SBS: Enhancing Parameter-Efficiency of Neural Representations for Neural Networks via Spectral Bias Suppression

Qihu Xie; Yi Kang; Yuan Li

REVIEW 4 major objections 4 minor 35 references

SBS: Enhancing Parameter-Efficiency of Neural Representations for Neural Networks via Spectral Bias Suppression

T0 review · 4 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read A small MLP can regenerate a pretrained CNN's weights with 2–3x better parameter efficiency if its spectral bias is suppressed in both output and input space.

desk verdict A plausible incremental win over NeRN with a garbled theory section and a sigma-selection rule that is weaker than the authors claim. read the letter →

arxiv 2509.07373 v1 pith:YXWJGXKX submitted 2025-09-09 cs.LG cs.AI

Qihu Xie , Yuan Li , Yi Kang This is my paper

classification cs.LGcs.AI

keywords ImplicitNeuralRepresentationSpectralBiasWeightGenerationParameterEfficiencyRandomFourierFeaturesNetworkCompressionResNet

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that the standard recipe for compressing a pretrained CNN — train a small coordinate-based MLP to output its weights — is held back by spectral bias: ReLU networks learn low-frequency structure early and smear high-frequency detail. The authors propose two complementary fixes: reorder each layer's kernels along one direction so the weight signal becomes smoother and lower-frequency, and encode the MLP's input coordinates with random Fourier features whose frequency bandwidth shrinks for wider layers. On CIFAR-10, CIFAR-100, and ImageNet with ResNet backbones, the combined method reconstructs higher-accuracy networks from smaller MLPs than the NeRN baseline, and on ImageNet it matches NeRN's accuracy at about a third of NeRN's MLP parameters while using no external teacher. If correct, this makes weight-generation compression noticeably more practical for memory-limited deployment.

What carries the argument

The two load-bearing mechanisms are the UOS permutation and the UOS-RFF encoding. UOS is a greedy reordering of CNN kernels within each layer along a single axis, the filter index, minimizing Euclidean distance between neighboring kernels; this reshapes the target weight signal so its energy sits in the low-frequency eigenmodes that a ReLU-MLP learns fastest, as measured by the neural tangent kernel (NTK), the Gram matrix governing frequency-wise convergence under gradient descent. UOS-RFF is a random Fourier feature input encoding whose Gaussian bandwidth sigma is reduced as layer-wise parameter count grows, preventing the input coordinates from collapsing into too narrow a frequency band a

What would settle it

Take a CNN with larger layers than ResNet18 (for instance, ResNet50) on ImageNet, fix UOS and the SBS training objective, and sweep the RFF bandwidth sigma. The paper's rule predicts the optimal sigma should drop below the value used for ResNet18 (100); finding that the best sigma is set by dataset or architecture in a way uncorrelated with layer count would undercut the UOS-RFF contribution.

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Extended reading notes

Core claim

The paper's claim is that the limiting factor in NeRN-style MLPs that generate CNN weights is spectral bias: the ReLU-MLP acts as a low-pass filter, so it reconstructs smooth, low-frequency weight arrangements well but loses high-frequency kernel detail. SBS attacks this on both sides of the MLP. In output space, UOS greedily reorders kernels within each layer along one direction (filter-wise) using Euclidean distance, concentrating energy at low frequencies so the target signal is easier for the MLP to fit. In input space, UOS-RFF maps coordinates through random Fourier features and sets the bandwidth sigma inversely to layer-wise parameter count, rebalancing the frequency content the MLP s

Load-bearing premise

The method's central premise is that the ideal frequency bandwidth of the input encoding depends mainly on how many parameters the CNN layer has, so the rule 'wider layers need smaller bandwidth' carries over to new networks rather than being a per-dataset hyperparameter choice.

