{"id":"a2859dc6-408a-4ab1-98a0-aafa055bd1c3","arxiv_id":"2504.13214","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"Using Haar wavelet coefficients as the latent representation of a VAE, with L1 sparsity regularization, reduces blur in reconstructions compared with a Gaussian latent VAE in reported single-run experiments.","lead":"This paper describes a wavelet-based variational autoencoder that replaces the usual Gaussian latent codes with multi-scale Haar wavelet coefficients and a learned noise level. Reported experiments on CIFAR-10 show lower reconstruction loss, higher SSIM, and lower FID than a conventional VAE baseline, but no code, full architecture, or generated samples are provided.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No generative sampling path is specified: Eq. (22) omits the KL term, the decoder is a fixed IDWT, and experiments report reconstructions only, so the central generation claim is unsupported.","rationale":"The reader's weakest assumption identifies Eq. (22) as invalid because it discards the KL divergence and because s can collapse to zero. My reading converges on the same point but sharpens it: even if s stays positive, the model is not generative because there is no specified or trained procedure for sampling from a prior over wavelet coefficients and decoding them into images. The decoder is a fixed inverse wavelet transform, so the only learned component on the generation side is absent; the encoder, trained on real images, does not define a marginal prior that can be sampled. This is internally inconsistent with the paper's stated goal of generation, not merely a deviation from current consensus. The experiments confirm the gap: Table 1 reports reconstruction loss, SSIM, and FID, but no generated samples or sampling protocol appear anywhere in Section 4. The unresolved cross-reference 'Section??' and duplicated reference identifiers (both [15] and [16] cite arXiv:2504.03821) are additional signs of incompleteness, but the missing generative mechanism is decisive. I therefore agree with the REJECT verdict; the paper could become conditionally acceptable only if the authors restore a proper variational objective, define and evaluate an actual sampling procedure from a prior, and report generated-image metrics rather than reconstruction-only numbers.","tokens_in":11045,"tokens_out":5890,"duration_ms":59987,"concrete_test":"Implement the model exactly as specified on CIFAR-10 at 128x128 with lambda fixed and s initialized to 1.0. After convergence, (a) record the final learned value of s; (b) set s=0 and measure reconstruction MSE and SSIM; (c) draw c from the Laplacian prior p(c) = (lambda/2) exp(-lambda|c|), decode with IDWT, and compute FID against the training set. If s collapses to approximately 0, or if prior samples have FID close to that of random noise or substantially worse than a standard VAE, the model is not functioning as a stochastic generative model.","verdict_should_be":"REJECT","load_bearing_attack":"The load-bearing problem is that the objective and architecture do not define a generative model. In Section 3.3.2, the KL term is replaced by an L1 penalty on the deterministic encoder outputs, giving Eq. (22): L = -E_{q(c~|x)}[log p(x|c~)] + lambda * sum_{i in detail} |c_{i,NN}|. This is not an ELBO for any prior p(c): the D_KL(q(c|x) || p(c)) term is absent, so the regularization does not couple the posterior to a distribution that can be sampled. In Section 3.2.2 the decoder is fixed as IDWT(c~), so the only stochasticity is additive noise s*epsilon around the encoder's output for a given input; there is no trained map from a prior latent distribution to images. To generate, one would have to sample c from the Laplacian prior in Eq. (20) and apply IDWT, but the encoder was trained to produce DWT-like coefficients for real images, the fixed decoder was never trained on prior samples, and no such sampling procedure is specified anywhere. Section 4 reports only reconstruction metrics (Table 1) and qualitative reconstructions, not generated samples; the FID number cannot be interpreted as evidence of generation without a defined sampling process. Even if s remains positive, the model is a noisy sparse autoencoder, not a variational generative model, so the central claim of high-resolution image generation fails. The learnable s also has a trivial optimum: for a fixed reconstruction likelihood, the gradient of the loss with respect to s points toward zero, and Section 4.5 provides only qualitative, not quantitative, evidence that s stays positive.