Narun Raman, Taylor Lundy, Thiago Amin, Jesse Perla, Kevin Leyton-Brown*

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How should one judge whether a given large language model (LLM) can reliably perform economic reasoning? Most existing LLM benchmarks focus on specific applications and fail to present the model with a rich variety of economic tasks. A notable exception is Raman et al. [2024], who offer an approach for comprehensively benchmarking strategic decision-making; however, this approach fails to address the non-strategic settings prevalent in microeconomics, such as supply-and-demand analysis. We address this gap by taxonomizing microeconomic reasoning into 58 distinct elements, focusing on the logic of supply and demand, each grounded in up to 10 distinct domains, 5 perspectives, and 3  types. The generation of benchmark data across this combinatorial space is powered by a novel LLM-assisted data generation protocol that we dub auto-STEER, which generates a set of questions by adapting handwritten templates to target new domains and perspectives. Because it offers an automated way of generating fresh questions, auto-STEER mitigates the risk that LLMs will be trained to over-fit evaluation benchmarks; we thus hope that it will serve as a useful tool both for evaluating and fine-tuning models for years to come. We demonstrate the usefulness of our benchmark via a case study on 27 LLMs, ranging from small open-source models to the current state of the art. We examined each model's ability to solve microeconomic problems across our whole taxonomy and present the results across a range of prompting strategies and scoring metrics.

Ziyu Wan, Yunxiang Li, Xiaoyu Wen, Yan Song, Hanjing Wang, Linyi Yang, Mark Schmidt*, Jun Wang, Weinan Zhang, Shuyue Hu, Ying Wen

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Recent research on Reasoning of Large Language Models (LLMs) has sought to further enhance their performance by integrating meta-thinking -- enabling models to monitor, evaluate, and control their reasoning processes for more adaptive and effective problem-solving. However, current single-agent work lacks a specialized design for acquiring meta-thinking, resulting in low efficacy. To address this challenge, we introduce Reinforced Meta-thinking Agents (ReMA), a novel framework that leverages Multi-Agent Reinforcement Learning (MARL) to elicit meta-thinking behaviors, encouraging LLMs to think about thinking. ReMA decouples the reasoning process into two hierarchical agents: a high-level meta-thinking agent responsible for generating strategic oversight and plans, and a low-level reasoning agent for detailed executions. Through iterative reinforcement learning with aligned objectives, these agents explore and learn collaboration, leading to improved generalization and robustness. Empirical results from single-turn experiments demonstrate that ReMA outperforms single-agent RL baselines on complex reasoning tasks, including competitive-level mathematical benchmarks and LLM-as-a-Judge benchmarks. Additionally, we further extend ReMA to multi-turn interaction settings, leveraging turn-level ratio and parameter sharing to improve efficiency. Comprehensive ablation studies further illustrate the evolving dynamics of each distinct agent, providing valuable insights into how the meta-thinking reasoning process enhances the reasoning capabilities of LLMs. Our code can be found in this https URL

Chen Fan, Mark Schmidt*, Christos Thrampoulidis

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Different gradient-based methods for optimizing overparameterized models can all achieve zero training error yet converge to distinctly different solutions inducing different generalization properties. We provide the first complete characterization of implicit optimization bias for p-norm normalized steepest descent (NSD) and momentum steepest descent (NMD) algorithms in multi-class linear classification with cross-entropy loss. Our key theoretical contribution is proving that these algorithms converge to solutions maximizing the margin with respect to the classifier matrix's p-norm, with established convergence rates. These results encompass important special cases including Spectral Descent and Muon, which we show converge to max-margin solutions with respect to the spectral norm. A key insight of our contribution is that the analysis of general entry-wise and Schatten p-norms can be reduced to the analysis of NSD/NMD with max-norm by exploiting a natural ordering property between all p-norms relative to the max-norm and its dual sum-norm. For the specific case of descent with respect to the max-norm, we further extend our analysis to include preconditioning, showing that Adam converges to the matrix's max-norm solution. Our results demonstrate that the multi-class linear setting, which is inherently richer than the binary counterpart, provides the most transparent framework for studying implicit biases of matrix-parameter optimization algorithms.

