The approximation and convergence properties of implicit neural representations (INRs) are known to be highly sensitive to parameter initialization strategies. While several data-driven initialization methods demonstrate significant improvements over standard random sampling, the reasons for their success -- specifically, whether they encode classical statistical signal priors or more complex features -- remain poorly understood. In this study, we explore this phenomenon through a series of experimental analyses leveraging noise pretraining. We pretrain INRs on diverse noise classes (e.g., Gaussian, Dead Leaves, Spectral) and measure their ability to both fit unseen signals and encode priors for an inverse imaging task (denoising). Our analyses on image and video data reveal a surprising finding: simply pretraining on unstructured noise (Uniform, Gaussian) dramatically improves signal fitting capacity compared to all other baselines. However, unstructured noise also yields poor deep image priors for denoising. In contrast, we also find that noise with the classic 1/∣fα∣ spectral structure of natural images achieves an excellent balance of signal fitting and inverse imaging capabilities, performing on par with the best data-driven initialization methods. This finding enables more efficient INR training in applications lacking sufficient prior domain-specific data. For more details, visit project page at https://kushalvyas.github.io/noisepretraining.html
Figures & tables
Figure 2: Early reconstruction quality at T=200 steps. Strainer , Snp (Spectrum and Uniform) learn high quality reconstructions in 200 steps (PSNR ≈40db+ ), while the Siren output remains blurry. Power spectrum insets show that: Snp : Uniform matches closely with the ground truth, Strainer has a noisy high-frequency coverage, and Snp : Spectrum recovers most high frequencies while Siren lacks critical frequencies.
Figure 3: Signal fitting results on CelebA-HQ images. Snp initialized using various noises demonstrate strong signal representation ability and convergence compared to widely known baseline methods such as Siren [ 39 ] , IPC [ 24 ] , and Strainer [ 43 ] . Interestingly, Snp pretrained with Gaussian and Uniform noises performed significantly better than all other approaches, converging rapidly to perfect fitting.
Method
CelebA-HQ
AFHQ
OASIS-MRI
Siren [ 39 ]
44.9
45.1
53.03
Strainer [ 43 ]
57.8
58.0
62.80
Metalearned [ 40 ]
53.1
53.3
67.0
TransINR [ 5 ] (CelebA-HQ)
51.9
49.0
55.5
IPC [ 24 ] (CelebA-HQ)
49.7
47.2
51.4
Snp : Dead Leaves oriented
55.0
55.4
59.0
Table 1: Image fitting results. We present PSNR values (in dB) for all test methods at T=2000 iterations, from vanilla randomized initialization (SIREN) to data-driven initialization methods ( Strainer , Metalearned [ 41 ] , TransINR [ 5 ] , IPC [ 24 ] ) to noise pretraining with Strainer ( Snp ). We provide the pretraining dataset name in parentheses. Snp with unstructured noises (Uniform, Gaussian) perform surprisingly best, with remarkably higher PSNR values than all other methods.
Figure 4: Video fitting results: Snp improves fitting performance. We show frames from representation of two example videos with randomly initialized (vanilla) ResFields [ 31 ] , and Snp : Spectrum-initialized Resfields. In both examples, Snp -initialization results in a higher accuracy with clearer visible details. This implies Snp advantages also expand beyond images to videos.
Figure 5: Video denoising results. The figure above shows denoised frames of sample videos with randomly initialized ResFields [ 31 ] , and Snp : Spectrum-initialized ResFields. In both examples, Snp : Spectrum outperforms by more than 2dB, with dramatically visual improvement, underscoring the effectiveness of Snp trained INRs for solving inverse problems.
Task
Method
Mean PSNR
Fitting
Vanilla ResFields [ 31 ]
29.5
ResFields + Snp (Spectrum)
31.1
ResFields + Snp (Uniform)
30.9
Denoising
Vanilla ResFields [ 31 ]
27.0
ResFields + Snp (Spectrum)
28.0
ResFields + Snp (Uniform)
27.6
Table 2: Video fitting and denoising results. We present mean PSNR values (in dB) for various methods at 100k iterations over all 10 videos from the Pexel video set. We use the ResFields [ 31 ] video INR framework, both with standard random parameter initialization and with Snp initialization for its per-frame weight parameters. Snp : Spectrum performs best for both fitting and denoising tasks. See Fig. 4 for sample video fitting results.
