AI-generated summaries
Today's ML research,
without the noise.
Daily summaries of the latest machine learning papers from arXiv, processed every 8 hours.
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Robust data-driven discovery of fractional differential equations via weak formulations and Pareto-based subset selection
Theory
- Weak-Pareto combines weak formulations with Pareto-based selection for robust FPDE discovery.
- The framework effectively mitigates noise amplification issues associated with fractional differentiation.
- Weak-Pareto outperforms traditional methods in recovering equations from noisy data.
- The methodology allows for continuous-order optimization, avoiding discretization biases.
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Robust data-driven discovery of fractional differential equations via weak formulations and Pareto-based subset selection
Summary
This paper presents Weak-Pareto, a novel framework for discovering fractional partial differential equations (FPDEs) from noisy data. The challenge in this domain arises from the amplification of high-frequency noise due to fractional differentiation and the unknown nature of derivative orders. Weak-Pareto integrates an adjoint-consistent weak formulation of fractional terms with a Pareto-based subset selection approach, allowing for effective handling of both linear and nonlinear terms. The methodology replaces traditional pointwise differentiation with smoothing integration, enhancing noise robustness. Coefficients are fitted using ridge regression within a differential-evolution search that accounts for the continuous nature of derivative orders. The framework demonstrates superior performance in recovering parsimonious structures from both clean and noisy measurements across various benchmarks, including fractional advection-diffusion and Burgers equations. The results indicate that Weak-Pareto retains the correct support even under high noise levels, outperforming traditional strong-form methods. Additionally, a two-dimensional extension of Weak-Pareto successfully identifies coordinate-dependent orders, showcasing its versatility in complex scenarios.
Methodology
The Weak-Pareto framework employs an adjoint-consistent weak formulation for fractional operators, replacing pointwise differentiation with integral measurements. It utilizes ridge regression for coefficient fitting and a differential-evolution search for continuous-order optimization. The Pareto-based subset selection enhances model robustness by selecting features based on validation error and complexity.
Results
Weak-Pareto successfully recovers parsimonious structures from both clean and noisy data across various benchmarks. It maintains correct support at all tested noise levels, significantly outperforming strong-form counterparts. The framework also shows improved operator recovery consistency and reduced runtime compared to neural network baselines.
Implications
The proposed framework has significant implications for data-driven modeling of complex systems described by fractional differential equations, which are prevalent in fields such as physics, biology, and finance. Its robustness against noise makes it a valuable tool for real-world applications where data quality is often compromised.
Novel Knowledge-Guided Generative Methods for Synthetic Transcriptomic Data
Generative Models
Graph Learning
- Synthetic data generation can mitigate challenges in accessing high-quality transcriptomic data.
- Integrating biological knowledge through gene graphs enhances the realism and utility of synthetic data.
- MK-TGAN outperforms other generative models in terms of data realism and biological coherence.
- The study highlights the importance of explicit knowledge integration mechanisms in generative models.
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Novel Knowledge-Guided Generative Methods for Synthetic Transcriptomic Data
Summary
This paper addresses the challenges of generating synthetic transcriptomic data, which is crucial for biomedical research but often limited by issues such as data imbalance, biases, and ethical constraints. The authors present a comparative analysis of generative models, particularly focusing on the integration of prior biological knowledge through gene graphs to enhance the realism and utility of synthetic data. They introduce three variants of Generative Adversarial Networks (GANs), with a particular emphasis on MK-TGAN, a multi-kernel, Graph Neural Network-based model that effectively incorporates biological knowledge. The study demonstrates that integrating prior knowledge significantly improves the performance of generative models, with MK-TGAN achieving superior realism and biological plausibility in the generated samples. The evaluation is conducted on breast cancer transcriptomic data, specifically targeting Epithelial-to-Mesenchymal Transition (EMT)-related genes, providing a biologically relevant context for assessing the effectiveness of different knowledge integration strategies.
Methodology
The authors developed three GAN variants: Graph-Modulated GAN (GM-GAN), Graph-Regularized GAN (GR-GAN), and MK-TGAN. GM-GAN and GR-GAN incorporate biological knowledge implicitly, while MK-TGAN explicitly utilizes multiple graph neural network kernels to enhance representation capacity. The models were evaluated using breast cancer transcriptomic data focused on EMT-related genes.
Results
MK-TGAN achieved state-of-the-art performance across metrics such as precision and recall, demonstrating superior fidelity, diversity, and biological coherence in the generated synthetic samples compared to other models.
Implications
The findings suggest that knowledge-guided generative methods can significantly improve the generation of synthetic transcriptomic data, which may facilitate research in genomics and personalized medicine by providing high-quality datasets without ethical constraints.
A Cloud-Edge System for Multimodal Clinical Screening in Resource-Constrained Rural Settings
Multimodal
Efficient ML
Interpretability
- Introduces a cloud-edge collaborative architecture for multimodal clinical screening.
- Utilizes lightweight edge models for data processing and a cloud LLM for reasoning.
- Achieves high diagnostic accuracy and factual grounding while minimizing data transmission.
- Demonstrates the system's effectiveness under various simulated bandwidth conditions.
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A Cloud-Edge System for Multimodal Clinical Screening in Resource-Constrained Rural Settings
Summary
This paper presents a novel cloud-edge collaborative architecture designed to enhance multimodal clinical screening in resource-constrained rural settings. The authors identify significant barriers to effective medical AI deployment in these areas, including limited bandwidth, computational resources, and the need for integrating diverse medical modalities. To address these challenges, the proposed system utilizes lightweight, domain-specific models at the edge to convert raw medical data into structured outputs, while a cloud-based large language model (LLM) synthesizes these outputs into coherent clinical summaries. An orchestrator on the edge dynamically selects diagnostic tools based on patient context, ensuring relevant modalities are utilized without unnecessary data processing. The evaluation of the system involved 100 multimodal clinical cases across various medical domains, simulating different network conditions. The results demonstrate that the hybrid architecture achieves high oracle accuracy and factual grounding while significantly reducing data transmission size compared to cloud-only systems. The findings emphasize the importance of architectural design in improving clinical decision-making and efficiency in rural healthcare settings.
Methodology
The study employs a cloud-edge collaborative system where edge models process medical data into structured outputs, and a cloud-based LLM synthesizes these outputs into clinical summaries. The system was evaluated using 100 clinical cases under three simulated network profiles, focusing on bandwidth constraints and clinical quality metrics.
Results
The hybrid system achieved oracle accuracy ranging from 0.87 to 0.90, with knowledge graph precision up to 0.96 and coverage precision between 0.95 and 0.99. It maintained a bandwidth-invariant latency of 25-38 seconds while transmitting approximately 6.5 KB of structured evidence, significantly less than cloud-only baselines.
Implications
This research has significant implications for improving healthcare delivery in rural areas by enabling efficient and accurate clinical decision-making through advanced AI systems. The proposed architecture could facilitate better access to specialist-level diagnostics and reduce patient attrition due to follow-up visits.