Editorial extensions

If this is right

NeRN-style weight reconstruction can reach a given accuracy with roughly one-third to one-half of the MLP parameters previously needed, making weight-representation compression more practical for mobile and edge deployment.
The same ReLU-MLP backbone no longer needs a stronger teacher or extra distillation signal: at equal MLP size, SBS outperforms the stronger-teacher variant while using no external supervision.
The bandwidth rule makes the method transfer across CNN widths: wider layers automatically receive smaller RFF bandwidth, reducing per-dataset frequency hyperparameter search.
The gains grow as the MLP shrinks, so the method is most effective exactly in the low-parameter regime where compression matters.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural extension is per-layer or per-block bandwidth selection instead of one global sigma; the paper's inverse-relationship rule suggests such adaptivity could remove the remaining hyperparameter tuning.
Because UOS concentrates kernel energy at low frequencies, the reconstructed weights may also compress better under standard quantization or sparsification downstream — the paper does not test this.
The unidirectional-over-multidirectional insight may transfer to other INR tasks where the target signal has a natural axis ordering (e.g., video frames along time, volumetric slices), not just CNN kernels.
The paper's comparison against a distillation-augmented baseline suggests a fairer protocol for weight-space INRs: measure gains over unaugmented baselines before importing external supervision.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The empirical core is believable; the theory around it is not. SBS combines a unidirectional greedy permutation of CNN kernels (UOS, Euclidean distance) with an RFF input encoding whose bandwidth is scaled down for wider layers. That specific combination is new relative to NeRN, Choi et al., and Tancik et al., and the tables consistently show SBS beating NeRN at the same MLP size and matching NeRN's accuracy at roughly half to a third of the MLP parameters. I think the 2–3x parameter-efficiency claim is numerically supported for the tested ResNets.

Where it gets soft is the explanatory apparatus. Eq. (5) is garbled and not derivable as written; Eq. (7) is asserted, not derived; and the loss weights alpha/beta in Fig. 1 never appear in the experiments. The paper reads as a heuristic that works, wrapped in NTK language it doesn't fully earn. That doesn't kill the empirical contribution, but it needs cleanup.

The stress-test about sigma is worth taking seriously but is subtler than it looks. Table 5 does show ResNet20 accuracy still increasing at sigma=1000 (91.44 vs 91.25 at sigma=100), and the main CIFAR experiments fix sigma=400. That means the headline CIFAR numbers are not at SBS's best configuration; if anything, the gains would be slightly larger with sigma=1000. So the main efficiency claim is not inflated. What is weakened is the UOS-RFF design rule: the evidence for 'reduce sigma as layer count grows' is a two-point comparison that changes dataset and architecture at once, and the ResNet20 side of the grid never reaches a peak. That rule should be treated as a per-dataset tuning heuristic, not a validated law. Also, there is no code, no error bars, and the alpha/beta omissions make the training objective under-specified.

Who gets value: researchers working on INR-based weight compression or weight-generating hardware. For them the empirical comparison is useful even without the theory. It deserves a serious referee — ideally one who will push for derivations for Eqs. (5) and (7), a proper sigma ablation that includes the CIFAR-10 optimum, and code release. Desk rejection would be premature.

Referee Report

4 major / 4 minor

Summary. The paper proposes SBS, a parameter-efficiency enhancement to NeRN (neural representation for neural networks). SBS augments a coordinate-based ReLU-MLP that generates CNN weights with two mechanisms: (1) Unidirectional Ordering-based Smoothing (UOS), a greedy permutation that reorders CNN kernels along one direction using Euclidean distance to increase low-frequency energy in the output space; and (2) UOS-RFF, a Random Fourier Feature input encoding whose bandwidth σ² is reduced for wider CNNs, based on the authors' observation that larger models exhibit stronger low-frequency bias under UOS. The method is evaluated on ResNet20/ResNet56 for CIFAR-10, ResNet56 for CIFAR-100, and ResNet18 for ImageNet, comparing against NeRN and a stronger-teacher variant. The central claim is a 2–3× improvement in parameter efficiency, e.g., reaching NeRN's 46%-parameter-usage accuracy with about 15% of the MLP parameters on ImageNet.

Significance. If the empirical claims hold, the paper makes a useful practical contribution: it improves NeRN's parameter efficiency without external supervision, with consistent gains across CIFAR-10, CIFAR-100, and ImageNet. The experimental tables are the main strength: SBS consistently outperforms NeRN at the same MLP hidden sizes, the ImageNet result (Table 3) is competitive even against a stronger-teacher variant, and the UOS ablation (Table 4) supports the ordering strategy. However, the paper's theoretical scaffolding is substantially weaker than claimed. Equations (5) and (7) are asserted without derivations, the UOS-RFF bandwidth rule rests on a confounded two-point comparison, and the claim of a proof for RFF's advantage is unsupported. These gaps do not invalidate the empirical comparison, but they prevent the paper from supporting its advertised principled design rules.

major comments (4)

