{"id":"16cb4a6e-dd1e-4661-b7fe-4bd0496aec88","arxiv_id":"2505.04969","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"General Transform learns scalar weights to combine multiple discrete transforms, improving image and text classification accuracy by 0.1 to 1.6 percentage points over fixed-transform baselines.","lead":"A machine learning method blends several classic math transforms, such as Fourier and cosine, into one learnable transform so a model can pick the best mix for its data. Tests on image and text classification show small accuracy gains over using a single fixed transform.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Missing variance estimates and best-epoch selection leave the reported 0.05–1.56 pp gains within plausible training noise; the 'consistently outperform' claim needs a seeded, fixed-epoch re-evaluation.","rationale":"I read the paper as proposing a learnable linear combination of discrete transforms, with the main contribution being the empirical claim that this 3-parameter combination improves on fixed-transform baselines. The method itself is coherent: Eq. (10) defines a valid linear interpolation family, and the use of p3 in Eqs. (12) and (18) is well-defined. The load-bearing risk is not internal inconsistency but the strength of the empirical evidence. The reported gains are small, the ImageNet results come from one run per configuration with best-epoch selection, the NLP results are averaged without variance estimates, and the evaluation protocol is not pre-registered. The reader's weakest_assumption identifies exactly this issue, and I agree with it: if the differences are within run-to-run noise, the central claim of consistent improvement collapses. This concern is concrete and correctable. I would keep the verdict CONDITIONAL rather than reject, because the construction is plausible and the missing statistics can be supplied by re-running with seeds or reporting existing per-run values. The secondary issues I considered, such as the unconstrained p_i values and the lack of code, are real but less decisive than the statistical support. The quantum section is explicitly preliminary and does not affect the main verdict.","tokens_in":14388,"tokens_out":7341,"duration_ms":82727,"concrete_test":"Obtain from the authors the per-run best-epoch validation accuracies for the 10 fine-tuning repetitions of FNet-base and GTNet-base on SST-2 and CoLA, and compute a paired 95% confidence interval for the GTNet-minus-FNet difference. If either interval includes zero, the claim of consistent improvement on NLP is not supported. For the ImageNet part, retrain DCTNet-48 and GTNet-48 with at least 5 seeds each and evaluate at a pre-registered epoch (e.g., epoch 63, the last epoch before the first learning-rate decay); if the mean validation accuracy advantage of GTNet is less than one standard deviation, the CV part of the claim is also unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that models incorporating GT consistently outperform fixed-transform baselines. The evidence consists of three ImageNet comparisons with validation top-1 improvements of 0.09, 0.27, and 0.05 percentage points, and four NLP comparisons with improvements of 0.66 to 1.56 percentage points. These margins are small, and the protocol in Sections 3.2.1 and 3.2.2 has two properties that can inflate them. First, each ImageNet model is trained once, and the epoch with the highest validation accuracy among 80 epochs is selected for comparison; with a single seed, this best-epoch value is an optimistic upper bound, and the bias is not controlled across models. Second, the NLP results are averaged over 10 runs, but no standard deviation, per-run values, or confidence intervals are reported, and again the best validation epoch among the first five epochs is chosen. Because the fixed DCT/DFT baseline is a special case of GT under specific parameter values, GT has at least as much training capacity; the interesting question is whether the small generalization advantages exceed noise. With a gap as small as 0.05 pp at 64 channels, and no error bars anywhere, the reported consistency could be explained by seed variance or best-epoch selection. The paper does not provide code or seeds, so the results cannot be independently checked. The QGT section is explicitly described by the authors as a proof of concept and not optimized, so it does not bear on the main claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes General Transform (GT), a trainable linear combination of discrete transforms such as DCT, DFT, DWT in vision and DFT, DLT, identity in NLP, with an additional parameter p3 blending the real and imaginary parts of the transformed output. The transform weights are optimized jointly with the network. The authors replace DCT-based feature extraction in a ResNet-50 ImageNet pipeline with GTNet and DFT-based token mixing in FNet-style encoders with GTNet, reporting small validation accuracy improvements in all tested configurations. A quantum extension, QGT, is presented as a proof of concept using linear combinations of unitaries. The main claim is that models incorporating GT consistently