When Local Variance Optimality Is Not Enough: RoPE-Aligned Q/K Rotations for Dynamic 4-Bit Quantisation
NLP
Large Language Models
Optimization
- Introduces a local benchmark for RoPE-commuting orthogonal transformations, focusing on independent pairwise rotations.
- Demonstrates that the head-shared pairwise configuration yields higher perplexity than full-head mixing in dynamic quantization settings.
- Establishes that the optimization of a surrogate does not guarantee improved quantization accuracy due to misalignment with quantizer statistics.
- Highlights the relationship between mixing support size and quantization error, suggesting broader mixing leads to better performance.
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When Local Variance Optimality Is Not Enough: RoPE-Aligned Q/K Rotations for Dynamic 4-Bit Quantisation
Summary
This paper investigates the effectiveness of rotation-based post-training quantization methods in the context of transformer models, specifically focusing on RoPE (Rotary Position Embedding) aligned Q/K rotations. The authors challenge the conventional approach of applying orthogonal transforms across entire attention heads, proposing instead to respect the two-dimensional frequency pairs defined by RoPE. They derive the optimal rotation angle that minimizes channel variance under a pooled-covariance surrogate and verify its implementation. However, their experimental results reveal that this head-shared pairwise configuration does not enhance accuracy compared to full-head mixing, leading to increased perplexity across various checkpoints. The study highlights the misalignment between the surrogate's optimization and the quantizer's scale-setting statistic, suggesting that optimality in structured surrogates does not necessarily translate to reduced quantization error. The findings emphasize the importance of mixing support and the need for careful consideration of the quantization process in low-bit post-training quantization strategies.
Methodology
The authors derive the optimal rotation angle for minimizing channel variance using a pooled-covariance, position-averaged surrogate. They conduct experiments on various checkpoints, comparing the performance of head-shared pairwise configurations against full-head mixing in a dynamic quantization setting (W4A4KV4). The analysis includes evaluating perplexity and quantization error across different contexts and configurations.
Results
The experiments show that replacing the full-head Hadamard mixing with the head-shared pairwise configuration consistently increases perplexity across all evaluated contexts. Although the pairwise rotation can be optimized to attain a local minimum, it does not outperform the full-head mixing approach. Additionally, estimating the shared angle from K alone improves performance but still falls short of the full-head configuration.
Implications
The findings suggest that while structured surrogates can provide theoretical benefits, practical implementations must consider the alignment of optimization objectives with quantization processes. This has implications for the design of quantization strategies in transformer models, particularly in low-bit settings, where careful consideration of mixing support and quantization statistics is crucial.
Decentralized Multi-Player Q-Learning in Episodic Markov Decision Processes with Information Asymmetry
Reinforcement Learning
Theory
Robotics
- Introduces decentralized multi-player Q-learning under information asymmetry.
- Proposes algorithms mQ-learning and mQ-learning-intervals for common rewards and independent rewards scenarios.
- Demonstrates that decentralized learning can achieve regret bounds similar to centralized benchmarks.
- Highlights the challenges posed by exponential growth in joint action space with increasing players.
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Decentralized Multi-Player Q-Learning in Episodic Markov Decision Processes with Information Asymmetry
Summary
This paper investigates decentralized multi-player reinforcement learning in episodic tabular Markov Decision Processes (MDPs) under conditions of information asymmetry. The authors categorize the problem into three scenarios: (A) unobserved actions with common rewards, (B) observed actions with independent rewards, and (C) unobserved actions with independent rewards. They propose two algorithms, mQ-learning and mQ-learning-intervals, for Problems A and B, achieving a regret bound of ˜O(√H4SAjoint T). For Problem C, they introduce mEXC and mEXC-Bellman, which are explore-then-commit algorithms with a regret bound of ˜O(H(SAjoint)1/3T 2/3). The results indicate that decentralized learning under information asymmetry can match the performance of centralized joint-action Q-learning, with regret bounds that are polynomially close to single-agent Q-learning rates. The findings highlight the potential for decentralized learning frameworks in cooperative systems where players cannot communicate during learning but can agree on a protocol in advance.
Methodology
The authors develop decentralized algorithms tailored for three types of information asymmetry in multi-player settings. They utilize a lexicographic ordering of joint actions and maintain confidence bounds to facilitate coordination among players without communication. The algorithms are designed to explore and commit to strategies based on observed rewards and actions, ensuring efficient learning in episodic MDPs.
Results
The proposed algorithms achieve regret bounds of ˜O(√H4SAjoint T) for Problems A and B, and ˜O(H(SAjoint)1/3T 2/3) for Problem C. These results show that decentralized learning can perform comparably to centralized approaches, with regret rates that are logarithmically close to those of single-agent Q-learning, despite the challenges introduced by information asymmetry.
Implications
The findings suggest that decentralized reinforcement learning can be effectively applied in scenarios where agents must operate independently without communication, such as in multi-robot coordination and distributed resource allocation. The results also indicate that information asymmetry does not impose significant additional costs on learning efficiency compared to centralized methods.
A Contract-Grade Verifier for LLM-Generated GPU Kernels, and a Native Blackwell Backward for the Gated-Linear-Recurrence Family
Large Language Models
Theory
Optimization
- Introduction of a twelve-gate contract-grade verifier for GPU kernels.
- Audit of 2,638 machine-generated kernels revealing significant correctness issues.
- Development of the first native Blackwell tcgen05 training backward for the GDN family.
- Demonstration of the verifier's effectiveness through independent validation methods.
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A Contract-Grade Verifier for LLM-Generated GPU Kernels, and a Native Blackwell Backward for the Gated-Linear-Recurrence Family
Summary
This paper addresses the reliability of GPU kernels generated by large language models (LLMs), which often report high correctness rates based on loose testing methods. The authors introduce a contract-grade verifier that evaluates GPU kernels against twelve adversarial gates, ensuring rigorous correctness checks beyond simple output comparisons. The verifier was applied to audit 2,638 machine-generated kernels, revealing that 39.5% were fundamentally broken and 62.1% had at least one violation. This starkly contrasts with the results of existing testing methods, which accepted many of these kernels as correct. The authors also present a novel native Blackwell tcgen05 training backward for the gated-linear-recurrence family, verified against a double-precision oracle. The findings suggest that the perceived correctness of generated kernels is often overstated, and implementing tolerance-free contracts could significantly enhance the reliability of kernel generation.
Methodology
The authors developed a contract-grade verifier that operationalizes the Kernel Contracts taxonomy, consisting of twelve adversarial gates. The verifier was used to audit a large corpus of machine-generated kernels, assessing their correctness against a high-precision reference. The methodology included both tolerance-free checks and those with derived tolerances, ensuring a robust evaluation framework.