Method
Early Stopping
PSNR
Iteration
Siren [ 39 ]
28.3
139
Strainer [ 43 ]
27.3
70
Snp : Spectrum
27.6
78
Snp : Uniform
23.0
73
Snp : Gaussian
23.8
70
Table 3: Denoising results for CelebA-HQ images at T=2000 iterations. Strainer and Snp : Spectrum achieve similar denoising performance as Siren , but 2× faster. Snp pretrained on unstructured noises (Uniform, Gaussian) perform poorly.
Figure 6: NTK eigenvectors of INRs using different initialization schemes. NTK eigenvectors characterize the function space spanned by a network in the vicinity of its initialization, and can help us depict how pretraining encodes priors in an INR’s function space to influence its ability to fit signals. We visualize the top 4 NTK eigenvectors. Standard Siren initialization yields noticeably blurred and random eigenvectors. Strainer pretrained on CelebA-HQ exhibits face-like structures in its eigenvectors. Snp : Dead Leaves and Snp : Spectrum exhibits smooth regions akin to its structured noise images. Finally, Snp : Uniform pretrained on Uniform noise has essentially no noticeable structural features.
Figure 7: Underlying functional local complexity of INR layers. . Using a measure of local complexity (LC) [ 16 ] , we visualize learned geometry of Siren , Strainer , and Snp INRs fit to a test signal from CelebA-HQ. Siren ’s internal function geometry aligns with the signal morphology. Strainer and Snp : Spectrum exhibit geometry of their pretraining signals in initial layers, while later layers are adapted towards the test signal morphology. Finally, seemingly random geometry is exhibited by initial layers of Snp : Uniform much due to its pretraining on uniform noise.
Figure 8: Visualizing loss landscapes of Snp INRs. SNP: Uniform yields a smooth landscape with a strong minima, justifying its impressive fitting results. STRAINER and SNP: Spectrum exhibit strikingly similar loss surfaces.
Figure 9: Energy distribution across eigenmodes . The x -axis denotes the eigenvalue percentile threshold; at a given point on the x -axis, we consider only eigenvalues above that percentile. The y-axis reports the fraction of the target-images energy captured by the eigenvectors associated with those eigenvalues. In other words, the curve summarizes how much cumulative energy is explained as we progressively include eigenvectors corresponding to eigenvalues in descending order.
Figure 10: Tradeoff in signal representation and denoising ability of Snp INRs on CelebA-HQ images. At early stages of signal fitting ( T=500 ) and denoising ( T=50 ), Snp : Spectrum and Strainer perform well. In contrast, Snp : Uniform and Gaussian excel at signal fitting, but are poor denoisers. SIREN is a good denoiser but a poor signal fitter. Hence, there is a tradeoff to consider when choosing an appropriate initialization method for a task.
Method
CelebA
PSNR ↑
SSIM ↑
LPIPS ↓
Siren [ 39 ]
44.9±2.13
0.991±0.007
0.0026±0.002
Strainer [ 43 ]
57.8±3.46
0.999±0.001
0.00002±0.07
Meta-learned [ 40 ]
53.1±3.36
0.994±0.053
0.0046±6.2e-5
Snp : Dead leaves oriented
55±2.8
0.999±0.0006
0.00096±0.001
Snp : Dead leaves texture
55±2.9
0.999±0.0006
0.0009±0.001
Table 4: Image fitting results on CelebA-HQ. We present mean PSNR(in db), SSIM and LPIPS with 1 std.dev. for all test methods at T=2000 iterations, from vanilla randomly initialized ( Siren ), to data driven methods such as Metalearned [ 40 ] , Strainer [ 43 ] , and Snp variants trained on structured and unstructured noises.
Figure 12: Signal fitting results on AFHQ images. Snp initialized using various noises demonstrate strong signal representation ability and convergence compared to widely known baseline methods such as Siren [ 39 ] , IPC [ 24 ] , and Strainer [ 43 ] . Interestingly, Snp trained with Gaussian and Uniform noises performed significantly better than all other approaches. converging rapidly to perfect fitting.
Figure 13: Signal fitting results on OASIS-MRI images. Snp initialized using various noises demonstrate strong signal representation ability and convergence compared to widely known baseline methods such as Siren [ 39 ] , IPC [ 24 ] , and Strainer [ 43 ] . Interestingly, Snp trained with Gaussian and Uniform noises performed significantly better than all other approaches. converging rapidly to perfect fitting.