outperform conventional fixed-transform baselines while adding only a few parameters.","tokens_in":14662,"tokens_out":6320,"duration_ms":60858,"significance":"The core idea is simple and attractive: rather than hand-selecting a discrete transform, learn a weighted mixture that contains standard transforms as special cases. This makes the method easy to integrate into existing architectures, and the per-channel adaptation is a reasonable inductive bias. If the reported gains were robust, the contribution would be useful. The QGT extension is conceptually interesting but explicitly preliminary. The paper's main weakness is that the central claim of consistent improvement rests on small accuracy differences, with no variance estimates, single-run ImageNet experiments, and best-epoch selection; the reported numbers are not sufficient to establish the claim. The paper also does not provide code or seeds, so the comparisons cannot be independently checked.","major_comments":[{"comment":"The ImageNet comparisons rest on a single training run per configuration, with the epoch of highest validation top-1 accuracy selected from 80 epochs, as stated in Section 3.2.1. The reported validation gains of 0.09, 0.27, and 0.05 percentage points for 24, 48, and 64 channels are smaller than typical run-to-run variation for ResNet-50 training on ImageNet. Without multiple seeds and error bars, Table 1 cannot support the claim that GTNet consistently outperforms DCTNet. Please report mean and standard deviation over at least three seeds and evaluate both models with the same fixed checkpoint rule, such as the last epoch or a pre-specified early-stopping rule.","section":"3.2.1, Table 1"},{"comment":"The NLP fine-tuning results are averaged over 10 runs, but no standard deviations, confidence intervals, or per-run values are reported, and the best validation epoch among the first five is selected for comparison. With gains of 0.66 to 1.56 percentage points, these differences could be within run-to-run variance, especially given the observed over-fitting beyond epoch five. Please report means with standard deviations and, ideally, paired significance tests over the 10 runs, and use a fixed epoch-selection rule for both FNet and GTNet.","section":"3.2.2, Table 3"},{"comment":"The claim that optimized p_i values capture meaningful differences across input channels is a post-hoc interpretation of fitted parameters. The observed differences between the Y, Cb, and Cr channels are not validated independently; they could reflect optimization noise or idiosyncrasies of a single run. Please support this claim with an ablation, such as tying parameters across channels and showing a significant performance drop, or evaluating the fitted parameters on held-out data. As written, the contribution bullet that GT is proven to capture meaningful channel differences is not supported.","section":"4.1, Table 2"},{"comment":"The experimental comparisons are not reproducible as reported: no code, seeds, or checkpoints are provided, and the baselines appear to be reimplementations rather than official released models. Since the conclusion depends on the baselines being fairly tuned, please release code and seeds, or provide exact training configurations and compare against numbers from the original DCTNet and FNet papers where available.","section":"3.2.1-3.2.2"}],"minor_comments":[{"comment":"The statement that GT adds only three additional parameters is inconsistent with Table 2, which lists p1, p2, and p3 separately for each of the Y, Cb, and Cr channels. If the parameters are per channel, the total is three times the number of channels, not three. Please clarify the parameterization of Eq. (11).","section":"1, 3.1, Table 2"},{"comment":"In the 64-channel panels of Figure 2, the legend refers to DCTNet-48; this should presumably be DCTNet-64.","section":"Figure 2"},{"comment":"The text states that the primary analysis focuses on the first five epochs because severe over-fitting was observed beyond this point, but no quantitative criterion is given. Please report validation metrics at later epochs to justify the five-epoch cutoff.","section":"3.2.2"},{"comment":"The DCT definition in Eq. (2) omits the conventional normalization factor; this is not harmful for the method but should be stated for reproducibility.","section":"Eq. (2)"},{"comment":"The QGT experiments are explicitly a proof of concept with no tuning, which is acceptable, but the section should be clearly separated from the main empirical claim. Additionally, the S1-S4 labels in Figure 5 should match the S-1 to S-4 labels in Table 4.","section":"5.2.2"}],"recommendation":"major_revision","confidential_remarks":"The core methodology is reasonable, but the empirical evidence is currently too thin for the strength of the claims. The authors should re-run with multiple seeds, report variance, and provide code and seeds. If the differences disappear under a fixed-epoch protocol, the claim should be scaled down substantially. The QGT section is not load-bearing for the main claim and could be removed or clearly marked as preliminary."