David Abel, Michael Bowling*, André Barreto, Will Dabney, Shi Dong, Steven Hansen, Anna Harutyunyan, Khimya Khetarpal, Clare Lyle, Razvan Pascanu, Georgios Piliouras, Doina Precup, Jonathan Richens, Mark Rowland, Tom Schaul, Satinder Singh

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Agents are minimally entities that are influenced by their past observations and act to influence future observations. This latter capacity is captured by empowerment, which has served as a vital framing concept across artificial intelligence and cognitive science. This former capacity, however, is equally foundational: In what ways, and to what extent, can an agent be influenced by what it observes? In this paper, we ground this concept in a universal agent-centric measure that we refer to as plasticity, and reveal a fundamental connection to empowerment. Following a set of desiderata on a suitable definition, we define plasticity using a new information-theoretic quantity we call the generalized directed information. We show that this new quantity strictly generalizes the directed information introduced by Massey (1990) while preserving all of its desirable properties. Under this definition, we find that plasticity is well thought of as the mirror of empowerment: The two concepts are defined using the same measure, with only the direction of influence reversed. Our main result establishes a tension between the plasticity and empowerment of an agent, suggesting that agent design needs to be mindful of both characteristics. We explore the implications of these findings, and suggest that plasticity, empowerment, and their relationship are essential to understanding agency

Marzi Heidari, Hanping Zhang, Yuhong Guo*

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The challenge of learning with noisy labels is significant in machine learning, as it can severely degrade the performance of prediction models if not addressed properly. This paper introduces a novel framework that conceptualizes noisy label correction as a reinforcement learning (RL) problem. The proposed approach, Reinforcement Learning for Noisy Label Correction (RLNLC), defines a comprehensive state space representing data and their associated labels, an action space that indicates possible label corrections, and a reward mechanism that evaluates the efficacy of label corrections. RLNLC learns a deep feature representation based policy network to perform label correction through reinforcement learning, utilizing an actor-critic method. The learned policy is subsequently deployed to iteratively correct noisy training labels and facilitate the training of the prediction model. The effectiveness of RLNLC is demonstrated through extensive experiments on multiple benchmark datasets, where it consistently outperforms existing state-of-the-art techniques for learning with noisy labels.

Hon Tik Tse*, Siddarth Chandrasekar*, Marlos C. Machado*

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In recent years, the successor representation (SR) has attracted increasing attention in reinforcement learning (RL), and it has been used to address some of its key challenges, such as exploration, credit assignment, and generalization. The SR can be seen as representing the underlying credit assignment structure of the environment by implicitly encoding its induced transition dynamics. However, the SR is reward-agnostic. In this paper, we discuss a similar representation that also takes into account the reward dynamics of the problem. We study the default representation (DR), a recently proposed representation with limited theoretical (and empirical) analysis. Here, we lay some of the theoretical foundation underlying the DR in the tabular case by (1) deriving dynamic programming and (2) temporal-difference methods to learn the DR, (3) characterizing the basis for the vector space of the DR, and (4) formally extending the DR to the function approximation case through default features. Empirically, we analyze the benefits of the DR in many of the settings in which the SR has been applied, including (1) reward shaping, (2) option discovery, (3) exploration, and (4) transfer learning. Our results show that, compared to the SR, the DR gives rise to qualitatively different, reward-aware behaviour and quantitatively better performance in several settings.

Alex Lewandowski*, Aditya A. Ramesh, Edan Meyer*, Dale Schuurmans*, Marlos C. Machado*

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Continual learning is often motivated by the idea, known as the big world hypothesis, that the world is bigger than the agent. Recent problem formulations capture this idea by explicitly constraining an agent relative to the environment. These constraints lead to solutions in which the agent continually adapts to best use its limited capacity, rather than converging to a fixed solution. However, explicit constraints can be ad hoc, difficult to incorporate, and limiting to the effectiveness of scaling up the agent's capacity. In this paper, we characterize a problem setting in which an agent, regardless of its capacity, is implicitly constrained by being embedded in the environment. In particular, we introduce a computationally-embedded perspective that represents an embedded agent as an automaton simulated within a universal (formal) computer. We prove that such an automaton is implicitly constrained and that it is equivalent to an agent that interacts with a reward-free and partially-observable Markov decision process over a countably infinite state-space. We propose an objective for this setting, which we call interactivity, that measures an agent's ability to continually adapt its behaviour to learn new predictions. To support experimentation on continual adaptation, we develop a synthetic benchmark in which an interactivity-seeking agent constructs its own non-stationary stream of experience from which it must continually learn to predict.