Results
The verifier found that 39.5% of the audited kernels were broken beyond any tolerance argument, while 62.1% exhibited at least one violation. The standard testing method accepted 1,487 kernels that the verifier rejected, indicating a significant gap in correctness assessment. The authors also verified their own kernel against a double-precision oracle, confirming its correctness.
Implications
The findings suggest that current methods for assessing the correctness of LLM-generated GPU kernels are inadequate, potentially leading to the acceptance of faulty kernels. The introduction of a rigorous verification framework could improve the reliability of GPU kernel generation, impacting fields that rely on high-performance computing and machine learning applications.
Exploring Oversmoothing with Householder Matrices
Graph Learning
- Introduces Householder Graph Neural Network (HouseGNN) to combat oversmoothing in GNNs.
- Uses Householder matrices for node embedding updates, preserving Euclidean norms.
- Proves properties of Householder reflectors that contribute to maintaining node representation diversity.
- Offers a novel perspective on the oversmoothing issue by utilizing orthogonal transformations.
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Exploring Oversmoothing with Householder Matrices
Summary
This paper addresses the issue of oversmoothing in deep graph neural networks (GNNs), where node representations converge towards a low-information subspace as the network depth increases. The author introduces the Householder Graph Neural Network (HouseGNN), which employs Householder matrices to update node embeddings. Instead of directly updating hidden states like traditional GCNs, HouseGNN uses aggregated neighborhood messages to estimate a reflection direction. The node embedding is then updated using a Householder reflector followed by a GroupSort operation, ensuring that the Euclidean norm is preserved at every node and depth. The paper proves three key properties: (i) each internal layer maintains the node-wise Euclidean norm, (ii) the Householder reflector is invariant to scale and sign in the message, and (iii) pairwise distances between nodes can vary due to mismatches in node-wise orthogonal operators. This approach aims to mitigate the oversmoothing phenomenon and enhance the discriminative power of deep GNNs.
Methodology
The methodology involves using Householder matrices to define a reflection direction based on neighborhood messages, followed by updating the node state through a Householder reflection and a GroupSort operation. This approach differs from standard GCNs, which directly update hidden states, and instead focuses on maintaining the orthogonality and norm of node representations.
Results
The proposed HouseGNN demonstrates that by employing Householder reflectors, it effectively mitigates the oversmoothing problem, allowing for better separation of node representations even at greater depths. The theoretical properties established in the paper support the effectiveness of this approach in preserving the discriminative variation across nodes.
Implications
The findings suggest that using Householder transformations in GNNs can lead to more robust models that maintain representation diversity, potentially improving performance in tasks such as node classification and link prediction. This approach may inspire further research into orthogonal transformations in neural networks.
A Compositional Theory of Curvature in Probabilistic Circuits
Generative Models
Optimization
Theory
- Probabilistic Circuits (PCs) allow for exact inference and tractable curvature measures unlike deep neural networks.
- Global sharpness regularization can lead to underfitting in PCs due to the compositional nature of their curvature.
- The contribution of each sum node to the Hessian trace can be decomposed into contextual usage and local curvature.
- An adaptive sharpness-aware regularizer improves generalization by focusing on nodes with high intrinsic local curvature.
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A Compositional Theory of Curvature in Probabilistic Circuits
Summary
This paper presents a novel perspective on the curvature of loss surfaces in Probabilistic Circuits (PCs), which are generative models that allow for exact inference. The authors argue that treating curvature as a global regularizer can be misleading due to the compositional nature of PCs. They demonstrate that the contribution of each sum node to the Hessian trace can be decomposed into two components: the circuit flow, which indicates how heavily a node is utilized, and a local sharpness term that reflects the node's output distribution. This decomposition reveals that sharpness is contextually influenced and suggests that global regularization may lead to underfitting. To address this, the authors propose an adaptive sharpness-aware regularizer that penalizes nodes based on their intrinsic local curvature while maintaining efficient updates. Empirical results show that this targeted approach improves generalization compared to traditional global regularization methods, particularly in low-data scenarios.
Methodology
The authors analyze the curvature of loss surfaces in PCs by decomposing the contribution of sum nodes to the Hessian trace into two distinct components: circuit flow and local sharpness. They develop an adaptive regularization technique that targets nodes based on their local curvature, allowing for efficient updates while preserving the tractability of the learning process.
Results
The proposed adaptive sharpness-aware regularizer demonstrated improved generalization performance in empirical tests, particularly in low-data regimes, compared to traditional global regularization methods. The results indicated that while global regularization can achieve flatter optima, it may sacrifice training and test log-likelihood, leading to underfitting.
Implications
This work suggests that more nuanced approaches to regularization in generative models like PCs can enhance their performance, particularly in scenarios with limited data. The findings may influence future research on model training strategies and the design of regularization techniques in machine learning.
Latent On-Policy Self-Distillation
Reinforcement Learning
Large Language Models
Robotics
- Introduces a learnable privileged context for on-policy self-distillation.
- Demonstrates superior performance over existing OPSD methods.
- Achieves high learning efficiency with reduced rollout budget.
- Employs a privileged-margin objective to enhance teacher-student dynamics.
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Latent On-Policy Self-Distillation
Summary
This paper introduces Latent On-Policy Self-Distillation (LOPD), a novel framework aimed at enhancing the learning process of agents by allowing them to learn from their own experiences without relying on pre-defined privileged contexts. Traditional on-policy self-distillation methods depend on designer-specified artifacts for supervision, which limits their scalability and adaptability. LOPD addresses this by making the privileged context learnable and end-to-end, allowing the self-teacher to derive relevant experiences from the agent's interaction history. The framework retrieves experiences and composes them into continuous latent tokens that condition the self-teacher, which then provides dense token-level supervision to the student. A privileged-margin objective is introduced to ensure that the teacher maintains an advantage over the student during training. Empirical results show that LOPD outperforms existing methods in both agentic tool use and code generation tasks while demonstrating high learning efficiency, requiring less than 30% of the rollout budget compared to other methods. The findings suggest that making the privileged context learnable is crucial for achieving significant performance gains, positioning LOPD as a scalable solution for self-directed agent evolution.
Methodology
LOPD utilizes a framework where the student agent generates trajectories from its task and interaction history. A self-teacher, conditioned on learnable latent tokens derived from relevant experiences, provides dense supervision. The training process employs reverse-KL distillation, and a privileged-margin constraint ensures the teacher maintains a verifiable advantage over the student.
Results
LOPD outperformed traditional methods such as OPSD, RLVR, and Skill-SD in various tasks, including agentic tool use and code generation. It demonstrated high learning efficiency, achieving results with less than 30% of the rollout budget compared to competitors. Ablation studies confirmed the necessity of learnable privileged context for performance improvements.
Implications
The findings suggest that LOPD can lead to more scalable and adaptable AI systems capable of self-improvement through experience. This approach could be applied in various domains requiring continual learning and adaptation, such as robotics, autonomous systems, and interactive AI applications.
