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arxiv: 2506.14167 · v14 · submitted 2025-06-17 · 💻 cs.LG

Kolmogorov-Arnold Energy Models: Fast, Interpretable Generative Modeling

Prithvi Raj This is my paper

Pith reviewed 2026-05-19 09:41 UTC · model grok-4.3

classification 💻 cs.LG
keywords energy-based modelsKolmogorov-Arnold networksgenerative modelslatent variablesimportance samplingFréchet Inception Distanceinterpretable priors
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The pith

Adapting the Kolmogorov-Arnold theorem to energy models yields fast single-pass sampling with interpretable univariate priors and top FID scores on image benchmarks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Generative models face a trade-off between fast but limited simple priors and slow but powerful iterative samplers. This paper proposes Kolmogorov-Arnold Energy Models that adapt the representation theorem to create a prior from univariate densities in a low-dimensional latent space. This structure allows exact inference using the inverse transform and efficient importance sampling for the posterior. The result is generative performance that surpasses other latent-prior approaches on SVHN and CIFAR-10 while remaining computationally light and exposing the prior's components for inspection. Readers should care because it points toward generative systems that are both practical for deployment and more transparent in their internal distributions.

Core claim

The Kolmogorov-Arnold Energy Model imposes a univariate latent structure on the energy function by adapting the Kolmogorov-Arnold Representation Theorem. This enables exact inference via the inverse transform method and makes importance sampling a tractable way to perform unbiased posterior inference. For cases of poor mixing, a population-based annealed strategy is introduced. On SVHN and CIFAR10, KAEM achieves the best Fréchet Inception Distance among compared latent-prior models, with sampling performed in a single forward pass.

What carries the argument

The Kolmogorov-Arnold adapted energy function that decomposes into univariate functions, carrying the argument by creating an interpretable product prior over low-dimensional latents.

If this is right

  • Sampling reduces to a single forward pass through the model.
  • The prior can be inspected as independent one-dimensional densities.
  • Posterior inference is possible via unbiased importance sampling without MCMC.
  • Performance on image generation benchmarks exceeds that of standard VAEs and neural latent EBMs.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This univariate decomposition might generalize to other representation theorems for even simpler structures.
  • In applications requiring uncertainty quantification, the explicit 1D densities could aid in understanding model confidence.
  • Future work could test whether the annealed population strategy scales to higher-dimensional or more complex data distributions.

Load-bearing premise

The assumption that a low-dimensional univariate latent structure retains sufficient modeling capacity for the complexity of natural image distributions.

What would settle it

A direct comparison on a more challenging dataset such as ImageNet where KAEM's FID scores fall significantly below those of diffusion models even with the proposed inference techniques.

Figures

Figures reproduced from arXiv: 2506.14167 by Prithvi Raj.