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a simple, plausible idea with uniformly positive but small gains, and an evaluation protocol that is not yet rigorous enough to support the headline claim. The actual novelty is modest—a trainable scalar-weighted sum of standard discrete transforms (DCT/DFT/DWT for vision, DFT/DLT/identity for text) plus a real/imaginary blend parameter p3. I checked the cited papers; I don't see that exact formulation anywhere, so it is a new combination, though a fairly natural one. The writing is clear and the authors are honest about the quantum section being a proof of concept.\n\nWhat they do well: all seven comparison points (three ImageNet sizes, four NLP configurations) favor GT over the fixed-transform baseline. That uniform direction is worth something. The model adds very few parameters, and the validation curves are shown, not just tables. The QGT section is explicitly unoptimized and does not overclaim.\n\nThe soft spots are the usual ones, and they matter here because the effects are small. ImageNet numbers come from a single run, with the best validation epoch among 80 selected for comparison; that selection is an optimistic upper bound and can systematically favor the more flexible model. NLP is averaged over 10 runs, but no standard deviation, per-run values, or confidence intervals are given, and again the best epoch among five is chosen. The largest ImageNet gain is 0.27 pp and the smallest 0.05 pp; gaps that size can easily be training noise. No code or seeds are provided, so the experiments are not independently checkable. I also want the parameter count clarified: the text says three additional parameters, but Table 2 shows per-channel p1,p2,p3 for Y/Cb/Cr, which is nine for RGB images. That is still cheap, but the text is off. The post-hoc reading of optimized p_i values as capturing 'meaningful differences' between channels is speculative—with no regularization or repeated runs, those values are not evidence about the data.\n\nWho should read this: people working on transform-based feature extraction or token mixing, and anyone who wants an example of why best-epoch selection without error bars cannot carry a claim. I would not desk-reject it: the idea is clean and the experiments are honest. But I would send it for review with a request for a fixed-epoch, multi-seed protocol and release of code. As it stands, the empirical support is directionally suggestive, not statistically established.","headline":"A simple, plausible trainable blend of fixed transforms with uniformly positive but small gains; the evaluation lacks error bars and uses best-epoch selection, so the 'consistently outperform' claim is not yet established.","tokens_in":15202,"tokens_out":3246,"would_cite":false,"duration_ms":34344,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A trainable combination of discrete transforms, adding only three parameters, consistently outperforms single fixed transforms in both image and text classification.","keywords":["General Transform","adaptive transforms","discrete Fourier transform","discrete cosine transform","wavelet transform","token mixing","image classification","text classification"],"falsifier":"Train each model variant (DCTNet versus GTNet and FNet versus GTNet) with at least five random seeds and compare the distributions of validation accuracy; if the intervals overlap on every configuration, the claim of consistent improvement is unsupported. A companion check is to freeze or randomly initialize the $p_i$ weights and see whether the gains persist, which would show whether the learned adaptation is the active ingredient.","tokens_in":14184,"feed_emoji":"🔀","tokens_out":9708,"duration_ms":84269,"temperature":0.7,"pith_summary":"The paper proposes General Transform (GT), a parameterized linear combination of discrete transforms whose blending weights are learned from data, and it argues that models using GT outperform their fixed-transform counterparts in both computer vision and natural language processing. In vision, replacing the DCT feature extraction of a ResNet-50 pipeline with GT raises ImageNet validation top-1 accuracy by 0.09 to 0.27 percentage points across three frequency-channel configurations. In NLP, replacing the DFT token mixing of an FNet-style model with GT raises validation accuracy by 0.66 to 1.56 percentage points on SST-2 and CoLA, for both base and large model sizes. These gains come from only three additional scalar parameters. The paper also sketches a quantum extension in which the same blending idea is implemented through a linear combination of unitaries with postselection.","feed_headline":"Three learned numbers beat fixed transforms in vision and NLP","feed_subtitle":"General Transform learns a data-driven mix of cosine, Fourier, and wavelet kernels with just three added parameters.","key_machinery":"The central object is the General Transform operator, a parameterized blend of $m+1$ discrete transform kernels in which the coefficients $p_i$ are trainable scalars and the form $\\left(1-\\sum_i p_i\\right)$ forces the coefficients to sum to one. At specific parameter values the operator recovers each standard transform, so it can replace