Constant-Target Energy Matching: A Unified Framework for Continuous and Discrete Density Estimation
Researchers have introduced Constant-Target Energy Matching (CTEM), a novel unified framework for density estimation that effectively handles continuous, discrete, and mixed-variable domains. Traditional probabilistic modeling often treats these data types separately, limiting the exploitation of common statistical structures. While continuous methods rely on log-density gradients, discrete extensions frequently suffer from instability due to unbounded targets in low-probability states. CTEM addresses these limitations by replacing ordinary density-ratio regression with a bounded energy-difference transform. This approach yields a sample-only training objective with a constant target of 1, allowing the learned scalar potential to recover log probability without requiring partition-function estimation or explicit unbounded ratio regression. Benchmark tests across various data types demonstrate that CTEM substantially improves density estimation accuracy compared to competitive baselines. Furthermore, the framework produces higher-quality samples under standard sampling procedures, offering a robust solution for general state spaces in artificial intelligence and probabilistic modeling.
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Constant-Target Energy Matching: A Unified Framework for Continuous and Discrete Density Estimation
Researchers have introduced Constant-Target Energy Matching (CTEM), a novel unified framework for density estimation that effectively handles continuous, discrete, and mixed-variable domains. Traditional probabilistic modeling often treats these data types separately, limiting the exploitation of common statistical structures. While continuous methods rely on log-density gradients, discrete extensions frequently suffer from instability due to unbounded targets in low-probability states. CTEM addresses these limitations by replacing ordinary density-ratio regression with a bounded energy-difference transform. This approach yields a sample-only training objective with a constant target of 1, allowing the learned scalar potential to recover log probability without requiring partition-function estimation or explicit unbounded ratio regression. Benchmark tests across various data types demonstrate that CTEM substantially improves density estimation accuracy compared to competitive baselines. Furthermore, the framework produces higher-quality samples under standard sampling procedures, offering a robust solution for general state spaces in artificial intelligence and probabilistic modeling.
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