natural definition of smoothness. We give an algorithm for dynamic machine speed predictions that is $(1+\epsilon)$-consistent and $O(1)$-robust. For offline machine speed predictions and job speed predictions, we provide an algorithm that achieves the stronger guarantee of $(1+\epsilon)$-smoothness, while maintaining $O(1)$-robustness. These guarantees are comparable to previous work, but do not require predicting the entire input.

Large-scale Ising optimization underlies critical optimization and learning applications, including correlation clustering, MAP inference, and energy-based models. Spectral relaxation methods run in polynomial time but yield solutions with significant optimality gaps while metaheuristics close those gaps but scale poorly to large instances. In particular, spectral methods are inherently single-shot as they solve exactly one eigenvalue problem. We introduce $\textit{Spectral Annealing}$ (SpecAnn), a new spectral optimization approach that transforms traditional spectral methods from single-shot approximations into exploration-based optimization, by sweeping a parametrized normalization path from the raw adjacency to the signed normalized Laplacian, with an $O(n)$ diagonal predictor that warm-starts successive eigensolves and GPU-batched local search refining candidates in parallel. Experiments on general Ising problems demonstrate that SpecAnn achieves competitive to near-optimal solutions depending on instance structure, with runtimes less than 7 minutes for instances of 8.4M variables. SpecAnn delivers up to 83$\times$ speedup over recent GPU-accelerated methods while maintaining superior solution quality, and scales successfully beyond 524K variables where traditional metaheuristics fail.

Recurrent spiking neural networks (RSNNs) are a promising substrate for energy-efficient control policies, but training them for high-dimensional, long-horizon reinforcement learning remains challenging. Population-based, gradient-free optimization circumvents backpropagation through non-differentiable spike dynamics by estimating gradients. However, with finite populations, high variance of these estimates can induce harmful and overly aggressive update steps. Inspired by trust-region methods in reinforcement learning that constrain policy updates in distribution space, we propose **Signal-Adaptive Trust Regions (SATR)**, a distributional update rule that constrains relative change by bounding KL divergence normalized by an estimated signal energy. SATR automatically expands the trust region under strong signals and contracts it when updates are noise-dominated. We instantiate SATR for Bernoulli connectivity distributions, which have shown strong empirical performance for RSNN optimization. Across a suite of high-dimensional continuous-control benchmarks, SATR improves stability under limited populations and reaches competitive returns against strong baselines including PPO-LSTM. In addition, to make SATR practical at scale, we introduce a bitset implementation for binary spiking and binary weights, substantially reducing wall-clock training time and enabling fast RSNN policy search.

Language models routinely revise initial answers through intermediate edits, yet current alignment objectives restrict credit assignment to complete outputs or entire rollouts. To formalize the local geometry of improvement, we introduce Lifted State Policy Optimization (LSPO), which augments each textual answer with a continuous auxiliary coordinate to form a lifted state that encodes refinement context beyond surface text. Training rewards transitions that descend an energy landscape, subject to edit and step penalties, and internalizes the resulting answers into the generative model. Across the Qwen3.5 family on mathematics, science, code, logic, and broad reasoning benchmarks, LSPO improves aggregate accuracy while bypassing the latency of explicit revision loops. Component ablations, together with evaluations of internalization and energy ordering on unseen tasks, confirm that this gain originates from the lifted representation and from credit assigned at the transition level.