Enze Shi, Pankaj Bhagwat, Zhixian Yang, Linglong Kong*, Bei Jiang*

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Machine learning models have achieved widespread success but often inherit and amplify historical biases, resulting in unfair outcomes. Traditional fairness methods typically impose constraints at the prediction level, without addressing underlying biases in data representations. In this work, we propose a principled framework that adjusts data representations to balance predictive utility and fairness. Using sufficient dimension reduction, we decompose the feature space into target-relevant, sensitive, and shared components, and control the fairness-utility trade-off by selectively removing sensitive information. We provide a theoretical analysis of how prediction error and fairness gaps evolve as shared subspaces are added, and employ influence functions to quantify their effects on the asymptotic behavior of parameter estimates. Experiments on both synthetic and real-world datasets validate our theoretical insights and show that the proposed method effectively improves fairness while preserving predictive performance.

Ke Sun, Yingnan Zhao, Enze Shi, Yafei Wang, Xiaodong Yan, Linglong Kong*, Bei Jiang*

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Machine learning models have achieved widespread success but often inherit and amplify historical biases, resulting in unfair outcomes. Traditional fairness methods typically impose constraints at the prediction level, without addressing underlying biases in data representations. In this work, we propose a principled framework that adjusts data representations to balance predictive utility and fairness. Using sufficient dimension reduction, we decompose the feature space into target-relevant, sensitive, and shared components, and control the fairness-utility trade-off by selectively removing sensitive information. We provide a theoretical analysis of how prediction error and fairness gaps evolve as shared subspaces are added, and employ influence functions to quantify their effects on the asymptotic behavior of parameter estimates. Experiments on both synthetic and real-world datasets validate our theoretical insights and show that the proposed method effectively improves fairness while preserving predictive performance.

Samuel McLaughlin Robertson*, Thang D. Chu*, Bo Dai, Dale Schuurmans*, Csaba Szepesvari*, Jincheng Mei

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Machine learning models have achieved widespread success but often inherit and amplify historical biases, resulting in unfair outcomes. Traditional fairness methods typically impose constraints at the prediction level, without addressing underlying biases in data representations. In this work, we propose a principled framework that adjusts data representations to balance predictive utility and fairness. Using sufficient dimension reduction, we decompose the feature space into target-relevant, sensitive, and shared components, and control the fairness-utility trade-off by selectively removing sensitive information. We provide a theoretical analysis of how prediction error and fairness gaps evolve as shared subspaces are added, and employ influence functions to quantify their effects on the asymptotic behavior of parameter estimates. Experiments on both synthetic and real-world datasets validate our theoretical insights and show that the proposed method effectively improves fairness while preserving predictive performance.

Alireza Bakhtiari*, Alex Ayoub*, Samuel McLaughlin Robertson*, David Janz, Csaba Szepesvari*

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We establish a lower bound on the eluder dimension in generalised linear model classes, showing that standard eluder dimension-based analysis cannot lead to first-order regret bounds. To address this, we introduce a localisation method for the eluder dimension; our analysis immediately recovers and improves on classic results for Bernoulli bandits, and allows for the first genuine first-order bounds for finite-horizon reinforcement learning tasks with bounded cumulative returns.

Davide Maran, Csaba Szepesvari*

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Abstract not available here. Check out the full paper.

