Generating diverse responses from large language models (LLMs) is crucial for applications such as adversarial testing, search, and synthetic data generation, where diversity provides distinct answers across generations. Previous approaches rely solely on increasing the temperature, sacrificing quality. Furthermore, the model's next-token probabilities may not be representative of the true answer distribution. To combat these challenges, we propose SimpleStrat, an alternative that uses the language sample. To model measure itself resampling to partition divers the ity solution, we introduce space int Co o verageQA, strata from a dataset which of to underspecified questions with multiple equally plausible answers. We propose measuring resampling diversity as the KLDivergence between the response distribution and the uniform distribution over valid ground truth answers and use recall as an alternative when assessing proprietary models. On CoverageQA, SimpleStrat improves diversity across all temperatures, showing orthogonal benefits. Quantifiably, we achieve as much as 4X better recall when applied to GPT-4o, and an average reLineduction in KL divergence by 0.36 when applied to Llama 3. Furthermore, we showthat SimpleStrat achieves more resampling diversity at temperature T=0 than scaling and temperature dataset available to T=1 at on https://github.com/j

We consider random instances of non-convex perceptron problems in the highdimensional limit of a large number of examples M and weights N, with finite load α = M/N. We develop a formalism based on replica theory to predict the fundamental limits of efficiently sampling the solution space using generative diffusion algorithms, conjectured to be saturated when the score function is provided by Approximate Message Passing. For the spherical perceptron with negative margin κ, we find that the uniform distribution over solutions can be efficiently sampled in most of the Replica Symmetric region of the α-κplane. In contrast, for binary weights, sampling from the uniform distribution remains intractable. A theoretical analysis of this obstruction leads us to identify a potential U(s)= log(s), under which the corresponding tilted distribution becomes efficiently samplable via diffusion. Moreover, we show numerically that an annealing procedure over the shape of this potential yields a fast and robust Markov Chain Monte Carlo algorithm for sampling the solution space of the binary perceptron.

G.1 Monoids Monoids are one of the simplest algebraic structure.

Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural networks to define, in a mesh-free manner, signals that are highly-detailed, continuous, and fully differentiable. In this work, we present a novel machine learning approach for topology optimization--an important class of inverse problems with high-dimensional parameter spaces and highly nonlinear objective landscapes. To effectively leverage neural representations in the context of mesh-free topology optimization, we use multilayer perceptrons to parameterize both density and displacement fields. Our experiments indicate that our method is highly competitive for minimizing structural compliance objectives, and it enables self-supervised learning of continuous solution spaces for topology optimization problems.

Large vision-language models (LVLMs) have recently achieved rapid progress, exhibiting great perception and reasoning abilities concerning visual information. However, when faced with prompts in different sizes of solution spaces, LVLMs fail to always give consistent answers regarding the same knowledge point. This inconsistency of answers between different solution spaces is prevalent in LVLMs and erodes trust. To this end, we provide a multi-modal benchmark ConBench, to intuitively analyze how LVLMs perform when the solution space of a prompt revolves around a knowledge point. Based on the ConBench tool, we are the first to reveal the tapestry and get the following findings: (1) In the discriminate realm, the larger the solution space of the prompt, the lower the accuracy of the answers.

Deep neural networks are starting to show their potential for solving partial differential equations (PDEs)inavarietyofproblemdomains,includingturbulentflow,heattransfer,elastodynamics,and many more [1, 2, 3, 4, 5]. Thanks to their smooth and analytically-differentiable nature, implicit neural representations with periodic activation functions are emerging as a particularly attractive and powerful option in this context [4].