Deep reinforcement learning (RL) for quantum circuit optimization faces three fundamental bottlenecks: replay buffers that ignore the reliability of temporal-difference (TD) targets, curriculum-based architecture search that triggers a full quantum-classical evaluation at every environment step, and the routine discard of noiseless trajectories when retraining under hardware noise. We address all three by treating the replay buffer as a primary algorithmic lever. We introduce ReaPER$+$, an annealed replay rule transitioning from TD error-driven prioritization to reliability-aware sampling as value estimates mature, achieving up to 4$\times$ improved sample efficiency over the strongest off-policy baselines (fixed PER, ReaPER, and uniform replay) and matching prior on-policy solution quality at up to 32$\times$ fewer interactions. At 12-qubit scale, ReaPER achieves the lowest energy error in the fewest steps which is consistent with ReaPER$+$'s annealing direction, while PER and Vanilla replay find more compact circuits at the cost of higher energy error. Validation on LunarLander-v3 confirms the annealing principle is domain-agnostic obtaining +9% AUC over PER and fixed ReaPER. We further introduce OptCRLQAS, which amortizes expensive quantum-classical evaluations over multiple architectural edits, cutting wall-clock time per episode by up to 67.5% on a 12-qubit task without degrading solution quality. Finally, a lightweight replay-buffer transfer scheme warm-starts noisy-setting learning from noiseless trajectories, without network-weight transfer or $\epsilon$-greedy pretraining, reducing steps to chemical accuracy by up to 85-90% and final energy error by up to 90% over from-scratch baselines, with transfer advantages that grow with system size. Together, these results establish that experience storage, sampling, and transfer are decisive levers for scalable, noise-robust quantum circuit optimization. The anonymized repository is available at : https://anonymous.4open.science/r/annealed-replay-buffer-transfer-for-quantum-optimization-6861/.

Deep decarbonization is transforming power grids into safety-critical, low-carbon cyber-physical systems, where AI controllers must jointly manage economic efficiency, carbon reduction, and operational security. This operational energy trilemma is challenging for reinforcement learning: cost and carbon objectives are naturally optimized in expectation, whereas security violations are rare, heavy-tailed events whose consequences can be catastrophic and therefore require explicit tail-risk control. Existing safe reinforcement learning methods either constrain safety only in expectation or rely on light-tailed approximations, which can underestimate rare but severe grid violations. We propose a heterogeneous risk-constrained reinforcement learning framework for low-carbon grid operation. The key idea is to assign different risk semantics to different objectives: safety-critical security constraints are enforced through Conditional Value-at-Risk (CVaR), while economic and carbon-related objectives are optimized in expectation to preserve operational flexibility. To better capture extreme scenarios, a mixture distribution model is introduced to characterize heavy-tailed constraint violations. We further develop a residual policy learning scheme built on a distributionally robust chance-constrained reference module: the robust module provides a feasible and economically efficient baseline policy, and the learned residual refines it toward lower-carbon operation while respecting tail-risk bounds. Experiments on power-system operation tasks show that the proposed framework reduces economic cost by over 25% compared with expectation-based CMDP baselines and improves safety by two orders of magnitude over Gaussian-tail methods. These results suggest that risk-aware reinforcement learning can support reliable decarbonization by reconciling efficiency, sustainability, and security within a unified decision-making framework.

Langevin Dynamics (LD) provides a principled framework for solving combinatorial optimization problems (COPs) via gradient-guided stochastic search. However, classical LD faces two bottlenecks: 1) the utilization of uniform initialization may affect its convergence speed; 2) when applied to COPs such as routing problems that cannot be naturally formulated as Quadratic Unconstrained Binary Optimization (QUBO), classical LD suffers from slow convergence and inferior performance compared to existing learning-to-construct (L2C) methods, as it requires manually designed discrete proposals for updates. These proposals are typically local and induce abrupt transitions in the solution space, hindering escape from local optima and degrading performance. To address these issues, we propose NLD4CO, a unified framework that synergizes data-driven learning with LD. It introduces two instantiations: explicit-gradient (EG) and implicit-gradient (IG). NLD-EG accelerates sampling efficiency for energy-based problems via neural warm-start initialization. NLD-IG utilizes the corrective direction predicted by a consistency model as an implicit score function to guide the search, making structured, globally coordinated transitions for general COPs. Extensive evaluations on MIS, MWIS, TSP, and CVRP demonstrate that NLD4CO achieves SOTA performance, delivering superior solution quality with competitive or lower runtime.