Martin Ondrus*, Ivor Cribben, Yang Feng

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Networks have been extensively used and have provided novel insights across a wide variety of research areas. However, many real-world systems are, in fact, a ``network of networks'', or a multilayer network, which interact as components of a larger multimodal system. A major difficulty in this multilayer framework is the estimation of interlayer edges or connections. In this work, we propose a new estimation method, called multilayer sparse + low-rank inverse covariance estimation (multiSLICE), which estimates the interlayer edges. multiSLICE bridges latent variable Gaussian graphical methods with multilayer networks, offering a flexible framework for modeling processes with irregular sampling and heterogeneous graph structures. We develop an effective algorithm to compute the estimator. We also establish theoretical conditions for the recoverability of the joint space, analyze how inter-layer interactions influence joint parameter estimation, and provide theoretical bounds on their relationships. Finally, we rigorously evaluate our method on both simulated and multimodal neuroimaging data, demonstrating improvements over state-of-the-art approaches. Finally, all the relevant R code implementing the method in the article is available on GitHub.

Farnam Mansouri, Hans U. Simon, Adish Singla, Yuxin Chen, Sandra Zilles*

Machine learning can greatly benefit from providing learning algorithms with pairs of contrastive training examples -- typically pairs of instances that differ only slightly, yet have different class labels. Intuitively, the difference in the instances helps explain the difference in the class labels. This paper proposes a theoretical framework in which the effect of various types of contrastive examples on active learners is studied formally. The focus is on the sample complexity of learning concept classes and how it is influenced by the choice of contrastive examples. We illustrate our results with geometric concept classes and classes of Boolean functions. Interestingly, we reveal a connection between learning from contrastive examples and the classical model of self-directed learning.

Reginald McLean*, Evangelos Chatzaroulas, Luc McCutcheon, Frank Röder, Tianhe Yu, Zhanpeng He, K.R. Zentner, Ryan Julian, J K Terry, Isaac Woungang, Nariman Farsad, Pablo Samuel Castro

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Meta-World is widely used for evaluating multi-task and meta-reinforcement learning agents, which are challenged to master diverse skills simultaneously. Since its introduction however, there have been numerous undocumented changes which inhibit a fair comparison of algorithms. This work strives to disambiguate these results from the literature, while also leveraging the past versions of Meta-World to provide insights into multi-task and meta-reinforcement learning benchmark design. Through this process we release a new open-source version of Meta-World (this https URL) that has full reproducibility of past results, is more technically ergonomic, and gives users more control over the tasks that are included in a task set.

Zhijian Zhou, Xunye Tian, Liuhua Peng, Chao Lei, Antonin Schrab, Danica J. Sutherland*, Feng Liu

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To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly maximizing multiple kernel-based statistics may result in highly similar kernels that capture highly overlapping information, limiting the effectiveness of aggregation. To address this, we propose an aggregated statistic that explicitly incorporates kernel diversity based on the covariance between different kernels. Moreover, we identify a fundamental challenge: a trade-off between the diversity among kernels and the test power of individual kernels, i.e., the selected kernels should be both effective and diverse. This motivates a testing framework with selection inference, which leverages information from the training phase to select kernels with strong individual performance from the learned diverse kernel pool. We provide rigorous theoretical statements and proofs to show the consistency on the test power and control of Type-I error, along with asymptotic analysis of the proposed statistics. Lastly, we conducted extensive empirical experiments demonstrating the superior performance of our proposed approach across various benchmarks for both two-sample and independence testing.

Zheng He, Roman Pogodin, Yazhe Li, Namrata Deka, Arthur Gretton, Danica J. Sutherland*

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Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed that, contrary to the unconditional case, no universally finite-sample valid test can ever achieve nontrivial power. While informative, this result (based on “hiding” dependence) does not seem to explain the frequent practical failures observed with popular CI tests. We investigate the Kernel-based Conditional Independence (KCI) test – of which we show the Generalized Covariance Measure underlying many recent tests is nearly a special case – and identify the major factors underlying its practical behavior. We highlight the key role of errors in the conditional mean embedding estimate for the Type I error, while pointing out the importance of selecting an appropriate conditioning kernel (not recognized in previous work) as being necessary for good test power but also tending to inflate Type I error.