CAKE: Compiler-Agent Co-Design for Frontier Kernel Evolution
Optimization
Efficient ML
Theory
- CAKE integrates compiler and agent co-design to improve GPU kernel evolution.
- The framework uses a typed intermediate representation (IR) for better hardware-specific control.
- Localized correctness and performance diagnostics are provided to agents, enhancing decision-making.
- Significant performance improvements were observed in benchmarks compared to traditional methods.
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CAKE: Compiler-Agent Co-Design for Frontier Kernel Evolution
Summary
The paper introduces CAKE, a novel framework that integrates compiler and agent co-design to enhance the evolution of GPU kernels. Traditional approaches treat the compiler as a black box, limiting the feedback available to agents when optimizing kernels. CAKE addresses this by allowing agents to work with a typed intermediate representation (IR) that provides detailed insights into hardware-specific scheduling and performance diagnostics. This enables agents to make informed decisions during the kernel evolution process. The framework evolves both the kernels and the compiler, allowing for continuous improvement based on performance feedback and correctness diagnostics. The authors demonstrate CAKE's effectiveness through various benchmarks, showing significant performance improvements over traditional CUDA/PTX implementations. The results indicate that CAKE can facilitate the development of high-performance GPU kernels that are tailored to specific workloads, thereby bridging the gap between expert kernel programming and automated kernel generation.
Methodology
The authors developed CAKE by creating a typed intermediate representation (IR) that allows agents to edit and optimize GPU kernels with explicit hardware scheduling. The framework includes a feedback loop where the compiler provides detailed diagnostics on correctness and performance, enabling agents to refine their approaches iteratively. The methodology was validated through a series of benchmarks across various kernel families, demonstrating the effectiveness of the CAKE framework in real-world scenarios.
Results
In benchmarks, the best candidate using CAKE IR achieved a median performance of 1.144 times the tuned FlashML baseline, compared to 0.928 times for direct CUDA/PTX. Additionally, the agent-generated Kimi Delta Attention achieved a geometric mean speedup of 2.05 times over the official FlashKDA. Performance improvements for dispatcher-backed KNN and KMeans families ranged from 1.42 to 2.12 times across over 400 shapes, with four kernel changes made available as upstream pull requests.
Implications
The CAKE framework has the potential to revolutionize GPU programming by enabling more efficient kernel development and optimization. It can lead to the creation of high-performance kernels that are better suited for specific applications, ultimately enhancing the capabilities of GPU computing in various domains such as machine learning, scientific computing, and real-time data processing.
Defensive Boosting for Online Probabilistic Forecasting
Theory
Efficient ML
Optimization
- The Defensive Booster algorithm achieves both competitive Brier scores and low classification error under varying conditions.
- It operates efficiently with only one weak-class learner, unlike previous methods that require multiple learners.
- The algorithm provides local hard-core certificates, enhancing its adaptability to different time intervals.
- Experimental results show substantial improvements in predictive performance and runtime efficiency over existing methods.
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Defensive Boosting for Online Probabilistic Forecasting
Summary
This paper addresses the challenge of online probabilistic forecasting of binary outcomes in the presence of an adaptive adversary. The authors propose a novel algorithm called the Defensive Booster, which combines the strengths of existing online boosting techniques to provide two key guarantees: competitive Brier scores with the best predictor from a weak hypothesis class and the ability to drive classification error to zero under a weak-learning condition. The Defensive Booster operates efficiently by utilizing a single weak-class learner, contrasting with prior methods that require maintaining large ensembles of weak learners. The paper also introduces a strongly adaptive variant of the algorithm that provides local hard-core certificates on every time interval, ensuring robust performance across varying conditions. Experimental results demonstrate that the Defensive Booster not only outperforms existing baselines in terms of predictive accuracy but also achieves significantly faster runtimes, making it a promising approach for real-time forecasting tasks.
Methodology
The Defensive Booster is developed as a black-box reduction from an online learning algorithm for a weak hypothesis class. It operationalizes the dual view of boosting, utilizing mistake weights to certify the failure of the weak-learning condition when errors persist. The algorithm is designed to be efficient, requiring only one weak learner while maintaining strong performance guarantees.
Results
The Defensive Booster demonstrates competitive Brier scores with the best predictor in the span of weak hypotheses and achieves low classification error when the smooth weak-learning condition is satisfied. The algorithm's performance is validated through experiments on synthetic and real data streams, showing improvements over prior baselines in both accuracy and runtime.
Implications
The findings suggest that the Defensive Booster can be effectively applied in scenarios requiring real-time probabilistic forecasting, such as financial predictions, risk assessment, and adaptive decision-making systems. Its efficiency and strong performance guarantees make it a valuable tool in online learning contexts.
Fast A/B/n Testing: Exact Multi-Policy Comparison via Tree-Coupled Feedback Sharing
Theory
Efficient ML
Optimization
- Introduces Tree-Coupled A/B Testing (TCAB) for efficient multi-policy comparisons.
- Reduces the number of reward-bearing interactions by sharing outcomes among policies.
- Maintains each policy's standalone trajectory distribution despite shared feedback.
- Achieves conditionally optimal query costs compared to traditional independent A/B/n testing.
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Fast A/B/n Testing: Exact Multi-Policy Comparison via Tree-Coupled Feedback Sharing
Summary
This paper introduces Tree-Coupled A/B Testing (TCAB), a novel method for conducting A/B/n tests that allows for exact multi-policy comparisons while sharing feedback efficiently. Traditional A/B/n testing requires independent trajectories for each policy, leading to a high number of reward-bearing interactions. TCAB addresses this by coupling the trajectories of policies through a predictable tree structure, enabling shared outcomes for policies that would make the same decision in identical contexts. The method ensures that each policy retains its standalone trajectory distribution while minimizing redundant interactions, thus reducing the total number of reward queries. The paper establishes that the expected query cost for TCAB is T plus the cumulative total variation over the selected tree edges, which is significantly lower than the JT cost of independent runs. Experimental results demonstrate that TCAB achieves substantial improvements in the cost-precision frontier across various applications, including reward-model evaluation and adaptive search policies.
Methodology
The TCAB method utilizes a tree structure to couple the trajectories of multiple policies. At each round, it samples from a tree that connects the histories of the policies, allowing for shared outcomes when policies make the same decision. The algorithm operates in a round-synchronous manner, enabling efficient parallelism in querying outcomes and updating policies.
Results
The expected number of reward queries in TCAB is T plus the cumulative total variation over the tree edges, leading to a cost of E[N(T)] = T + o(T) for fixed J, which is significantly lower than the JT cost associated with independent A/B/n testing. The experiments conducted show substantial improvements in cost-effectiveness and precision in various applications.
Implications
The TCAB framework can be applied in online experimentation across various digital platforms, particularly in scenarios where multiple adaptive decision policies are evaluated. It offers a more efficient way to conduct A/B/n tests, potentially leading to faster iterations and better resource utilization in machine learning evaluations.
