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OPERA: Automatic Offline Policy Evaluation with Re-weighted Aggregates of Multiple Estimators
Get PDFOffline policy evaluation (OPE) allows us to evaluate and estimate a new sequential decision-making policy\u27s performance by leveraging historical interaction data collected from other policies. Evaluating a new policy online without a confident estimate of its performance can lead to costly, unsafe, or hazardous outcomes, especially in education and healthcare. Several OPE estimators have been proposed in the last decade, many of which have hyperparameters and require training. Unfortunately, choosing the best OPE algorithm for each task and domain is still unclear. In this paper, we propose a new algorithm that adaptively blends a set of OPE estimators given a dataset without relying on an explicit selection using a statistical procedure. We prove that our estimator is consistent and satisfies several desirable properties for policy evaluation. Additionally, we demonstrate that when compared to alternative approaches, our estimator can be used to select higher-performing policies in healthcare and robotics. Our work contributes to improving ease of use for a general-purpose, estimator-agnostic, off-policy evaluation framework for offline RL.22 page
LRM-Zero: Training Large Reconstruction Models with Synthesized Data
Get PDFWe present LRM-Zero, a Large Reconstruction Model (LRM) trained entirely on synthesized 3D data, achieving high-quality sparse-view 3D reconstruction. The core of LRM-Zero is our procedural 3D dataset, Zeroverse, which is automatically synthesized from simple primitive shapes with random texturing and augmentations (e.g., height fields, boolean differences, and wireframes). Unlike previous 3D datasets (e.g., Objaverse) which are often captured or crafted by humans to approximate real 3D data, Zeroverse completely ignores realistic global semantics but is rich in complex geometric and texture details that are locally similar to or even more intricate than real objects. We demonstrate that our LRM-Zero, trained with our fully synthesized Zeroverse, can achieve high visual quality in the reconstruction of real-world objects, competitive with models trained on Objaverse. We also analyze several critical design choices of Zeroverse that contribute to LRM-Zero\u27s capability and training stability. Our work demonstrates that 3D reconstruction, one of the core tasks in 3D vision, can potentially be addressed without the semantics of real-world objects. The Zeroverse\u27s procedural synthesis code and interactive visualization are available at: https://desaixie.github.io/lrm-zero/.23 pages, 8 figures. Our code and interactive visualization are available at: https://desaixie.github.io/lrm-zero/. v2: NeurIPS 2024 Camera Ready versio
Elliptical Attention
Get PDFPairwise dot-product self-attention is key to the success of transformers that achieve state-of-the-art performance across a variety of applications in language and vision. This dot-product self-attention computes attention weights among the input tokens using Euclidean distance, which makes the model prone to representation collapse and vulnerable to contaminated samples. In this paper, we propose using a Mahalanobis distance metric for computing the attention weights to stretch the underlying feature space in directions of high contextual relevance. In particular, we define a hyper-ellipsoidal neighborhood around each query to increase the attention weights of the tokens lying in the contextually important directions. We term this novel class of attention Elliptical Attention. Our Elliptical Attention provides two benefits: 1) reducing representation collapse and 2) enhancing the model\u27s robustness as Elliptical Attention pays more attention to contextually relevant information rather than focusing on some small subset of informative features. We empirically demonstrate the advantages of Elliptical Attention over the baseline dot-product attention and state-of-the-art attention methods on various practical tasks, including object classification, image segmentation, and language modeling across different data modalities.10 pages in the main text. Published at NeurIPS 2024. The code is available at https://github.com/stefvk/Elliptical-Attentio
Gravitational waves from a curvature-induced phase transition of a Higgs-portal dark matter sector
Get PDFThe study of interactions between dark matter and the Higgs field opens an exciting connection between cosmology and particle physics, since such scenarios can impact the features of dark matter as well as interfering with the spontaneous breaking of the electroweak symmetry. Furthermore, such Higgs-portal models of dark matter should be suitably harmonised with the various epochs of the universe and the phenomenological constraints imposed by collider experiments. At the same time, the prospect of a stochastic gravitational wave background offers a promising new window into the primordial universe, which can complement the insights gained from accelerators. In this study, we examined whether gravitational waves can be generated from a curvature-induced phase transition of a non-minimally coupled dark scalar field with a portal coupling to the Higgs field. The main requirement is that the phase transition is of first order, which can be achieved through the introduction of a cubic term on the scalar potential and the sign change of the curvature scalar. This mechanism was investigated in the context of a dynamical spacetime during the transition from inflation to kination, while also considering the possibility for inducing electroweak symmetry breaking in this manner for a sufficiently low reheating temperature when the Higgs-portal coupling is extremely weak. We considered a large range of inflationary scales and both cases of positive and negative values for the non-minimal coupling, while taking into account the bound imposed by Big Bang Nucleosythesis. The resulting gravitational wave amplitudes are boosted by kination and thus constrain the parameter space of the couplings significantly. Even though the spectra lie at high frequencies for the standard high inflationary scales, there are combinations of parameter space where they could be probed with future experiments.28 pages, 6 figure
CMM-Math: A Chinese Multimodal Math Dataset To Evaluate and Enhance the Mathematics Reasoning of Large Multimodal Models