Wenlong Deng, Yi Ren, Muchen Li, Danica J. Sutherland*, Xiaoxiao Li, Christos Thrampoulidis

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Reinforcement learning (RL) has become popular in enhancing the reasoning capabilities of large language models (LLMs), with Group Relative Policy Optimization (GRPO) emerging as a widely used algorithm in recent systems. Despite GRPO's widespread adoption, we identify a previously unrecognized phenomenon we term Lazy Likelihood Displacement (LLD), wherein the likelihood of correct responses marginally increases or even decreases during training. This behavior mirrors a recently discovered misalignment issue in Direct Preference Optimization (DPO), attributed to the influence of negative gradients. We provide a theoretical analysis of GRPO's learning dynamic, identifying the source of LLD as the naive penalization of all tokens in incorrect responses with the same strength. To address this, we develop a method called NTHR, which downweights penalties on tokens contributing to the LLD. Unlike prior DPO-based approaches, NTHR takes advantage of GRPO's group-based structure, using correct responses as anchors to identify influential tokens. Experiments on math reasoning benchmarks demonstrate that NTHR effectively mitigates LLD, yielding consistent performance gains across models ranging from 0.5B to 3B parameters.

Luca Ghafourpour, Valentin Duruisseaux, Bahareh Tolooshams*, Philip H. Wong, Costas A. Anastassiou, Anima Anandkumar

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Characterizing the cellular properties of neurons is fundamental to understanding their function in the brain. In this quest, the generation of bio-realistic models is central towards integrating multimodal cellular data sets and establishing causal relationships. However, current modeling approaches remain constrained by the limited availability and intrinsic variability of experimental neuronal data. The deterministic formalism of bio-realistic models currently precludes accounting for the natural variability observed experimentally. While deep learning is becoming increasingly relevant in this space, it fails to capture the full biophysical complexity of neurons, their nonlinear voltage dynamics, and variability. To address these shortcomings, we introduce NOBLE, a neural operator framework that learns a mapping from a continuous frequency-modulated embedding of interpretable neuron features to the somatic voltage response induced by current injection. Trained on synthetic data generated from bio-realistic neuron models, NOBLE predicts distributions of neural dynamics accounting for the intrinsic experimental variability. Unlike conventional bio-realistic neuron models, interpolating within the embedding space offers models whose dynamics are consistent with experimentally observed responses. NOBLE enables the efficient generation of synthetic neurons that closely resemble experimental data and exhibit trial-to-trial variability, offering a 4200× speedup over the numerical solver. NOBLE is the first scaled-up deep learning framework that validates its generalization with real experimental data. To this end, NOBLE captures fundamental neural properties in a unique and emergent manner that opens the door to a better understanding of cellular composition and computations, neuromorphic architectures, large-scale brain circuits, and general neuroAI applications.

Valérie Costa, Thomas Fel, Ekdeep Singh Lubana, Bahareh Tolooshams, Demba Ba

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Motivated by the hypothesis that neural network representations encode abstract, interpretable features as linearly accessible, approximately orthogonal directions, sparse autoencoders (SAEs) have become a popular tool in interpretability literature. However, recent work has demonstrated phenomenology of model representations that lies outside the scope of this hypothesis, showing signatures of hierarchical, nonlinear, and multi-dimensional features. This raises the question: do SAEs represent features that possess structure at odds with their motivating hypothesis? If not, does avoiding this mismatch help identify said features and gain further insights into neural network representations? To answer these questions, we take a construction-based approach and re-contextualize the popular matching pursuit (MP) algorithm from sparse coding to design MP-SAE—an SAE that unrolls its encoder into a sequence of residual-guided steps, allowing it to capture hierarchical and nonlinearly accessible features. Comparing this architecture with existing SAEs on a mixture of synthetic and natural data settings, we show: (i) hierarchical concepts induce conditionally orthogonal features, which existing SAEs are unable to faithfully capture, and (ii) the nonlinear encoding step of MP-SAE recovers highly meaningful features, helping us unravel shared structure in the seemingly dichotomous representation spaces of different modalities in a vision-language model, hence demonstrating the assumption that useful features are solely linearly accessible is insufficient. We also show that the sequential encoder principle of MPSAE affords an additional benefit of adaptive sparsity at inference time, which may be of independent interest. Overall, we argue our results provide credence to the idea that interpretability should begin with the phenomenology of representations, with methods emerging from assumptions that fit it.