Learning an energy-based model from data samples is a central problem in machine learning. Many recent and popular methods, such as denoising score matching for training energy-based diffusion models, use stochastic interpolants to corrupt data samples at different noise levels indexed by a time variable. This defines a joint density over both the data space and time, and most methods learn its energy through either spatial or temporal differences. We identify distinct failure modes for both of these approaches. To solve them, we propose Spatiotemporal Noise-Contrastive Estimation (stNCE), a framework for learning the energy through joint spatiotemporal differences. stNCE unifies many existing methods and leads to new training objectives. Experiments on images and molecules demonstrate performance competitive with state-of-the-art density estimation methods.

A major recent advance in quantization is given by microscaled 4-bit formats such as NVFP4 and MXFP4, quantizing values into small groups sharing a scale, assuming a fixed floating-point grid. In this paper, we study the following natural extension: assume that, for each group of values, we are free to select the "better" among two or more 4-bit grids marked by one or more bits in the scale value. We formalize the power-of-two-grids (PO2) problem, and provide theoretical results showing that practical small-group formats such as MXFP or NVFP can benefit significantly from PO2 grids, while the advantage vanishes for very large groups. On the practical side, we instantiate several grid families, including 1) PO2(NF4), which pairs the standard NF4 normal grid with a learned grid, 2) MPO2, a grid pair that is fully learned over real weights and activations, and 3) SFP4, a TensorCore-implementable triple which pairs NVFP4 with two shifted variants. Results for post-training quantization of standard open models and pre-training of Llama-like models show that adaptive grids consistently improve accuracy vs single-grid FP4 under both weight-only and weight+activation quantization.

Generative modeling of discrete data, such as graphs, underpins many scientific and industrial applications, including molecular discovery and materials design. In these domains, probabilistic inference is particularly valuable, as it enables composable generation and principled incorporation of desired constraints, such as structural or functional properties. Energy-based models naturally support this goal by capturing relative likelihoods and enabling composable inference by directly enforcing constraints during inference. However, discrete energy-based models typically struggle with efficient and high-quality sampling, as off-support regions often contain spurious local minima, trapping samplers and causing training instabilities, resulting in a fidelity gap compared to discrete diffusion models. To address this gap, we introduce Graph Energy Matching (GEM), a discrete generative framework inspired by the Jordan--Kinderlehrer--Otto (JKO) transport-map optimization perspective. GEM learns a permutation-invariant potential energy that simultaneously guides discrete transport from noise toward high-likelihood graph regions and refines samples within these regions. We further introduce a sampling protocol leveraging an energy-based switching strategy, seamlessly bridging rapid, gradient-guided transport and a local mixing regime for effective exploration. On molecular graph benchmarks, GEM matches or surpasses strong discrete diffusion baselines on most reported metrics. Beyond improving generation quality, GEM's relative likelihood modeling enables targeted exploration, facilitating compositional generation, property-constrained sampling, and interpolation between graphs.

Free energy estimation is a fundamental yet challenging problem, from physics to statistics. Classical approaches rely on thermodynamic transformations, ranging from direct estimation, quasistatic integration, to finite-time averaging. Recent work learns neural transports to significantly accelerate the efficiency in the finite-time regime. In this paper, we generalize this framework to arbitrary state spaces. Building on this view, we develop a generalized neural transport learning approach for efficient estimation. Experiments validate the effectiveness and efficiency of the proposed method beyond continuous settings, extending to discrete and multimodal spaces as well as autoregressive settings.