Figure 14: Video fitting results on the all video in our dataset. . Snp initialization accelerates the training of ResField by approximately a factor of five compared to the vanilla model across all videos.
Figure 15: The Snp pretrained model provides a superior initialization, resulting in substantial starting gains and a consistently faster convergence rate during test-time fine-tuning across all videos.
Task
Method
Cat
Coin
Cooking
Dance
Aquapark
Stadium
Train
Shibuya
Juggler
Traffic
All
Fitting
Vanilla Resfield
34.1
50.0
33.5
35.5
28.6
20.1
21.8
25.9
21.9
24.0
29.5
ResField+ Snp (Uniform)
35.1
50.5
33.9
36.1
29.8
22.1
23.2
27.8
25.7
24.4
30.9
ResField+ Snp (Spectrum)
35.6
50.5
33.9
36.3
29.9
22.5
23.6
28.2
26.1
24.7
31.1
Denoising
Vanilla Resfield
32.2
37.5
31.6
29.7
27.1
19.9
21.6
25.4
21.5
23.5
27.0
ResField+ Snp (Uniform)
32.8
34.3
31.6
28.5
27.9
21.8
22.8
27.2
24.8
23.9
27.6
ResField+ Snp (Spectrum)
33.3
35.4
31.8
29.1
28.0
22.2
23.2
27.5
25.1
24.1
28.0
Table 5: PSNR (dB) comparison across scenes for video representation and video denoising.
Method
AFHQ
PSNR ↑
SSIM ↑
LPIPS ↓
Siren [ 39 ]
45.1±3.13
0.991±0.005
0.0025±0.004
Strainer [ 43 ]
58±3.75
0.999±0.001
0.00003±0.06
Meta-learned [ 40 ]
53.3±2.52
0.996±0.044
0.003±8.0e-5
Snp : Dead leaves oriented
55.4±2.93
0.999±0.0006
0.0008±0.0011
Snp : Dead leaves texture
55.3±3.5
0.999±0.0007
0.0007±0.001
Table 6: Image fitting results on AFHQ. We present mean PSNR(in db), SSIM and LPIPS with 1 std.dev. for all test methods at T=2000 iterations, from vanilla randomly initialized ( Siren ), to data driven methods such as Metalearned [ 40 ] , Strainer [ 43 ] , and Snp variants trained on structured and unstructured noises.
Method
OASIS-MRI
PSNR ↑
SSIM ↑
LPIPS ↓
Siren [ 39 ]
53.03±1.72
0.999±0.0002
0.0009±0.0002
Strainer [ 43 ]
62.8±3.17
0.999±0.0003
0.00001±2.0e-5
Meta-learned [ 40 ]
67±2.27
0.999±1.0e-5
0.000005±2.5e-6
Snp : Dead leaves oriented
59±3.5
0.999±0.0001
0.0003±0.0003
Snp : Dead leaves texture
58.9±3.38
0.999±0.0002
0.0003±0.0003
Table 7: Image fitting results on OASIS-MRI. We present mean PSNR(in db), SSIM and LPIPS with 1 std.dev. for all test methods at T=2000 iterations, from vanilla randomly initialized ( Siren ), to data driven methods such as Metalearned [ 40 ] , Strainer [ 43 ] , and Snp variants trained on structured and unstructured noises.
Figure 16: Fitting performance v/s number of pretraining signals. We show that initialization learned by Snp pretrained on multiple pretraining images, such as N=10 , learns a richer and powerful initialization achieving significantly better reconstruction quality than Snp pretrained on N=1 signals. ( Snp - k denotes INRs pretrained on k images).
Method
PSNR
SSIM
LPIPS
FINER [ 28 ]
51.2±3.1
0.998±0.0012
0.001±0.002
Snp Finer: Spectrum
52.3±2.4
0.998±0.001
0.003±0.002
Snp Finer: Uniform
117.2±14
0.999±2.1E−6
1.8E−7±2.1E−6
Table 8: Snp readily extends to FINER activations [ 28 ] . We extend Snp framework to FINER [ 28 ] activations and evaluate image fitting performance on CelebA-HQ.