Figure 1
Figure 1. Figure 1: Demonstration of power posterior evolution with [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Exponentially-tilted priors, extracted after training on MNIST with RBFs. These plots [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Generated NIST images using RBFs and different exponentially-tilted priors, initialized [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Generated Darcy flow pressures with exponentially-tilted priors initialized from standard [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of exponentially-tilted lognormal priors, extracted after training on Darcy [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Generated samples from T-KAM trained on SVHN using a mixture prior. (a) SVHN with deep prior and MLE (b) SVHN with deep prior and SE [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Benchmarks for varying latent dimensions, [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Benchmarks for varying amounts of ULA iterations, [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Benchmarks for varying amounts of temperatures, [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Power-law schedule. (a) p = 0.35 schedule has more bins clustered towards t = 1. (b) p = 1 schedule is uniformly distributed between the bounds. (c) p = 4 schedule has more bins clustered towards t = 0 [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Effect of power-law schedule clusters on integral approximation error. Evaluation points [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Generated MNIST, (Deng, 2012), after 2,000 parameter updates using MLE / IS [PITH_FULL_IMAGE:figures/full_fig_p036_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Generated MNIST, (Deng, 2012), after 2,000 parameter updates using MLE / IS [PITH_FULL_IMAGE:figures/full_fig_p036_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Generated FMNIST, (Xiao et al., 2017), after 2,000 parameter updates using MLE / IS [PITH_FULL_IMAGE:figures/full_fig_p037_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Generated FMNIST, (Xiao et al., 2017), after 2,000 parameter updates using MLE / IS [PITH_FULL_IMAGE:figures/full_fig_p037_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Generated 2D Darcy flow pressures, (Li et al., 2021), after 12,000 parameter updates [PITH_FULL_IMAGE:figures/full_fig_p038_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Generated 2D Darcy flow pressures, (Li et al., 2021), after 12,000 parameter updates [PITH_FULL_IMAGE:figures/full_fig_p038_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Generated 2D Darcy flow pressures, (Li et al., 2021), after 12,000 parameter updates [PITH_FULL_IMAGE:figures/full_fig_p039_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Generated samples from T-KAM trained on SVHN using a mixture Chebyshev KAN [PITH_FULL_IMAGE:figures/full_fig_p039_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Generated samples from T-KAM trained on SVHN using a deep Chebyshev KAN prior, [PITH_FULL_IMAGE:figures/full_fig_p040_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Generated samples from T-KAM trained on CIFAR-10 using a mixture Chebyshev KAN [PITH_FULL_IMAGE:figures/full_fig_p040_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Samples from T-KAM trained on CIFAR-10 using a deep Chebyshev KAN prior, (SS [PITH_FULL_IMAGE:figures/full_fig_p041_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Three components from T-KAM’s prior after training on MNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p041_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Three components from T-KAM’s prior after training on MNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p042_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Three components from T-KAM’s prior after training on MNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p042_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Three components from T-KAM’s prior after training on MNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p042_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Three components from T-KAM’s prior after training on MNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p043_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Three components from T-KAM’s prior after training on MNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p043_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Three components from T-KAM’s prior after training on FMNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p043_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Three components from T-KAM’s prior after training on FMNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p044_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: Three components from T-KAM’s prior after training on FMNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p044_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: Three components from T-KAM’s prior after training on FMNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p044_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: Three components from T-KAM’s prior after training on FMNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p045_34.png] view at source ↗
Figure 35
Figure 35. Figure 35: Three components from T-KAM’s prior after training on FMNIST for 2,000 parameter [PITH_FULL_IMAGE:figures/full_fig_p045_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: Three components from T-KAM’s prior after training on Darcy flow pressures for [PITH_FULL_IMAGE:figures/full_fig_p045_36.png] view at source ↗
Figure 37
Figure 37. Figure 37: Three components from T-KAM’s prior after training on Darcy flow pressures for [PITH_FULL_IMAGE:figures/full_fig_p046_37.png] view at source ↗
Figure 38
Figure 38. Figure 38: Three components from T-KAM’s prior after training on Darcy flow pressures for [PITH_FULL_IMAGE:figures/full_fig_p046_38.png] view at source ↗
Figure 39
Figure 39. Figure 39: Three components from T-KAM’s prior after training on Darcy flow pressures for [PITH_FULL_IMAGE:figures/full_fig_p046_39.png] view at source ↗
Figure 40
Figure 40. Figure 40: Three components from T-KAM’s prior after training on Darcy flow pressures for [PITH_FULL_IMAGE:figures/full_fig_p047_40.png] view at source ↗
Figure 41
Figure 41. Figure 41: Three components from T-KAM’s prior after training on Darcy flow pressures for [PITH_FULL_IMAGE:figures/full_fig_p047_41.png] view at source ↗
read the original abstract

Generative models typically rely on either simple latent priors (e.g., Variational Autoencoders, VAEs), which are efficient but limited, or highly expressive iterative samplers (e.g., Diffusion and Energy-based Models), which are costly and opaque. We introduce the Kolmogorov-Arnold Energy Model (KAEM) to bridge this trade-off and provide new opportunities for latent-space interpretability. Based on a novel adaptation of the Kolmogorov-Arnold Representation Theorem, KAEM imposes a univariate latent structure on the prior, enabling exact inference via the inverse transform method. With a low-dimensional latent space and appropriate inductive biases, importance sampling becomes a tractable, unbiased, and efficient posterior inference method. For settings where this fails, we propose a population-based strategy that decomposes the posterior into a sequence of annealed distributions, a new remedy for poor mixing in Energy-based Models. We compare KAEM against VAEs and the neural latent EBM architecture. KAEM attains the best Fr\'echet Inception Distance among latent-prior models on SVHN and CIFAR10, while sampling in a single forward pass and exposing an interpretable prior built from 1D densities.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces Kolmogorov-Arnold Energy Models (KAEM), a generative modeling approach that adapts the Kolmogorov-Arnold Representation Theorem to impose a univariate latent structure on the energy-based prior. This structure is claimed to enable exact inference via the inverse transform method from 1D densities, tractable importance sampling for posterior inference, and a population-based annealing strategy for cases of poor mixing. KAEM is positioned as bridging simple latent priors (e.g., VAEs) and expressive iterative samplers (e.g., diffusion or EBMs), with empirical claims of achieving the best Fréchet Inception Distance among latent-prior models on SVHN and CIFAR10 while supporting single forward-pass sampling and interpretability through the 1D density components.

