Local attention strictly enlarges the class of regular languages recognizable by fixed-precision transformers by introducing a second temporal operator in LTL, with global and local attention being expressively complementary.
IEEE Standard for Floating-Point Arithmetic.IEEE Std 754-2019 (Revision of IEEE 754-2008)(2019), 1–84
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LLMs match or exceed state-of-the-art traditional methods for stabilizing numerical expressions in scientific software, succeeding on 97.9% of expressions where baselines fail to improve accuracy, but struggle with control flow and high-precision literals.
Establishes sufficient more-general conditions for FastTwoSum as an error-free transformation under faithful rounding modes and introduces a configurable ExtractScalar splitting for round-to-odd.
Error analysis and cost estimator for recasting floating-point matrix multiplication as accumulated integer products on mixed-precision hardware.
The Parker-Sochacki method delivers 4 to 13 orders of magnitude better kinetic energy conservation than Runge-Kutta methods for charged particle motion in static magnetic fields while running faster at matched accuracy.
Augments incremental collision laws using the Bouc-Wen model to incorporate external forces as inputs, extends valid parameter ranges, and performs further identification studies on convex viscoplastic body collisions.
citing papers explorer
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Characterizing the Expressivity of Local Attention in Transformers
Local attention strictly enlarges the class of regular languages recognizable by fixed-precision transformers by introducing a second temporal operator in LTL, with global and local attention being expressively complementary.
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Assessing Large Language Models for Stabilizing Numerical Expressions in Scientific Software
LLMs match or exceed state-of-the-art traditional methods for stabilizing numerical expressions in scientific software, succeeding on 97.9% of expressions where baselines fail to improve accuracy, but struggle with control flow and high-precision literals.
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Odd but Error-Free FastTwoSum: More General Conditions for FastTwoSum as an Error-Free Transformation for Faithful Rounding Modes
Establishes sufficient more-general conditions for FastTwoSum as an error-free transformation under faithful rounding modes and introduces a configurable ExtractScalar splitting for round-to-odd.
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Analysis of Floating-Point Matrix Multiplication Computed via Integer Arithmetic
Error analysis and cost estimator for recasting floating-point matrix multiplication as accumulated integer products on mixed-precision hardware.
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High-Accuracy Numerical Solutions of Particle Motion in Static Magnetic Fields
The Parker-Sochacki method delivers 4 to 13 orders of magnitude better kinetic energy conservation than Runge-Kutta methods for charged particle motion in static magnetic fields while running faster at matched accuracy.
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Incremental Collision Laws Based on the Bouc-Wen Model: Improved Collision Models and Further Results
Augments incremental collision laws using the Bouc-Wen model to incorporate external forces as inputs, extends valid parameter ranges, and performs further identification studies on convex viscoplastic body collisions.