Finding the Needle in a Haystack: Test-Time Analog Circuit Representation Adaptation for Bayesian Optimization
Optimization
- TTARO introduces an online adaptation mechanism for circuit representations during Bayesian optimization.
- The framework allows for continuous learning and adjustment of circuit embeddings based on newly observed performance metrics.
- TTARO outperforms traditional fixed representation methods and DKL in terms of optimization efficiency.
- The approach is compatible with various acquisition functions and Gaussian-process kernels.
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Finding the Needle in a Haystack: Test-Time Analog Circuit Representation Adaptation for Bayesian Optimization
Summary
This paper presents Test-Time Analog Representation Adaptation for Bayesian Optimization (TTARO), a novel online deep-kernel Bayesian optimization framework aimed at improving the efficiency of analog circuit topology search. Traditional Bayesian optimization methods often rely on fixed circuit embeddings, which can misalign with the optimization objectives, leading to suboptimal search performance. TTARO addresses this issue by adapting circuit representations dynamically as new figure-of-merit (FoM) observations are collected during the optimization process. By jointly learning a nonlinear feature transformation and a Gaussian-process surrogate model, TTARO continuously refines the representation of circuit topologies, ensuring that the search space aligns more closely with the optimization goals. The authors conducted extensive experiments across various circuit encoders, kernels, and acquisition functions, demonstrating that TTARO significantly outperforms conventional methods, including fixed embedding approaches and Deep Kernel Learning (DKL). The results indicate that TTARO reduces regret area under the curve (AUC) by an average of 15.2% compared to standard Bayesian optimization and by 20.7% relative to DKL, showcasing its effectiveness in optimizing analog circuit designs.
Methodology
TTARO employs an online deep-kernel Bayesian optimization framework that adapts pretrained circuit embeddings by learning a nonlinear feature transformation and a Gaussian-process surrogate model. This adaptation occurs iteratively as new FoM observations are gathered, allowing the optimization process to align more closely with the objectives being pursued.
Results
TTARO demonstrated a reduction in regret AUC by 15.2% on average compared to conventional Bayesian optimization and 20.7% compared to DKL across 40 different configurations. In some settings, TTARO achieved reductions in regret as large as 46.7%, indicating substantial improvements in optimization performance.
Implications
The findings suggest that dynamic adaptation of representations can significantly enhance the efficiency of optimization processes in analog circuit design, potentially leading to faster and more effective design cycles in electronic design automation. This approach could be extended to other areas requiring optimization under similar constraints.
Simulation-to-real transfer learning for infrared spectroscopic chemical sensing and analysis from molecules to complex samples
Efficient ML
- UltraIR is a foundation model for IR spectroscopy with over 100 million parameters.
- The model utilizes simulation-to-real transfer learning to improve chemical inference from IR spectra.
- UltraIR outperforms traditional methods in various chemical sensing tasks and real-world applications.
- The approach allows for effective adaptation using limited labeled experimental spectra.
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Simulation-to-real transfer learning for infrared spectroscopic chemical sensing and analysis from molecules to complex samples
Summary
This paper presents UltraIR, a foundation model for infrared (IR) spectroscopy designed to enhance chemical sensing and analysis through simulation-to-real transfer learning. Traditional methods for interpreting IR spectra are labor-intensive and rely heavily on expert knowledge, making them less effective for unfamiliar compounds and complex samples. UltraIR addresses these limitations by leveraging a large-scale pretraining approach on approximately 60 million simulated IR spectra, employing three complementary objectives: spectral reconstruction, molecular fingerprint similarity alignment, and functional-group prediction. The model is then fine-tuned for specific tasks using limited labeled experimental spectra. The authors demonstrate UltraIR's effectiveness across various benchmarks, including functional-group prediction and mixture-component identification, as well as real-world applications such as bacterial classification and soil property prediction. The results indicate that UltraIR significantly outperforms conventional machine-learning methods and task-specific deep-learning baselines, showcasing its potential for adaptable and data-efficient chemical sensing systems.
Methodology
UltraIR employs a foundation model architecture with pretraining on simulated IR spectra. It uses three objectives for pretraining: spectral reconstruction, molecular fingerprint similarity alignment, and functional-group prediction. The pretrained model is then adapted to specific downstream tasks using limited labeled experimental data.
Results
UltraIR demonstrated superior performance in benchmark evaluations for functional-group prediction, molecular structure elucidation, and mixture-component identification. In real-world applications, it effectively classified bacteria, traced the geographic origin of medicinal herbs, quantified constituents, and predicted soil properties, outperforming conventional and task-specific deep-learning baselines.
Implications
The findings suggest that UltraIR can facilitate scalable and reliable chemical analysis in various fields, including environmental monitoring and clinical analysis, by providing a robust framework for interpreting complex IR spectra with limited labeled data.
Structure-preserving uncertainty quantification for GENERIC dynamics
Theory
- Introduction of S-PENNs for uncertainty quantification in hard-constrained models.
- Preservation of thermodynamic consistency in stochastic realizations.
- Significant reduction in computational costs compared to deep ensembles.
- Validation through multiple numerical examples demonstrating effectiveness.
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Structure-preserving uncertainty quantification for GENERIC dynamics
Summary
This paper introduces Structure-Preserving Epistemic Neural Networks (S-PENNs), a novel framework for uncertainty quantification (UQ) in scientific machine learning models that adhere to hard architectural constraints. The authors focus on the GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) dynamics, which is essential for modeling systems governed by both reversible and irreversible processes. S-PENNs maintain the structural integrity of a pretrained model by integrating lightweight epinets into its constrained components, ensuring that all sampled realizations are physically admissible. The framework is combined with split conformal prediction to generate prediction intervals with finite-sample coverage guarantees. The authors validate S-PENNs through three numerical examples: a harmonic oscillator coupled to a heat bath, an idealized chemical motor, and a one-dimensional viscoplastic model. The results demonstrate that S-PENNs yield thermodynamically consistent stochastic realizations and well-calibrated prediction intervals while significantly reducing computational costs compared to traditional deep ensembles. Although the study is centered on GENERIC dynamics, the proposed framework has broader applicability in scientific machine learning models with hard or soft constraints.
Methodology
The authors propose S-PENNs, which integrate lightweight epinets into existing constrained models to ensure physical admissibility. They also employ split conformal prediction for post-hoc calibration of prediction intervals. The methodology is validated through numerical simulations of various dynamical systems governed by ordinary and partial differential equations.
Results
S-PENNs produced thermodynamically consistent stochastic realizations and well-calibrated prediction intervals across three numerical examples, achieving a computational efficiency improvement of 1 to 3 orders of magnitude compared to deep ensembles.
Implications
The proposed framework can enhance the reliability of predictions in scientific machine learning applications, particularly in fields requiring adherence to physical laws. It opens avenues for more efficient modeling of complex systems in computational mechanics and beyond.