Significance. If the KART adaptation and empirical results hold, the work offers a meaningful contribution by combining single-pass sampling efficiency, unbiased importance sampling, and latent-space interpretability in a manner not standard in current latent-variable generative models. The explicit construction from univariate functions and the annealing remedy for mixing issues represent concrete technical advances that could influence future designs of interpretable energy-based models.

major comments (2)
  1. [Experimental Evaluation] Experimental section: the central claim that KAEM attains the best FID among latent-prior models on SVHN and CIFAR10 is presented without error bars, standard deviations across multiple runs, ablation studies isolating the KART prior components, or details on training stability and hyperparameter sensitivity. This absence directly weakens the ability to attribute performance gains to the proposed univariate structure rather than implementation artifacts or post-hoc tuning.
  2. [Model Definition / Prior Construction] Prior construction (around the KART adaptation section): the claim that the finite-sum univariate outer and inner functions preserve sufficient expressivity for modeling statistical dependencies in CIFAR10-level data rests on an untested assumption. If cross-dimensional correlations are primarily captured by the decoder rather than the prior, the reported FID improvements and the interpretability selling point would not be attributable to the univariate latent structure, threatening both the efficiency and the novelty claims.
minor comments (2)
  1. [Abstract] The abstract states comparisons against VAEs and neural latent EBMs but does not name the precise baseline architectures, latent dimensions, or training protocols used for those comparisons.
  2. [Model Definition] Notation for the univariate functions and the energy formulation could be clarified with an explicit equation showing how the Kolmogorov-Arnold sum is turned into a density or energy function.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address the major comments point by point below and outline the revisions we plan to make.

read point-by-point responses

  1. Referee: Experimental section: the central claim that KAEM attains the best FID among latent-prior models on SVHN and CIFAR10 is presented without error bars, standard deviations across multiple runs, ablation studies isolating the KART prior components, or details on training stability and hyperparameter sensitivity. This absence directly weakens the ability to attribute performance gains to the proposed univariate structure rather than implementation artifacts or post-hoc tuning.

    Authors: We agree with the referee that the experimental evaluation would benefit from additional statistical rigor. In the revised manuscript, we will include error bars and report standard deviations from at least three independent runs for the FID scores on both SVHN and CIFAR10. We will also conduct and report ablation studies that remove or modify the KART components to isolate their contribution to performance. Furthermore, we will provide more details on training procedures, stability, and hyperparameter sensitivity in the appendix. These changes will help attribute the gains more clearly to the proposed method. revision: yes

  2. Referee: Prior construction (around the KART adaptation section): the claim that the finite-sum univariate outer and inner functions preserve sufficient expressivity for modeling statistical dependencies in CIFAR10-level data rests on an untested assumption. If cross-dimensional correlations are primarily captured by the decoder rather than the prior, the reported FID improvements and the interpretability selling point would not be attributable to the univariate latent structure, threatening both the efficiency and the novelty claims.

    Authors: We appreciate this insightful observation regarding the source of expressivity. The adaptation of the Kolmogorov-Arnold Representation Theorem is intended to provide a structured prior that can capture dependencies through univariate functions, as guaranteed by the theorem in the infinite case and approximated in the finite sum. Our empirical results on CIFAR10, which has complex correlations, support that the overall model benefits from this structure. However, to directly test the assumption, we will add in the revision a discussion and possibly additional experiments analyzing the learned univariate functions and their impact on latent correlations, such as by comparing correlation matrices or visualizing the 1D densities. We believe the interpretability of the 1D priors remains a valid contribution even if some correlations are handled by the decoder. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation rests on external KART theorem