Get PDFLarge language models (LLMs) have obtained promising results in mathematical reasoning, which is a foundational skill for human intelligence. Most previous studies focus on improving and measuring the performance of LLMs based on textual math reasoning datasets (e.g., MATH, GSM8K). Recently, a few researchers have released English multimodal math datasets (e.g., MATHVISTA and MATH-V) to evaluate the effectiveness of large multimodal models (LMMs). In this paper, we release a Chinese multimodal math (CMM-Math) dataset, including benchmark and training parts, to evaluate and enhance the mathematical reasoning of LMMs. CMM-Math contains over 28,000 high-quality samples, featuring a variety of problem types (e.g., multiple-choice, fill-in-the-blank, and so on) with detailed solutions across 12 grade levels from elementary to high school in China. Specifically, the visual context may be present in the questions or opinions, which makes this dataset more challenging. Through comprehensive analysis, we discover that state-of-the-art LMMs on the CMM-Math dataset face challenges, emphasizing the necessity for further improvements in LMM development. We also propose a Multimodal Mathematical LMM (Math-LMM) to handle the problems with mixed input of multiple images and text segments. We train our model using three stages, including foundational pre-training, foundational fine-tuning, and mathematical fine-tuning. The extensive experiments indicate that our model effectively improves math reasoning performance by comparing it with the SOTA LMMs over three multimodal mathematical datasets
An Experimental Study of Competitive Market Behavior Through LLMs
Get PDFThis study explores the potential of large language models (LLMs) to conduct market experiments, aiming to understand their capability to comprehend competitive market dynamics. We model the behavior of market agents in a controlled experimental setting, assessing their ability to converge toward competitive equilibria. The results reveal the challenges current LLMs face in replicating the dynamic decision-making processes characteristic of human trading behavior. Unlike humans, LLMs lacked the capacity to achieve market equilibrium. The research demonstrates that while LLMs provide a valuable tool for scalable and reproducible market simulations, their current limitations necessitate further advancements to fully capture the complexities of market behavior. Future work that enhances dynamic learning capabilities and incorporates elements of behavioral economics could improve the effectiveness of LLMs in the economic domain, providing new insights into market dynamics and aiding in the refinement of economic policies
Maximal Circular Point Sets over Arbitrary Fields and an Application to Cryptography
No full textThe study of rational point sets on circles over the Euclidean plane is discussed in a more general framework, i.e. we generalize the notion rational and consider these circular point sets over arbitrary fields. We also determine the cardinality of maximal circular point sets which depends on the radius of the corresponding circle and the characteristic of the underlying field. For the construction of them we use the so called perfect distances which have the necessary compatibility properties to find new points on a circle such that all these points still have rational distance from each other. Then we define the rotation group where its elements are the points on a circle over an arbitrary field and find a connection between a subgroup of it and perfect distances if our field is a prime field. Furthermore, we describe a possible application in cryptography of the rotation group similar to the Diffie-Hellman key exchange.32 pages, 4 figure
Ergodicity and Mixing of invariant capacities and applications
No full textWe introduce the notion of common conditional expectation to investigate Birkhoff\u27s ergodic theorem and subadditive ergodic theorem for invariant upper probabilities. If in addition, the upper probability is ergodic, we construct an invariant probability to characterize the limit of the ergodic mean. Moreover, this skeleton probability is the unique ergodic probability in the core of the upper probability, that is equal to all probabilities in the core on all invariant sets. We have the following applications of these two theorems:
provide a strong law of large numbers for ergodic stationary sequence on upper probability spaces;
prove the multiplicative ergodic theorem on upper probability spaces;
establish a criterion for the ergodicity of upper probabilities in terms of independence.
Furthermore, we introduce and study weak mixing for capacity preserving systems. Using the skeleton idea, we also provide several characterizations of weak mixing for invariant upper probabilities.
Finally, we provide examples of ergodic and weakly mixing capacity preserving systems. As applications, we obtain new results in the classical ergodic theory. e.g. in characterizing dynamical properties on measure preserving systems, such as weak mixing, periodicity. Moreover, we use our results in the nonlinear theory to obtain the asymptotic independence, Birkhoff\u27s type ergodic theorem, subadditive ergodic theorem, and multiplicative ergodic theorem for non-invariant probabilities
On Fixed-Point Sets of -Tori in Positive Curvature
No full textIn recent work of Kennard, Khalili Samani, and the last author, they generalize the Half-Maximal Symmetry Rank result of Wilking for torus actions on positively curved manifolds to -tori with a fixed point. They show that if the rank is approximately one-fourth of the dimension of the manifold, then fixed point set components of small co-rank subgroups of the -torus are homotopy equivalent to spheres, real projective spaces, complex projective spaces, or lens spaces. In this paper, we lower the bound on the rank of the -torus to approximately and and are able to classify either the integral cohomology ring or the -cohomology ring, respectively, of the fixed point set of the -torus
Model Predictive Contouring Control with Barrier and Lyapunov Functions for Stable Path-Following in UAV systems
No full textIn this study, we propose a novel method that integrates Nonlinear Model Predictive Contour Control (NMPCC) with an Exponentially Stabilizing Control Lyapunov Function (ES-CLF) and Exponential Higher-Order Control Barrier Functions to achieve stable path-following and obstacle avoidance in UAV systems. This framework enables unmanned aerial vehicles (UAVs) to safely navigate around both static and dynamic obstacles while strictly adhering to desired paths. The quaternion-based formulation ensures precise orientation and attitude control, while a robust optimization solver enforces the constraints imposed by the Control Lyapunov Function (CLF) and Control Barrier Functions (CBF), ensuring reliable real-time performance. The method was validated in a Model-in-the-Loop (MiL) environment, demonstrating effective path tracking and obstacle avoidance. The results highlight the framework\u27s ability to minimize both orthogonal and tangential errors, ensuring stability and safety in complex environments.Submitted to IEEE Access for revie