Prof-K: Probabilistic One-Pass Filtering for Efficient Top-k Selection
Efficient ML
Optimization
Theory
- Prof-K provides a fast, scalable, and distribution-agnostic solution for top-k selection.
- The algorithm guarantees high-probability correctness and buffer size through a probabilistic filtering approach.
- Empirical results show 1.5×–10× speedups over existing top-k implementations, particularly beneficial for large datasets.
- Prof-K allows for flexible accuracy-speed trade-offs, enabling users to tune performance based on their requirements.
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Prof-K: Probabilistic One-Pass Filtering for Efficient Top-k Selection
Summary
The paper introduces Prof-K, a novel algorithm designed for efficient top-k selection, which is crucial in various computational fields such as databases and machine learning. Traditional methods for top-k selection face inefficiencies as data sizes increase, with exact methods being computationally expensive and approximate methods often failing under adversarial conditions. Prof-K addresses these challenges by employing a probabilistic one-pass filtering approach. It begins with a small random sample to estimate an adaptive threshold, allowing the algorithm to stream through the input data only once and retain elements above this threshold in a compact buffer. An exact top-k selection is then performed on this buffer, ensuring that the true top-k elements are recovered with a high probability, independent of the input distribution. The authors provide theoretical guarantees for the algorithm's correctness and buffer size, along with an optimal sample size that minimizes overhead. Empirical evaluations demonstrate that Prof-K achieves significant speedups (1.5×–10×) over existing optimized implementations, particularly in scenarios with large data sizes and small to moderate k values. The algorithm also allows for flexible accuracy-speed trade-offs, enabling users to adjust parameters based on their specific needs. Additionally, Prof-K shows promise in reducing training times for BatchTopK Sparse Autoencoders without compromising performance.
Methodology
Prof-K utilizes a one-pass filtering mechanism where a small random sample is used to estimate a threshold. The algorithm streams through the input data once, retaining only those elements above the threshold in a compact buffer, followed by an exact top-k selection from this buffer. The guarantees of the method are derived from the ranks induced by uniform sampling, making it robust against various input distributions.
Results
Prof-K achieves speed improvements of 1.5× to 10× compared to highly optimized implementations like PyTorch topk and RadiK, especially in large-scale scenarios with small to moderate k values. The algorithm maintains high accuracy and allows for a flexible trade-off between speed and exact recovery.
Implications
The implications of Prof-K are significant for applications requiring efficient top-k selection, particularly in large-scale machine learning workloads and real-time data processing. Its robustness to input distribution makes it suitable for adversarial settings, enhancing the reliability of systems that depend on top-k operations.
Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration
Theory
- SORT provides a framework for estimating sparse expansions in orthonormal bases from noisy data.
- The technique is particularly effective for discovering ordinary differential equations and supports nonlinear approximation.
- SORT demonstrates improved stability under sparse sampling and noisy conditions compared to traditional methods.
- The method allows for order-consistent model growth, maintaining low-order coefficients as model complexity increases.
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Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration
Summary
The paper introduces the Sparse Orthogonal Regression Technique (SORT), a novel framework designed for learning orthonormal-basis expansions from noisy and irregularly sampled data. SORT employs L1-regularized regression to estimate expansion coefficients directly from observations, eliminating the need for explicit quadrature or analytic inner-product evaluations. The primary application of SORT is in the data-driven discovery of ordinary differential equations, where vector fields are represented in selected orthogonal bases and learned as sparse coefficient expansions. This approach offers a complementary method to traditional symbolic regression and SINDy-style sparse identification by first establishing a compact spectral representation that can facilitate searches for simpler analytic forms. The authors demonstrate that SORT performs comparably or better than existing library-based sparse-regression methods, particularly when the orthogonal basis is well-suited to the problem. The technique also exhibits greater stability under conditions of sparse sampling, noisy derivative estimates, and representation mismatch. Furthermore, SORT supports nonlinear approximation and the estimation of complex, high-dimensional integrals through coefficient readout, making it a versatile tool for system identification, approximation, and integration. Overall, SORT emphasizes the importance of basis design in scientific modeling, providing a reusable representation that enhances the robustness and interpretability of learned models.
Methodology
SORT combines orthonormal basis representations with sparsity-promoting regression techniques. It estimates coefficients from sampled observations using L1-regularized regression, allowing for the recovery of sparse expansions without the need for explicit quadrature or inner-product evaluations. The framework is evaluated across various tasks, including dynamical-system identification, numerical integration, and nonlinear approximation.
Results
The experiments indicate that SORT matches or surpasses the performance of dense least-squares, kernel-based, and library-based sparse-regression baselines, particularly when the orthogonal basis aligns well with the problem. The results also show that dominant low-order coefficients remain stable as model order increases, supporting the concept of order-consistent model growth.
Implications
SORT has significant implications for scientific computing and machine learning, particularly in areas requiring robust function approximation, system identification, and numerical integration from irregularly sampled data. Its emphasis on basis design can lead to more interpretable and reliable models in various applications.
H-VAEP and H-xT: Valuing Offensive On-the-Ball Actions in Handball by Estimating Probabilities
Theory
- Introduction of H-xT and H-VAEP frameworks tailored for handball analytics.
- Development of a handball-native court zoning layout for improved action valuation.
- Demonstration of the robustness of H-xT compared to traditional rectangular grids.
- H-VAEP yields stable and intuitive player ratings that highlight contributions to build-up play.
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H-VAEP and H-xT: Valuing Offensive On-the-Ball Actions in Handball by Estimating Probabilities
Summary
This paper presents the first comprehensive adaptation of Expected Threat (xT) and Valuing Actions by Estimating Probabilities (VAEP) frameworks for handball, addressing the limitations of traditional player evaluation methods that rely on basic box-score metrics. The authors utilize five seasons of tracking-derived event data from the Handball Bundesliga to develop Handball-xT (H-xT) and Handball-VAEP (H-VAEP). H-xT employs a handball-specific court zoning layout, which is shown to be more robust than standard rectangular grids. H-VAEP is optimized to suit the rapid dynamics of handball while minimizing team-identity leakage. The evaluation demonstrates that H-VAEP provides stable, discriminative, and intuitive player ratings that emphasize the importance of build-up play. The authors also release their code repository to facilitate the practical application of these models in professional handball clubs.
Methodology
The authors adapted the xT and VAEP frameworks to handball by utilizing a handball-specific court zoning layout and optimizing the feature space and context length for H-VAEP. They conducted simulations to validate the robustness of H-xT and evaluated the performance of H-VAEP against traditional metrics using a comprehensive validation framework.
Results
The study found that H-xT is systematically more robust than standard rectangular grids for action valuation in handball. H-VAEP provided player ratings that were stable, reliable, and intuitive, effectively capturing the contributions of players in build-up play. The frameworks were validated against five seasons of event data, demonstrating strong face validity and discrimination compared to traditional performance indicators.