Faraz Zargari*, Hossein Nekouyan*, Lyndon Hallett, Bo Sun, Xiaoqi Tan*

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We study the online multi-class selection problem with group fairness guarantees, where limited resources must be allocated to sequentially arriving agents. Our work addresses two key limitations in the existing literature. First, we introduce a novel lossless rounding scheme that ensures the integral algorithm achieves the same expected performance as any fractional solution. Second, we explicitly address the challenges introduced by agents who belong to multiple classes. To this end, we develop a randomized algorithm based on a relax-and-round framework. The algorithm first computes a fractional solution using a resource reservation approach -- referred to as the set-aside mechanism -- to enforce fairness across classes. The subsequent rounding step preserves these fairness guarantees without degrading performance. Additionally, we propose a learning-augmented variant that incorporates untrusted machine-learned predictions to better balance fairness and efficiency in practical settings.

Shayan Karimi*, Xiaoqi Tan*

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This paper investigates the computational complexity of reinforcement learning in a novel linear function approximation regime, termed partial qπ-realizability. In this framework, the objective is to learn an ϵ-optimal policy with respect to a predefined policy set Π, under the assumption that all value functions for policies in Π are linearly realizable. The assumptions of this framework are weaker than those in qπ-realizability but stronger than those in q∗-realizability, providing a practical model where function approximation naturally arises. We prove that learning an ϵ-optimal policy in this setting is computationally hard. Specifically, we establish NP-hardness under a parameterized greedy policy set (argmax) and show that - unless NP = RP - an exponential lower bound (in feature vector dimension) holds when the policy set contains softmax policies, under the Randomized Exponential Time Hypothesis. Our hardness results mirror those in q∗-realizability and suggest computational difficulty persists even when Π is expanded beyond the optimal policy. To establish this, we reduce from two complexity problems, δ-Max-3SAT and δ-Max-3SAT(b), to instances of GLinear-κ-RL (greedy policy) and SLinear-κ

-RL (softmax policy). Our findings indicate that positive computational results are generally unattainable in partial qπ-realizability, in contrast to qπ-realizability under a generative access model.

Marco Mussi, Till Freihaut, Antoine Moulin, Giorgia Ramponi, Dirk van der Hoeven, Alberto Maria Metelli, Felix Berkenkamp, Francesco Trovòm Csaba Szepesvari*

WORKSHOP INFO

Speakers include: Danica J. Sutherland*, Bahareh Tolooshams*

WORKSHOP INFO

Matthew Schlegel*, Matthew Taylor*, Mostafa Farrokhabadi

Part of the "Tackling Climate Change with Machine Learning" workshop

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Time domain simulation, i.e., modeling the system’s evolution over time, is a crucial tool for studying and enhancing power system stability and dynamic performance. However, these simulations become computationally intractable for renewable penetrated grids, due to the small simulation time step required to capture renewable energy resources’ ultra-fast dynamic phenomena in the range of 1-50 microseconds.

This creates a critical need for solutions that are both fast and scalable, posing a major barrier for the stable integration of renewable energy resources and thus climate change mitigation. This paper explores operator learning, a family of machine learning methods that learn mappings between functions, as a surrogate model for these costly simulations. The paper investigates, for the first time, the fundamental concept of simulation time step-invariance, which enables models trained on coarse time steps to generalize to fine-resolution dynamics. Three operator learning methods are benchmarked on a simple test system that, while not incorporating practical complexities of renewable-penetrated grids, serves as a first proof-of-concept to demonstrate the viability of time step-invariance. Models are evaluated on (i) zero-shot super-resolution, where training is performed on a coarse simulation time step and inference is performed at super-resolution, and (ii) generalization between stable and unstable dynamic regimes. This work addresses a key challenge in the integration of renewable energy for the mitigation of climate change by benchmarking operator learning methods to model physical systems.