Accurate time-series forecasting is critical for a wide range of problems involving temporal data. Ensemble modeling is a well-established technique for leveraging multiple predictive models to increase accuracy and robustness, as the performance of a single predictor can be highly variable due to shifts in the underlying data distribution. This paper proposes a new methodology for building robust ensembles of time series forecasting models. Our approach uses Adaptive Robust Optimization (ARO) to construct a linear regression ensemble whose model weights adapt over time. We demonstrate the effectiveness of our method through a series of synthetic experiments and real-world applications, including air pollution management, energy consumption forecasting, and tropical cyclone intensity forecasting. Our results show that our adaptive ensembles outperform the best ensemble member in hindsight by 16-26\% in root mean square error and 14-28\% in conditional value at risk and improve over competitive ensemble techniques.

Denoising and score estimation are classically linked through Tweedie’s formula, which relates the posterior mean under Gaussian corruption to the Stein score of the noisy marginal. In this work, we extend this perspective beyond Gaussian noise to a broad class of elliptical, energy-based noise distributions, with particular emphasis on generalized Gaussian corruptions. We derive the Energy–Tweedie identity: when the denoising posterior is viewed through the lens of proper scoring rules, the path derivative of a matched, possibly non-Euclidean energy score recovers the Stein score of the noisy marginal. Thus, the familiar correspondence between Gaussian noise, posterior means, squared loss, and Tweedie’s formula is lifted to a distributional correspondence between generalized Gaussian noise, full posterior laws, Mahalanobis energy scores, and the Energy–Tweedie identity. Among its consequences, this identity gives a posterior-sample-based route to score estimation, yields a principled criterion for noise-parameter calibration, and supplies a score-based perspective on recent diffusion-style generative methods trained with scoring rules.

Efficient sampling from complex probability distributions is an important task across Bayesian inference and certain classes of deep generative models. Markov chain Monte Carlo (MCMC) remains one of the most widely used tools for this. However, even state-of-the-art samplers, such as the NUTS implementations in Stan and Turing.jl, can converge slowly on ill-conditioned, heavy-tailed, or near-degenerate targets. We identify that sampling error can be decomposed into two terms: mismatch in the potential energy (PE) marginal, and average conditional mismatch across PE level sets. We propose *Contour Monte Carlo (CMC)*, which corrects each of these in turn: first by drawing energies $u_i$ from the PE marginal, and then by sampling states on the corresponding level sets. For a broad family of radial targets, including the Gaussian and Student's $t$ distributions, both stages admit closed-form draws, so CMC is exact and requires no Markov chain. Beyond this, for general targets, we estimate the PE marginal using umbrella sampling with MBAR, then run constrained MCMC on the sampled level sets, initialised from energy-matched umbrella samples (which tend to lie in regions of high conditional mass). We show that this procedure essentially reduces the global sampling problem to approximating the one-dimensional PE marginal, after which posterior draws can be generated readily on demand. Furthermore, the level-set chains are embarrassingly parallel, and therefore well-suited to modern accelerator hardware. On a suite of challenging benchmarks -- composed of `posteriordb` models, synthetic targets, and real-world inference problems -- CMC converges substantially faster than HMC and NUTS baselines at a fixed computational budget.

Geometry is invariant to viewpoint, which makes any collection of images a redundant encoding of a single 3D state. Existing feed-forward reconstruction models fail to exploit this: per-view methods emit overlapping, unaligned pointmaps that grow linearly with input count, while global-latent methods commit to a fixed, low-resolution output. We introduce Surflo, which compresses a variable number of unposed RGB views into K latent tokens-one global state-and decodes oriented 3D surface points by independently transporting them from noise onto the surface via flow matching. This frees the output from any fixed grid or token budget: the same latent yields from a few thousand to a million points in a single forward pass. To suppress the local inconsistencies inherent to independent per-point decoding, an inference-time guidance term correlates nearby points by injecting a photometric gradient during ODE integration. Surflo matches or surpasses feed-forward baselines on surface metrics, run an order of magnitude faster than optimization-based methods that require hundreds of views, and is the only feed-forward approach to combine a global latent with arbitrary-resolution decoding.