[§4.3, Table 5, Fig. 4(c)] The UOS-RFF design rule ('for wider CNNs, reduce RFF bandwidth σ²') is supported only by two configurations that change architecture, dataset, and input resolution simultaneously (ResNet20/CIFAR-10 vs ResNet18/ImageNet), so the inverse relationship is confounded. Moreover, Table 5 is internally inconsistent with the main CIFAR setup: for ResNet20, accuracy increases monotonically from 91.05 at σ=10 to 91.44 at σ=1000, with no peak reached, yet the main CIFAR experiments fix σ=400. On the paper's own grid, σ=400 is suboptimal. The reported CIFAR gains are therefore not at SBS's best configuration, and the claimed adaptivity of UOS-RFF is not validated as a causal layer-count law. Controlled experiments (e.g., same dataset/architecture with varying layer widths) are needed.
[§4.1, Eq. (5)] The bound in Eq. (5) is stated without derivation and with several undefined quantities. What exactly are Δf_i, n_k, δ, and ε, and how does the first inequality follow from the linear-region argument? The step from this bound to the regularization term S(w) in Eq. (6) is the theoretical basis for UOS, but as written Eq. (5) is not checkable. Please provide a complete derivation or explicitly label the statement as heuristic motivation.
[§4.2, Eq. (7)] The claim that unidirectional smoothing yields faster convergence than multi-directional smoothing is asserted as Eq. (7) without derivation. The coefficients c1, c2, c3 are not defined, and the approximation ‖ft(X)-Y‖² ≈ |c1| e^{-ηλ1t} does not follow from Eqs. (2) and (4) as written: replacing the full eigenvalue sum by a single term requires an error bound. Since UOS is one of the paper's two main contributions, this step needs either a rigorous justification or an explicit statement that it is an empirical observation.
[§4.3, Eqs. (10)–(12)] The RFF kernel approximation contains a factor error. With B∼N(0,σ²I) and φ(x)=[cos(πBx), sin(πBx)], the expected inner product is exp(-π²σ²‖x-y‖²/2), not exp(-σ²‖x-y‖²/2) as written in Eq. (12). Additionally, the sentence in §4.3 claiming RFF's advantage is 'theoretically proven' is not backed by any theorem or proof in the paper; please correct the formula and soften or substantiate the claim.

minor comments (4)

[Tables 1–2] Typos: 'Achitecture' and 'Smothness' in the table headers. Also, the asterisk in Table 3 is not explained in the caption.
[§5.3] The phrase 'reaches the performance of NeRN at 46% parameter usage with only about 15% of the MLP parameters' is imprecise: in Table 3, SBS at 15% gives 68.57 while NeRN at 46% gives 68.74, a 0.17 accuracy gap. State the tolerance or compare within variance.
[§5] Training details are missing: values of α and β in the loss, learning-rate schedule, number of epochs, RFF feature dimension, number of random seeds, and standard deviations. These are needed to assess whether reported differences of 0.1–0.3% are significant.
[Fig. 4] The caption of Fig. 4 appears garbled in the reviewed version (e.g., '/uni00000013/...' tokens). Please ensure the final figure is legible and the caption renders correctly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the UOS-RFF bandwidth heuristic is under-validated but not self-referential.

full rationale

The paper's central derivation chain is not circular. The low-pass property (Eqs. 1–4) is imported from external NTK literature (Basri et al., Arora et al., Rahaman et al.), not from the authors' own results. The output-space UOS smoothing is an empirical algorithm whose effectiveness is measured against NeRN at matched MLP sizes on CIFAR-10/100 and ImageNet (Tables 1–3); these external head-to-head comparisons are independent of any internal design rule. The only arguably self-referential element is the UOS-RFF bandwidth rule in Sec. 4.3: the statement 'for wider CNNs ... reduce RFF bandwidth' is inferred from Fig. 4(b,c)/Table 5 and then used to set σ=400 for CIFAR and σ=100 for ImageNet. However, this is an empirical heuristic, not a fitted parameter renamed as a prediction: the paper does not estimate σ from the target accuracy, and the main efficiency claims do not mathematically reduce to the heuristic. In fact, Table 5 shows ResNet20 accuracy still increasing at σ=1000, so the chosen σ=400 is not even the paper's best observed setting; this is a validity/rigor issue, not circularity. There are no self-citations, no imported uniqueness theorems, and no ansatz smuggled via citation. The phrase 'theoretically proven' in Sec. 4.3 is an overstatement—the argument is heuristic—but it is not circular. Therefore the derivation chain is self-contained against external benchmarks and the circularity score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The method introduces no new physical or mathematical entities; all components (permutation, RFF, NTK) exist in prior work. The free parameters are the RFF bandwidth and the unreported loss weights, and the key domain assumption is that kernels can be smoothed by unidirectional reordering.

free parameters (3)