full rationale

The paper adapts the Kolmogorov-Arnold Representation Theorem (an external 1950s result) to impose a univariate latent structure on the energy-based prior, enabling inverse-transform sampling and tractable importance sampling. This construction is presented as a novel application rather than a self-referential definition or fitted parameter renamed as prediction. No self-citation chains, uniqueness theorems from the same authors, or ansatz smuggling appear in the abstract or described claims. Empirical FID results on SVHN/CIFAR10 are reported as comparisons against VAEs and neural latent EBMs without evidence that evaluation metrics are reused as inputs. The derivation chain remains self-contained against external mathematical benchmarks and does not reduce to its own fitted values by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the KART adaptation for the generative prior and on the assumption that low-dimensional univariate structure plus importance sampling suffices for posterior inference on image data.

axioms (1)
  • domain assumption Kolmogorov-Arnold Representation Theorem can be adapted to define a valid probability density over a low-dimensional latent space for generative modeling
    The model construction begins from this adaptation as stated in the abstract.

pith-pipeline@v0.9.0 · 5728 in / 1353 out tokens · 36058 ms · 2026-05-19T09:41:09.147505+00:00 · methodology

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Lean theorems connected to this paper

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Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages · 1 internal anchor

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    Auto-Encoding Variational Bayes

    doi: 10.1143/jpsj.65.1604. URL http://dx.doi.org/10.1143/JPSJ.65.1604. JuliaCI. Benchmarktools.jl, 2024. URL https://juliaci.github.io/ BenchmarkTools.jl/stable/. Accessed on August 20, 2024. George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. Physics-informed machine learning. Nature Reviews Physics , 3(6):422...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1143/jpsj.65.1604 2024

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    ∇f log P (z | f) # = EP(z|f)

    doi: 10.1090/S0025-5718-97-00861-2. Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. Nature, 521(7553):436–444, May 28 2015. ISSN 1476-4687. doi: 10.1038/nature14539. Ziyao Li. Kolmogorov-arnold networks are radial basis function networks, 2024. URL https: //arxiv.org/abs/2405.06721. Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burige...

    work page doi:10.1090/s0025-5718-97-00861-2 2015

  3. [3]

    Integer replication: The sample, s, is replicated rs times, where: rs = j Ns · wnorm(z(s)) k (68)

    work page

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    Residual weights: The total number of replicated samples after the previous stage will bePNs s=1 rs. Therefore, Ns −PNs s=1 rs remain, which must be resampled using the residuals: wresidual(z(s)) = wnorm(z(s)) · (Ns − rs) wnorm, residual(z(s)) = wresidual(z(s))PNs s=1 wresidual(z(s)) (69) If a sample has been replicated at the previous stage, then its cor...

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    (70) where k∗ represents the index of the sample to keep

    Resample: The remaining samples are drawn with multinomial resampling, based on the cumulative distribution function of the residuals: k∗ = min ( j | jX s=1 wnorm, residual(z(s)) ≥ ui ) where ui ∼ U ([0, 1]). (70) where k∗ represents the index of the sample to keep. A.6.3 M ETROPOLIS -ADJUSTED LANGEVIN ALGORITHM (MALA) The Metropolis-Adjusted Langevin Alg...

    work page 1998

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    Langevin diffusion: A new state z′ (i, t k) is proposed for a local chain, operating with a specific tk, using a transition kernel inspired by (overdamped) Langevin dynamics (Roberts 33 Pre-publication work. & Stramer, 2002; Brooks et al., 2011): Target: log γ z′ (i, t k) ∝ log P (x(b) | z, Φ)tk + log P (z | f) Proposal: z′ (i, t k) | z(i, t k) ∼ q z′ (i,...

    work page 2002

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    The criterion for the local proposal is: rlocal = γ z′ (i, t k) q z(i, t k) | z′ (i, t k) γ z(i, t k) q z′ (i, t k) | z(i, t k) , (73)

    MH criterion: Once Nunadjusted iterations have elapsed, Metropolis-Hastings adjustments, (MH) (Metropolis & Ulam, 1949), are introduced. The criterion for the local proposal is: rlocal = γ z′ (i, t k) q z(i, t k) | z′ (i, t k) γ z(i, t k) q z′ (i, t k) | z(i, t k) , (73)

    work page 1949

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    34 Convergence Under mild regularity conditions, the local Markov chain {z(i, t k)} generated by MALA converges in distribution to P (z | x(b), f , Φ, tk) as Nlocal → ∞