Modern power grids are increasingly exposed to coordinated cyber-physical disruptions, where the outage of a small number of transmission components can trigger severe post-contingency load shedding. Designing proactive _security defense_ against such adversarial contingencies is naturally modeled as a tri-level Defender-Attacker-Operator (DAO) problem: the defender allocates limited hardening resources, the attacker selects worst-case line outages, and the operator solves a post-attack DC/AC-optimal power flow (OPF). However, the resulting tri-level program is computationally prohibitive even for moderate network sizes. We develop a certified four-step reformulation pipeline that converts this intractable tri-level DAO problem into a tractable single-level optimization, yielding a Single-Level Mixed-Integer Linear Program (SL-MILP) under DC-OPF and a Single-Level Mixed-Integer Conic Program (SL-MICP) under AC-OPF. The construction combines exact dualization, exact Big-$M$ linearization, and a single controlled attacker relaxation. We prove that the resulting single-level optimum provides a conservative upper bound on the true worst-case load shedding and, more importantly, yields a robustness certificate for the deployed defense: no feasible binary attack can induce damage exceeding the reported single-level value. Extensive experiments on IEEE benchmark systems demonstrate substantial runtime improvements while maintaining strong worst-case security guarantees.

The rapid growth of generative AI is reshaping the energy footprint of modern computing infrastructure. Hyperscale AI data centers now operate at power levels comparable to large industrial facilities, creating new challenges for grid reliability, energy procurement, and real time demand flexibility. At the same time, their large controllable loads, cooling systems, and on site storage make them potential participants in grid services such as frequency regulation. However, existing evaluation environments do not capture the coupled decision making required for grid interactive operation. We introduce C2G-BENCH, a cyber-physical benchmark for hierarchical reinforcement learning in hyperscale data centers. C2G-BENCH simulates a real-world scenario, where a 250 MW-class hyperscale data center participates in grid frequency regulation while serving realistic AI workload demand under weather-driven ambient conditions. The benchmark explicitly links 15-minute market level orchestration with 5-second physical control, enabling agents to jointly reason over regulation commitments, workload flexibility, cooling, battery dispatch, and facility safety. C2G-BENCH achieves this through two coupled Gymnasium environments: C2GMacroEnv, where a high level controller bids into the regulation market, and C2GFastEnv, where a low level controller actuates the Dynamic Voltage and Frequency Scaling (DVFS), Coolant Distribution Unit (CDU) pump speed, HVAC effort, and Battery dispatch (BESS). The simulator models a 250 MW class two zone facility using seven modular physics engines covering workload, thermal, electrical, battery, grid signal, weather, and market dynamics, driven by real workload and weather traces. We benchmark a family of rule-based, LLM-based & RL-based controllers for both the macro and fast environments, and evaluate them on four stress-test environments in multiple grid markets. Baseline results show that active low level control substantially improves tracking quality: a rule-based macro controller paired with a RL-based low level controller reduces the tracking RMSE from 2,737 kW to 229 kW compared with a macro only configuration, while maintaining full throughput and zero thermal violations. These results demonstrate that C2G-BENCH exposes meaningful cross layer tradeoffs and provides a reusable benchmark for studying safe, hierarchical control of grid interactive AI data centers.

Reinforcement Learning (RL) is increasingly applied to large-scale decision-making problems like logistics, scheduling, and recommender systems, but existing algorithms struggle with the curse of dimensionality in such large discrete action spaces. We propose Distance-Guided Reinforcement Learning (DGRL), combining Sampled Dynamic Neighborhoods and Distance-Based Updates to enable efficient RL in problems with up to $10^{20}$ actions. Unlike prior methods, DGRL performs stochastic volumetric exploration and transforms policy optimization into a stable regression task, decoupling gradient variance from action space cardinality. On structured tasks, DGRL provably guarantees local value improvement.DGRL naturally generalizes to hybrid continuous-discrete action spaces. We demonstrate performance improvements of up to 66% against state-of-the-art benchmarks across regularly and irregularly structured environments, while simultaneously improving convergence speed and computational complexity.