Model
CelebA-HQ
AFHQ
OASIS-MRI
Siren
44.9
45.1
53.03
Strainer : ImageNet
50.87
44.11
53.37
Strainer (dataset-specific)
57.8
58.0
62.80
Snp : Spectrum
56.4 ↑
56.2 ↑
60.0 ↑
Snp : Uniform
85.7 ↑
79.9 ↑
79.3 ↑
Siren (10 layers)
51.3
52.6
57.3
Table 9: Fitting results on additional baselines and deeper INRs.
Figure 17: More examples on local complexity of INR layers for Snp and baselines. Using local complexity measure [ 16 ] , we visualize , in (a) and (b), the local complexity of Siren , Strainer and Snp (uniform and spectrum) fit to images from CelebA-HQ. We observe that Siren ’s internal layers quickly adapt to the underlying signal morphology. Strainer and Snp (spectrum) exhibit internal geometry akin to their pretraining signals. Finally, we observe that Snp Uniform exhibit seemingly random geometry in the initial layers, much due to its pretraining on uniform noise.
Implicit neural representations (INRs) have emerged as a powerful paradigm for medical imaging via physics-informed unsupervised learning. Classical INRs optimize an entire network from scratch for each subject, leading to inefficient training and suboptimal imaging quality. Recent initialization-based approaches attempt to inject population priors into pre-trained networks, yet they rely on high-quality images and often suffer from catastrophic forgetting during fine-tuning. We present DisINR, a novel INR framework that explicitly disentangles shared and subject-specific representations. DisINR introduces a shared encoder-decoder pair and subject-specific encoders, whose features are jointly decoded for image reconstruction. By integrating differentiable forward models, it pre-trains the shared modules directly from limited raw measurements, removing the need for pre-acquired high-quality images. During test-time adaptation, only the subject-specific encoder is optimized, while the shared pair remains frozen, effectively preserving learned priors. Extensive evaluations on three representative medical imaging tasks show that DisINR significantly outperforms state-of-the-art INRs in both reconstruction accuracy and efficiency.
Qing Wu, Xuanyu Tian, Chenhe Du +4
Medical AI Lab, Ant Group · ShanghaiTech University · Shanghai Jiao Tong University
Existing implicit neural representation (INR) approaches suffer from stochastic initialization that does not guarantee consistent or high-quality performance across runs, with variations reaching more than 2.5 dB (~78%) in image regression. This variation is problematic for scientific computing and simulation, where result reproducibility is crucial. To address this problem, we present Jacobi-Anger Sinusoidal Representation Network (JA-SIREN), a deterministic initialization scheme for sinusoidal networks grounded in classical spectral analysis. By computing the Discrete Sine Transform (DST) of the target signal and leveraging the Jacobi-Anger expansion, we derive closed-form weights for a two-layer sinusoidal MLP that analytically match the network's initial spectral response to the target signal, requiring no random seed or additional hyperparameter tuning. On the Kodak dataset, JA-SIREN achieves a mean PSNR of 67.18 dB, a 21.30 dB improvement over the best baseline. This is achieved with zero run-to-run variance, confirming that spectrally-informed initialization is a more effective and reproducible alternative to stochastic initialization for sinusoidal INRs.
Mohammed Alsakabi, Kejia Hu, John M. Dolan +1
Department of Electrical and Computer Engineering, College of Engineering · The Robotics Institute, School of Computer Science Carnegie Mellon University, Pittsburgh, PA, USA
Periodic Implicit Neural Representations (INRs) such as SIREN and FINER assign every neuron, the same global frequency, spending the representational budget inefficiently when local signal content varies. We introduce FiRe (Frequency Reparameterization), that accelerates optimization by reparameterizing per-neuron frequency of periodic INRs without changing their underlying activation function. FiRe gives each neuron a bounded, input-dependent frequency via a separate low-rank gating path and is applicable to any periodic activation function. The gate acts as an implicit preconditioner that improves optimization conditioning at initialization via the Neural Tangent Kernel (NTK). This better-conditioned initialization makes optimization converge faster, and the high-frequency content of the reconstruction tracks the target more closely at a fixed computational budget. On 2D image fitting, FiRe increases PSNR over a parameter-matched baseline (up to +1 dB at short training budgets), with gains that vary with resolution and diminish at full convergence. We characterize how performance depends on resolution, rank, and training budget, and give an NTK account that predicts these trends.
Harinandan Shukla, Rajarshi Verma, Jitin Singla
Department of Computer Science and Engineering, IIT Roorkee · Department of Biosciences and Bioengineering, IIT Roorkee