Implications
The development of H-xT and H-VAEP has significant implications for player recruitment, game tactics, and overall performance analysis in handball. By providing a more nuanced understanding of player contributions, these frameworks can help teams make data-driven decisions and improve their competitive edge.
HiRoute: Hierarchical Routed Prompt Tuning for Safety Alignment of Large Language Models
NLP
Large Language Models
Efficient ML
- HiRoute separates category-agnostic safety control from category-specific response guidance.
- The framework uses a hierarchical router to dynamically compose fine-grained prompts based on input risk.
- HiRoute maintains high safety rates while preserving the helpfulness of responses.
- The approach reduces over-refusal of benign inputs compared to traditional methods.
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HiRoute: Hierarchical Routed Prompt Tuning for Safety Alignment of Large Language Models
Summary
The paper introduces HiRoute, a novel framework for safety alignment in large language models (LLMs) that addresses vulnerabilities to harmful requests and jailbreak attacks. Traditional prompt tuning methods often rely on static prompts that fail to adapt to the diverse nature of harmful inputs, leading to generic refusals that can degrade model performance. HiRoute overcomes these limitations by employing a hierarchical routing mechanism that separates category-agnostic safety control from category-specific response guidance. The framework first trains a lightweight hierarchical router to detect harmful intents and predict multi-label risk scores based on representations from a frozen LLM. Following this, preference optimization is used to learn a shared coarse-grained prompt alongside fine-grained prompt experts. During inference, benign inputs bypass the safety mechanism, while risky inputs utilize a combination of the shared prompt and router-weighted fine-grained prompts. The experimental results demonstrate that HiRoute achieves high safety rates across multiple benchmarks while maintaining helpfulness in responses and reducing over-refusal of benign inputs.
Methodology
HiRoute employs a two-stage training process. Initially, a hierarchical router is trained on representations from a frozen LLM to identify harmful intents and predict risk scores. Subsequently, both the backbone model and the router are frozen, and only the prompts are optimized using preference optimization. During inference, the framework dynamically constructs prompt combinations based on the routing results, allowing benign inputs to bypass safety prompting.
Results
HiRoute demonstrated high safety and helpfulness rates across various safety benchmarks, effectively balancing safety alignment with the need for constructive responses. The results indicate a significant reduction in over-refusal of benign inputs while maintaining competitive performance on general-purpose tasks.
Implications
The HiRoute framework has potential applications in enhancing the safety and reliability of LLMs in real-world scenarios, particularly in sensitive domains where harmful requests may arise. Its adaptive approach to prompt tuning could lead to more robust models capable of providing safe and helpful responses.
Scaling Automatic Research Agents via World Models
Reinforcement Learning
Large Language Models
Efficient ML
- Introduction of World Model RL (WMRL) to replace expensive environment execution in AutoResearch agents.
- Development of Online Debiasing and Inverse-Variance Denoising mechanisms to enhance the performance of the world model.
- Theoretical grounding of the framework, proving improved convergence guarantees.
- Empirical validation showing 3-4x acceleration in training and superior performance compared to larger models.
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Scaling Automatic Research Agents via World Models
Summary
This paper addresses the challenge of scaling Automatic Research (AutoResearch) agents, which utilize large language models (LLMs) to conduct empirical research autonomously. The authors identify a critical bottleneck in the reinforcement learning (RL) training process, where the environment execution component of agent trajectories incurs significantly higher costs compared to the agent generation component. To mitigate this issue, they propose a novel approach called World Model RL (WMRL), which substitutes real environment execution with a world model that simulates execution outcomes. This allows for more efficient training by enabling the batching of trajectories, thus alleviating the execution cost bottleneck. The authors also introduce two correction mechanisms—Online Debiasing and Inverse-Variance Denoising—to address biases and noise in the world model's outputs. Theoretical proofs demonstrate that these mechanisms improve convergence guarantees. Empirical results show that WMRL accelerates training by 3-4 times across various tasks and scales, outperforming larger baseline models. The method's generalizability is further validated through its application to post-training embodied VLA policies.
Methodology
The authors propose World Model RL (WMRL), which replaces real environment execution with a simulated world model to generate execution outcomes. They implement Online Debiasing and Inverse-Variance Denoising to correct biases and reduce noise in the model's predictions. Theoretical analysis is provided to support the convergence guarantees of the proposed methods.
Results
WMRL accelerates training by 3-4 times on various AutoResearch tasks and scales, while achieving performance that exceeds that of larger open-weight models (48B and 120B parameters). The proposed methods also demonstrate generalizability to post-training embodied VLA policies.
Implications
The findings suggest that using world models can significantly enhance the efficiency of training RL agents, making it feasible to scale AutoResearch applications. This approach may also be applicable to other domains requiring efficient RL training, potentially leading to advancements in automated empirical research and other AI-driven tasks.
Learning Discrete Decisions for MIPs with Constraint-Aware Diffusion
Optimization
Generative Models
Graph Learning
- Introduction of Constrained Graph Diffusion (CGD) for MIPs, which enforces feasibility during the decision-making process.
- Decomposition of mixed-integer nonlinear programming (MINLP) problems into discrete and continuous components to improve optimization efficiency.
- Demonstrated effectiveness of CGD on diverse applications, achieving substantial improvements in solution quality and feasibility.
- Achieved significant computational speedups compared to traditional numerical solvers.
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Learning Discrete Decisions for MIPs with Constraint-Aware Diffusion
Summary
This paper presents a novel learning-based approach to tackle mixed-integer optimization problems (MIPs) using a method called Constrained Graph Diffusion (CGD). MIPs are challenging due to the need to simultaneously determine discrete and continuous variables while adhering to complex constraints. The CGD framework employs a graph-based generative diffusion model that learns the discrete decisions of MIPs and integrates a training-free feasibility projection operator into the reverse diffusion process. This integration ensures that intermediate samples remain within the feasible set during generation. Once the discrete decisions are established, the problem simplifies to a continuous optimization task that can be efficiently solved using existing numerical methods. The authors demonstrate the effectiveness of CGD on two distinct applications: optimal transmission switching for AC optimal power flow and mixed-integer portfolio optimization. The results show that CGD significantly enhances feasibility and solution quality compared to existing learning-based methods and achieves speedups of up to 425 times over state-of-the-art numerical solvers for mixed-integer nonlinear programs (MINLPs).
Methodology
The methodology involves a graph-based generative diffusion model that learns the distribution of discrete decisions while incorporating feasibility projections during the reverse diffusion process. This allows for the generation of feasible discrete decisions, which are then fixed to solve the remaining continuous optimization problem using standard numerical methods.
Results
The CGD framework was evaluated on optimal transmission switching for AC optimal power flow and mixed-integer portfolio optimization, showing improved feasibility and solution quality over existing learning-based approaches. The method also achieved speedups of up to 425 times compared to state-of-the-art numerical solvers for MINLPs.
Implications
The proposed CGD framework has the potential to enhance the efficiency and effectiveness of solving mixed-integer optimization problems across various domains, including power systems, finance, and logistics, where decision-making involves both discrete and continuous variables.