    Global Swaps: Global swaps are proposed and accepted subject to the criterion outlined in Eq. 34 Convergence Under mild regularity conditions, the local Markov chain {z(i, t k)} generated by MALA converges in distribution to P (z | x(b), f , Φ, tk) as Nlocal → ∞ . The proposal mechanism in Eq. 72 ensures that the chain mixes efficiently, particularly in h...

    work page 2024

  9. [10]

    Acceptance thresholds: Two bounding acceptance thresholds are sampled uniformly: a, b ∼ U (a, b) ;0, 1 , (a, b) ∈ [0, 1]2, b > a (75) 34 Pre-publication work

    work page

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    Here, Beta 01 [a, b; c, d] denotes a zero-one-inflated Beta distribution

    Mass matrix: Random pre-conditioning matrices are initialized per latent dimension: ε(i, t k) ∼ Beta 01 1, 1; 1 2 , 2 3 , M1/2 (i, t k , q ) p,p = ε(i, t k) · Σ−1/2 (i, t k, q ) p,p + (1 − ε(i, t k)), (76) where Σ(i, t k, q ) p,p = V ARs h ¯z(i, t k, s) q,p i . Here, Beta 01 [a, b; c, d] denotes a zero-one-inflated Beta distribution. The parameters a, b >...

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    Leapfrog proposal: The following transition is proposed for a local chain, tk, with an adaptive step size, η(i,tk): p(i, t k) ∼ N p; 0, M (i, t k) p′ (i, t k) 1/2 = p(i, t k) + η(i,tk) 2 ∇z log γ z′ (i, t k) z′ (i, t k) = z(i, t k) + η(i,tk) M −1p′ 1/2 (i, t k) ˆp(i, t k) = p′ (i, t k) 1/2 + η(i,tk) 2 ∇z log γ z′ (i, t k) p′ (i, t k) = −ˆp(i, t k), (77)

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    The MH acceptance criterion for the local proposal is: rlocal = γ z′ (i, t k) N p′ (i, t k); 0, M (i, t k) γ z(i, t k) N p(i, t k); 0, M (i, t k) , (78)

    MH criterion: Once Nunadjusted iterations have elapsed, Metropolis-Hastings (MH) adjust- ments are introduced. The MH acceptance criterion for the local proposal is: rlocal = γ z′ (i, t k) N p′ (i, t k); 0, M (i, t k) γ z(i, t k) N p(i, t k); 0, M (i, t k) , (78)

    work page

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    Step size adaptation: Starting with an initial estimate, η(i,tk) init , set as the average accepted step size from the previous training iteration, (used as a simple alternative to the round- based tuning algorithm proposed by Biron-Lattes et al. (2024)), the step size is adjusted as follows: • If a < r local < b, then η(i,tk) = η(i,tk) init • If rlocal ≤...

    work page 2024

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    77 is verified before proceeding with MH acceptance

    Reversibility check: If the step size was modified, the reversibility of the update in Eq. 77 is verified before proceeding with MH acceptance. If η(i,tk) init cannot be recovered from the reversed step-size adjustment process with the proposed state, z′ (i, t k), p ′ (i, t k), η(i,tk) , the proposal is rejected regardless of the outcome of the MH adjustment

    work page

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    If accepted, z(i+1, t k) = z′ (i, t k); otherwise, the current state is retained: z(i+1, t k) = z(i, t k)

    Acceptance: The proposal is accepted with probability min(1, rlocal). If accepted, z(i+1, t k) = z′ (i, t k); otherwise, the current state is retained: z(i+1, t k) = z(i, t k)

    work page

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    34 35 Pre-publication work

    Global Swaps: Global swaps are proposed and accepted subject to Eq. 34 35 Pre-publication work. A.7 20 × 20 IMAGE GRIDS A.7.1 MNIST Figure 13: Generated MNIST, (Deng, 2012), after 2,000 parameter updates using MLE / IS adhering to KART’s structure. Uniform, lognormal, and Gaussian priors are contrasted using Radial Basis Functions, (Li, 2024). Lognormal i...

    work page 2012