RFF bandwidth sigma = 400 (CIFAR-10/100), 100 (ImageNet)
Chosen per dataset/architecture; Table 5 shows ResNet20 accuracy still rising at sigma=1000, so the chosen value is not the best on the authors' own grid.
Loss weights alpha and beta = not reported
The training loss is L_recon + alpha L_atten + beta L_KD, but alpha and beta values are never given, so the reported numbers cannot be reproduced.
MLP hidden size = 140 to 1372 depending on experiment
Reported as a configurable capacity knob and swept; not fitted in a formal sense but contributes to the efficiency comparison.

assumptions (4)

standard math ReLU MLPs in the NTK regime act as low-pass filters with exponentially decaying eigenvalue spectra for high-frequency components
Invoked in Section 3 (Eqs. 1-4) from prior NTK results [4,1,28].
domain assumption CNN kernels can be reordered along a single dimension so that the resulting sequence is locally smooth and easier for an MLP to fit
Core premise of UOS in Section 4.2; no proof that such an ordering always exists for arbitrary pretrained weights.
domain assumption The number of linear regions K of the ReLU-MLP is much smaller than the number of weight samples n (K << n), so local linear-region behavior dominates approximation error
Used to justify Eq. (5) and the smoothness regularization; the bound itself is not derived.
standard math Random Fourier Features with high enough dimensionality approximate a Gaussian kernel that preserves sensitivity to high frequencies
Eq. (12) cites the standard RFF convergence result, though the statement 'As the D → ∞' leaves the feature dimension undefined.

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Cite this review

Pith. "Pith review of SBS: Enhancing Parameter-Efficiency of Neural Representations for Neural Networks via Spectral Bias Suppression." pith.science (2026). https://pith.science/paper/YXWJGXKX

@misc{pith2026250907373,
  author       = {Pith},
  title        = {Pith review of: SBS: Enhancing Parameter-Efficiency of Neural Representations for Neural Networks via Spectral Bias Suppression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YXWJGXKX}},
  note         = {Machine review of arXiv:2509.07373}
}

read the original abstract

Implicit neural representations have recently been extended to represent convolutional neural network weights via neural representation for neural networks, offering promising parameter compression benefits. However, standard multi-layer perceptrons used in neural representation for neural networks exhibit a pronounced spectral bias, hampering their ability to reconstruct high-frequency details effectively. In this paper, we propose SBS, a parameter-efficient enhancement to neural representation for neural networks that suppresses spectral bias using two techniques: (1) a unidirectional ordering-based smoothing that improves kernel smoothness in the output space, and (2) unidirectional ordering-based smoothing aware random fourier features that adaptively modulate the frequency bandwidth of input encodings based on layer-wise parameter count. Extensive evaluations on various ResNet models with datasets CIFAR-10, CIFAR-100, and ImageNet, demonstrate that SBS achieves significantly better reconstruction accuracy with less parameters compared to SOTA.

Figures

Figures reproduced from arXiv: 2509.07373 by the authors.

**Figure 1.** The framework of SBS. A single MLP is trained as an INR to generate CNN layer weights. Lrecon is the MSE between generated and smoothed weights, Latten is the MSE of feature maps across layers, and LKD is the distillation loss between model outputs. The overall training objective is defined as Lrecon + αLatten + βLKD. Bias Suppression framework for NeRN (SBS), as shown in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** The impact of various coordinate transformations on the regression speed of ReLU-MLPs, for both smooth and non-smooth functions, is analyzed within the framework of NTK theory. (A) Original (left) and order-based smoothed (right) 16 × 16 Gaussian random matrices. (B) Magnitude spectra obtained by FFT of the original and smoothed matrices, illustrating the concentration of energy in lower frequencies after smoothing.… view at source ↗

**Figure 3.** Different smoothing strategies applied to the CNN kernels in the l th layer of the pre-trained CNN. Here, c1 denotes the projection of Y, smoothed unidirectionally, onto the lowfrequency component of the NTK, thereby reflecting its concentrated energy in the low-frequency domain. When smoothing is applied along multi-directions, although Y may exhibit higher energy in relatively high-frequency directions, the conve… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: (a) Convergence rates of different smoothing strategies during the training of NeRN ResNet20 on CIFAR-10, with the MLP has a hidden size of 140. (b) Energy distributions under the UOS strategy for models with large and small parameter spaces. (c) Reconstruction error …

**Figure 5.** Figure 5: Reconstruction performance on ResNet20 with varying MLP sizes for SBS (Ours) and NeRN. Fig.5 shows that under smoothing, our method achieves better parameter efficiency compared to NeRN, and our method becomes more effective when the MLP size is smaller. The bandwidth…

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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

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