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Fast, close, non-singular and property-preserving approximations of entropic measures

Illia Horenko, Davide Bassetti, Lukáš Pospíšil · May 20, 2025 · Citations: 0

Automatic Metrics
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How to use this page

Low trust

Use this as background context only. Do not make protocol decisions from this page alone.

Best use

Background context only

What to verify

Read the full paper before copying any benchmark, metric, or protocol choices.

Evidence quality

Low

Derived from extracted protocol signals and abstract evidence.

Abstract

Entropic measures like Shannon entropy (SE), its quantum mechanical analogue von Neumann entropy, and Kullback-Leibler divergence (KL) are key components in many tools used in physics, information theory, machine learning (ML) and quantum computing. Besides of the significant amounts of SE and KL computations required in these fields, the singularity of their gradients near zero is one of the central mathematical reason inducing the high cost, frequently low robustness and slow convergence of computational tools that rely on these concepts. Here we propose the Fast Entropic Approximations (FEA) - non-singular rational approximations of SE and symmetrized KL, that preserve their main mathematical properties and achieve a mean absolute errors of around $10^-3$ ($10-20$ times better than comparable state-of-the-art computational approximations). We show that FEA allows up to around 2 times faster computation of SE and up to 37 times faster computation of symmetrized KL: it requires only $5$ to $7$ elementary computational operations, as compared to the tens of elementary operations behind SE and KL evaluations based on approximate logarithm schemes with table look-ups, bitshifts, or series approximations. On a set of common benchmarks for the feature selection problem in machine learning, we show that the combined effect of fewer elementary operations, low approximation error, preservation of main mathematical properties, and non-singular gradients allows much faster training of significantly-better models. We demonstrate that FEA enables ML feature extraction that is three orders of magnitude faster, and better in quality then the very popular LASSO feature extraction.

Abstract-only analysis — low confidence

All signals on this page are inferred from the abstract only and may be inaccurate. Do not use this page as a primary protocol reference.

  • This paper looks adjacent to evaluation work, but not like a strong protocol reference.
  • The available metadata is too thin to trust this as a primary source.
  • The abstract does not clearly name benchmarks or metrics.
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Should You Rely On This Paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

A secondary eval reference to pair with stronger protocol papers.

Main weakness

This paper looks adjacent to evaluation work, but not like a strong protocol reference.

Trust level

Low

Usefulness score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Detected

Usefulness for eval research

Adjacent candidate

Extraction confidence 35%

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

What We Could Verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

missing

None explicit

No explicit feedback protocol extracted.

"Entropic measures like Shannon entropy (SE), its quantum mechanical analogue von Neumann entropy, and Kullback-Leibler divergence (KL) are key components in many tools used in physics, information theory, machine learning (ML) and quantum computing."

Evaluation Modes

partial

Automatic Metrics

Includes extracted eval setup.

"Entropic measures like Shannon entropy (SE), its quantum mechanical analogue von Neumann entropy, and Kullback-Leibler divergence (KL) are key components in many tools used in physics, information theory, machine learning (ML) and quantum computing."

Quality Controls

missing

Not reported

No explicit QC controls found.

"Entropic measures like Shannon entropy (SE), its quantum mechanical analogue von Neumann entropy, and Kullback-Leibler divergence (KL) are key components in many tools used in physics, information theory, machine learning (ML) and quantum computing."

Benchmarks / Datasets

missing

Not extracted

No benchmark anchors detected.

"Entropic measures like Shannon entropy (SE), its quantum mechanical analogue von Neumann entropy, and Kullback-Leibler divergence (KL) are key components in many tools used in physics, information theory, machine learning (ML) and quantum computing."

Reported Metrics

missing

Not extracted

No metric anchors detected.

"Entropic measures like Shannon entropy (SE), its quantum mechanical analogue von Neumann entropy, and Kullback-Leibler divergence (KL) are key components in many tools used in physics, information theory, machine learning (ML) and quantum computing."

Human Feedback Details

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Not reported
  • Expertise required: Math

Evaluation Details

  • Evaluation modes: Automatic Metrics
  • Agentic eval: None
  • Quality controls: Not reported
  • Evidence quality: Low
  • Use this page as: Background context only

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

No metric terms were extracted from the available abstract.

Research Brief

Metadata summary

Entropic measures like Shannon entropy (SE), its quantum mechanical analogue von Neumann entropy, and Kullback-Leibler divergence (KL) are key components in many tools used in physics, information theory, machine learning (ML) and quantum computing.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

  • Entropic measures like Shannon entropy (SE), its quantum mechanical analogue von Neumann entropy, and Kullback-Leibler divergence (KL) are key components in many tools used in physics, information theory, machine learning (ML) and quantum computing.
  • Besides of the significant amounts of SE and KL computations required in these fields, the singularity of their gradients near zero is one of the central mathematical reason inducing the high cost, frequently low robustness and slow convergence of computational tools that rely on these concepts.
  • Here we propose the Fast Entropic Approximations (FEA) - non-singular rational approximations of SE and symmetrized KL, that preserve their main mathematical properties and achieve a mean absolute errors of around $10^-3$ ($10-20$ times better than comparable state-of-the-art computational approximations).

Researcher Actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Check the full text for explicit evaluation design choices (raters, protocol, and metrics).
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

Research Summary

Contribution Summary

  • Here we propose the Fast Entropic Approximations (FEA) - non-singular rational approximations of SE and symmetrized KL, that preserve their main mathematical properties and achieve a mean absolute errors of around 10^-3 (10-20 times better…
  • We show that FEA allows up to around 2 times faster computation of SE and up to 37 times faster computation of symmetrized KL: it requires only 5 to 7 elementary computational operations, as compared to the tens of elementary operations…
  • On a set of common benchmarks for the feature selection problem in machine learning, we show that the combined effect of fewer elementary operations, low approximation error, preservation of main mathematical properties, and non-singular…

Why It Matters For Eval

  • We show that FEA allows up to around 2 times faster computation of SE and up to 37 times faster computation of symmetrized KL: it requires only 5 to 7 elementary computational operations, as compared to the tens of elementary operations…
  • On a set of common benchmarks for the feature selection problem in machine learning, we show that the combined effect of fewer elementary operations, low approximation error, preservation of main mathematical properties, and non-singular…

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Pass: Evaluation mode is explicit

    Detected: Automatic Metrics

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Gap: Metric reporting is present

    No metric terms extracted.

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