The Objective Is the Bottleneck: Latent World Models Encode What Their Planners Cannot Use
Reinforcement Learning
Robotics
Optimization
- The predictor is not the bottleneck; it remains informative at long horizons.
- The planning objective can saturate and invert, affecting planning success.
- Long-horizon success is inversely related to one-step prediction accuracy.
- Reachability is a more effective objective than proximity for planning.
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The Objective Is the Bottleneck: Latent World Models Encode What Their Planners Cannot Use
Summary
This paper investigates the limitations of latent world models in planning tasks, specifically focusing on the LeWorldModel in the TwoRoom environment. The author argues that the bottleneck in planning is not the predictor's capacity or horizon, but rather the planner's objective. Through experiments, it is shown that the predictor remains informative even at long horizons, while the planner is constrained to a shorter horizon. The study reveals that the planning objective can saturate and even invert, leading to counterintuitive behaviors where moving away from the goal can reduce the planner's cost. The paper also discusses the dissociation between prediction accuracy and long-horizon planning success, highlighting that a learned cost must be trained on the distribution relevant to the planner's scoring. The findings suggest that reachability, rather than proximity, should be the focus of planning objectives. The author provides a method to improve planning performance without retraining the model, demonstrating that the learned cost can outperform linear costs under certain conditions.
Methodology
The study employs a reproduction of the LeWorldModel on the TwoRoom environment, utilizing an 18.03M-parameter joint-embedding predictive architecture. The planning is conducted using cross-entropy-method search over learned dynamics, with specific configurations for candidate sequences and refinement iterations. The experiments are run on a standard CPU without any retraining of the model.
Results
The experiments reveal that the predictor's performance does not degrade significantly over long horizons, while the planner's effectiveness is limited to a shorter horizon. The objective function used in planning can lead to unexpected outcomes, such as lower costs when moving away from the goal. A simple change in the objective resulted in a significant increase in planning success rates, demonstrating that the learned cost can outperform traditional metrics under certain conditions.
Implications
The findings suggest that improving planning in latent world models may require a reevaluation of the objectives used in training. This could lead to more effective planning strategies in various applications, particularly in reinforcement learning and robotics, where long-term planning is crucial. The insights on reachability versus proximity could influence the design of future models and objectives.
Neural Quadratic Forms: A Unified Minimal Model for Sudden Learning and Scaling Laws
Theory
Optimization
- Introduces Neural Quadratic Forms (NQF) as a minimal model for understanding sudden learning and scaling laws in neural networks.
- Demonstrates that neural architectures exhibit a symmetry that allows for a unified representation of different models through a structure matrix A(x).
- Establishes a connection between training dynamics and collective variables, leading to predictions about feature acquisition timing and power law behaviors.
- Validates the theoretical predictions through numerical experiments across diverse neural network architectures and training methodologies.
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Neural Quadratic Forms: A Unified Minimal Model for Sudden Learning and Scaling Laws
Summary
This paper introduces a unified minimal model termed Neural Quadratic Forms (NQF) that explains the abrupt learning dynamics observed in neural networks trained via gradient descent, alongside the smooth power laws governing training losses across various architectures. The authors leverage the symmetry inherent in neural network architectures, which allows for the characterization of training dynamics through a universal quadratic form. By establishing that neural network layers can be represented as sums of interchangeable components, the authors derive a structure matrix A(x) that encapsulates architectural details while maintaining a common framework for different models, including perceptrons, attention layers, and convolutions. The training dynamics are shown to converge on an order parameter M = WW⊺, leading to a Lotka-Volterra equation that describes the sequential activation of modes during training. This model successfully predicts the timing of feature acquisition and the emergence of power laws in training time, validated through numerical experiments across various architectures and training methods.
Methodology
The authors employ a theoretical framework based on symmetry principles to derive a universal quadratic form for neural network training dynamics. They analyze the implications of this form across various architectures, focusing on the role of the structure matrix A(x) and the order parameter M = WW⊺. Numerical simulations are conducted to validate the theoretical predictions regarding learning dynamics and scaling laws.
Results
The study confirms that the derived NQF accurately captures the abrupt learning phases and smooth power law behaviors observed in neural network training. The model predicts that the timing of feature acquisition is influenced by the scale of initial weights, with smaller weights leading to more pronounced plateaus in training dynamics. The theoretical framework aligns with empirical observations across multiple architectures, demonstrating the universality of the model.
Implications
The findings suggest that understanding the collective dynamics of neural networks can inform the design of more efficient architectures and training strategies. The NQF model provides a theoretical basis for predicting learning behaviors, which could enhance the scalability and performance of neural networks in various applications.
ProME: Prototype-Margin Environments with Repair-Aware Selection for Group-Robust Learning
Theory
Optimization
- ProME aligns environment construction and model selection with the deployed predictor without requiring training-group labels.
- The framework introduces a median split of prototype margins to create balanced environments for invariant learning.
- Theoretical bounds on worst risks are established, showing transferability to oracle groups under alignment conditions.
- ProME demonstrates superior performance in worst-group accuracy compared to existing methods across multiple benchmarks.
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ProME: Prototype-Margin Environments with Repair-Aware Selection for Group-Robust Learning
Summary
This paper addresses the challenge of group-robust learning, particularly in scenarios where training-group labels are unavailable. The authors propose a novel framework called ProME (Prototype-Margin Environments) that formulates the problem as endogenous environments with repair-aware selection (ERAS). ProME aims to align environment construction and model selection with the deployed predictor, thereby enhancing the accuracy of rare subpopulations. The methodology involves splitting prototype margins at their median to create balanced environments and fitting a group-balanced linear head on validation data to rank predictors based on worst-group accuracy (WGA). Theoretical bounds on the worst risk across inferred environments are established, demonstrating that these bounds can transfer to oracle groups under specific conditions. Extensive experiments on benchmarks such as Waterbirds, CelebA, and CivilComments reveal that ProME outperforms existing methods in achieving higher average worst-group accuracy while effectively addressing shortcut-conflicting examples and model selection misalignments.
Methodology
ProME constructs environments by assigning prototype margins between observed classes and competing classes using a cosine-prototype classifier. It employs a median split of these margins to create approximately balanced environments. In the second stage, it ranks encoder checkpoints based on validation worst-group accuracy after classifier repair, ensuring alignment with the deployed predictor.
Results
ProME achieves the highest average worst-group accuracy among compared methods on benchmarks like Waterbirds, CelebA, and CivilComments. The experiments demonstrate that the proposed method effectively enriches shortcut-conflicting examples and reshapes candidate evaluations, leading to improved group robustness.
Implications
The findings suggest that ProME can be applied in various domains where group robustness is critical, such as medical diagnosis and content moderation, particularly in situations with imbalanced group representations. The methodology can enhance the reliability of machine learning models in real-world applications by ensuring equitable performance across diverse subpopulations.