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Wavelet-VAE, a variational autoencoder variant whose latent space is composed of multi-scale Haar wavelet coefficients. The encoder outputs deterministic wavelet coefficients, to which a learnable noise scale s is added; the decoder is a fixed inverse discrete wavelet transform. The training objective in Eq. (22) drops the standard KL term and instead applies an L1 sparsity penalty to the encoder's detail coefficients. The authors claim that this approach reduces blur and recovers higher-resolution details, and they report reconstruction loss, SSIM, and FID for a conventional VAE and the Wavelet-VAE on CIFAR-10 upscaled to 128x128, while also stating that CelebA-HQ at 128x128 and 256x256 would be used.","tokens_in":11328,"tokens_out":6851,"duration_ms":59853,"significance":"If the model were a valid generative model with the reported gains, the wavelet-based structured latent representation would be a potentially useful contribution to VAE research, and the interpretability discussion in Section 5 is a genuine strength. The learnable-noise idea is also interesting, although its current formulation is problematic. However, the paper provides no code, no machine-checked proofs, and the central claims rest on an objective that is not a valid ELBO and on an experimental section that does not match the abstract's dataset claims. As presented, the method is a regularized sparse autoencoder with a fixed linear decoder, not a generative model; the reported FID and SSIM improvements are therefore not evidence for improved generation.","major_comments":[{"comment":"Equation (22) is not a valid ELBO. The standard objective in Eq. (14) contains the KL divergence D_KL(q_phi(c~|x) || p(c)), which is necessary for the objective to lower-bound the log-likelihood and to tie the posterior to a sampling prior. In Section 3.3.2, this term is replaced by an L1 penalty on the deterministic encoder outputs c_NN, with no derivation that this regularizer is a bound on the KL divergence or a surrogate that preserves the variational interpretation. A model trained with Eq. (22) is therefore a regularized autoencoder, not a variational autoencoder, and the paper's central claim of a 'wavelet-based variational autoencoder' is unsupported.","section":"3.3.2, Eq. (22)"},{"comment":"No generative sampling path is defined. The decoder is the fixed inverse discrete wavelet transform (IDWT) applied to noisy coefficients c~ = c_NN + s*epsilon, and training minimizes a reconstruction loss on input images. At generation time, one would need to sample coefficients from a prior, but the paper never specifies how to sample from a distribution that matches the trained coefficient statistics; simply invoking the Laplacian prior in Eq. (20) is insufficient because the encoder was trained to produce DWT-like coefficients of real images and the fixed decoder was never trained on prior samples. The FID values in Table 1 cannot be interpreted as generative quality if they were computed on reconstructions, and the paper does not describe a protocol for measuring generation quality.","section":"3.2.2, 4"},{"comment":"The learnable noise scale s is at risk of collapsing to zero. For a fixed encoder output c_NN and a reconstruction loss such as MSE, the expected loss over epsilon is minimized at s=0 because the additive noise is zero-mean and only inflates the reconstruction error; the gradient expression in Section 3.2.2 does not contain any mechanism (e.g., a KL term or variance constraint) that would counteract this collapse. Section 4.5 reports only that a learnable s outperforms a fixed s=0.01, but it does not report the learned value of s at convergence or demonstrate that the model remains stochastic. If s collapses, the model is a deterministic sparse autoencoder, contradicting the claim of stochastic generation.","section":"3.2.2, 4.5"},{"comment":"The experimental section does not support the datasets claimed in the abstract and introduction. Section 4.1 states that CelebA-HQ at 128x128 and 256x256 will be evaluated, but Table 1 and the quantitative discussion in Section 4.3 report results only for CIFAR-10 upscaled to 128x128. No CelebA-HQ quantitative or qualitative results appear anywhere in the manuscript. The abstract's claim of demonstrating improvements on 'CIFAR-10 and other high-resolution datasets' is therefore unsubstantiated.","section":"4.1, 4.3"},{"comment":"The comparison is not reproducible because the baseline VAE architecture, latent dimension, wavelet decomposition level L, and training hyperparameters are not specified, and no error bars or multiple-seed statistics are reported. With only a single run per model, the reported differences in reconstruction loss (0.045 vs 0.038) and SSIM (0.70 vs 0.79) may reflect run-to-run variability rather than a real improvement. A clearly specified baseline and confidence intervals (or a much larger experimental study) are needed to support the claimed gains.","section":"4.2, Table 1"}],"minor_comments":[{"comment":"The cross-reference 'Section??' in the contributions overview is unresolved; it should be replaced with the actual section number introducing the architecture.","section":"1.3"},{"comment":"Entries [15] and [16] both cite arXiv:2504.03821, which appears to be an erroneous duplicate identifier; the two cited works have distinct titles and should have distinct identifiers.","section":"References"},{"comment":"Notation for the encoder output is inconsistent: 'c_{i,NN}', 'cNN', and 'c_i,NN(x;phi)' are used interchangeably; please unify the notation throughout Section 3.","section":"3.2.2"},{"comment":"The 'Recon Loss' column in Table 1 is not defined; Section 4.2 mentions both MSE and BCE without stating which one is reported in the table.","section":"Table 1, Sec. 4.2"},{"comment":"The ablation states that a fixed noise scale gives 'approximately 8% higher MSE' but does not report the actual MSE values, the exact fixed scale used beyond an example of 0.01, or the converged value of the learnable s.","section":"4.5"}],"recommendation":"reject","confidential_remarks":"The editor may wish to check the reference list: entries [15] and [16] have the same arXiv identifier, and both appear to be the author's own recent work; the novelty claim relative to those papers should be clarified. The paper's fit for the journal is also questionable given the incomplete experimental section and the absence of a valid generative objective."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take: the paper is a clearly written proposal for a wavelet-coefficient VAE, but the central theoretical move in Eq. (22) removes the KL term without putting a valid bound in its place, and the paper never defines a sampling path for generation. The experiments only measure reconstruction; the promised generated samples and CelebA-HQ results are absent. So the headline claim of high-resolution image generation is unsupported.\n\nWhat's genuinely new: the specific combination of Haar DWT latents, a learnable noise scale, and L1 sparsity inside a VAE isn't in the cited wavelet-GAN or wavelet-CNN work. The paper also does a clear job explaining the DWT and the reparameterization trick in this context, and the ablation of the noise scale is a reasonable thing to check.\n\nThe soft spots are more than cosmetic. Equation (22) is not an ELBO: the KL term is gone, and the L1 penalty on encoder outputs does not couple the posterior to any prior you could sample from. The decoder is a fixed IDWT, so even with positive noise scale s the model is a noisy sparse autoencoder, not a generative model. The gradient of the reconstruction loss with respect to s points toward zero, so collapse is a real risk; Section 4.5 gives only qualitative reassurance. On the experimental side, the quantitative table has no error bars, the baseline VAE is not specified, and the CelebA-HQ experiments promised in Section 4.1 never appear. There are also mechanical issues: broken cross-reference (Section??), and refs [15] and [16] share the same arXiv identifier.\n\nThat said, the core idea isn't absurd. If the authors restored a proper variational objective (e.g., a KL term against a Laplacian prior, or a different stochastic decoder), and actually generated images from the prior rather than reconstructing inputs, the paper could become a modest but legitimate contribution. As submitted, I wouldn't send it to reviewers; I'd desk reject with an encouraging note to resubmit after a real generative formulation and proper experiments.\n\nFor reading group, it's a useful example of how easy it is to call something a VAE without the variational machinery. But I wouldn't cite it.","headline":"Interesting wavelet-VAE combination, but Eq. (22) is not a valid ELBO and no generative sampling path is defined, so the central claim of high-resolution image generation is unsupported; the experiments only show reconstruction.","tokens_in":11919,"tokens_out":2585,"would_cite":false,"duration_ms":24749,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-16T12:37:45.391059+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}