a fixed kernel in an existing architecture without any other change. The paper does exactly this: it drops GT into the DCT feature-extraction stage of the vision baseline and into the DFT token-mixing stage of the NLP baseline, making the learned kernel the only variable in the comparison. The quantum variant, QGT, replaces the kernels with unitaries and blends them through a linear combination of unitaries followed by postselection.","core_discovery":"The central claim is that the right transform for a task need not be chosen in advance: a weighted sum of discrete transform kernels, with the weights learned by gradient descent, can adapt to the data and match or beat any single fixed transform. GT is defined as $$X[k]=\\sum_{n=0}^{N-1}\\left(\\sum_{i=1}^{m}p_i f_i[n,k]+\\left(1-\\sum_{i=1}^{m}p_i\\right)f_{m+1}[n,k]\\right)x[n],$$ with an optional trainable mix $p_3$ of the real and imaginary parts of $X[k]$. The paper reports that the optimized weights settle on nontrivial mixtures rather than a single basis transform, that the mixtures differ between luminance and chrominance channels in images and between model sizes, and that initializing GT at pure DFT in the NLP setting still yields improvements over DFT. Those observations are offered as evidence that the learned mapping captures per-channel and per-task differences that a fixed transform cannot.","pith_inferences":["Because the ImageNet results come from a single training run per configuration, a multi-seed replication is the natural next test, and the paper does not report error bars for those numbers.","The same blending trick could apply to time series, speech, or graph data, where the appropriate transform is often unknown; nothing in the formulation restricts it to images or text.","The finding that luminance and chrominance channels learn different mixtures suggests GT could be used as a diagnostic probe for what frequency content different input channels carry.","If the classical gains really come from adapting the kernel to the data, QGT should show a similar advantage over any single fixed unitary once the LCU success probability and noise are controlled, a test the paper does not run."],"forward_implications":["Fixed-transform pipelines can be upgraded to GT without redesigning the network, because GT recovers the original transform at specific parameter values and adds only a handful of scalars.","Dataset-specific transform selection, normally a matter of domain expertise, can be handed to gradient descent, with the learned $p_i$ values indicating which frequency basis the data favors.","The reported gains place transform choice as a real but modest axis of model quality: 0.09 to 0.27 accuracy points on ImageNet and 0.66 to 1.56 points on SST-2 and CoLA.","The quantum variant offers a way to make a quantum feature map adaptive, although the paper presents the QGT experiments as a proof of concept rather than a performance claim."],"supporting_citations":[{"why":"This reference supplies the DCTNet vision baseline whose preprocessing pipeline and ResNet-50 setup GT is dropped into and compared against.","marker":"(Xu et al., 2020)"},{"why":"This reference supplies the FNet NLP baseline whose DFT token mixing GT replaces.","marker":"(Lee-Thorp et al., 2022)"},{"why":"This reference provides the ResNet-50 backbone used in all ImageNet experiments.","marker":"(He et al., 2016)"},{"why":"This reference provides the ImageNet ILSVRC-2012 dataset used for the vision evaluation.","marker":"(Deng et al., 2009)"},{"why":"This reference provides the SST-2 sentiment dataset used for one NLP fine-tuning evaluation.","marker":"(Socher et al., 2013)"},{"why":"This reference provides the CoLA acceptability dataset used for the other NLP fine-tuning evaluation.","marker":"(Warstadt et al., 2019)"}],"fun_headline_variants":["Learn the transform mix, not the transform","Adaptive kernel blend beats fixed transforms in vision and NLP","Data-driven transform weights outperform fixed baselines","General Transform: pick kernels via gradient descent"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central claim rests on the assumption that the reported accuracy differences, as small as 0.09 percentage points on ImageNet and averaged over 10 runs without standard deviations in NLP, are larger than run-to-run training noise.","fun_headline_variants_meta":{"raw":{"variants":["Learn the transform mix, not the transform","Adaptive kernel blend beats fixed transforms in vision and NLP","Data-driven transform weights outperform fixed baselines","General Transform: pick kernels via gradient descent"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000242,"raw_usage":{"total_tokens":1475,"prompt_tokens":848,"completion_tokens":627,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":464,"completion_tokens_details":{"reasoning_tokens":569}},"tokens_in":464,"tokens_out":627,"duration_ms":6170,"temperature":1.0,"reasoning_tokens":569,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:15:39.827496+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train each model variant (DCTNet versus GTNet and FNet versus GTNet) with at least five random seeds and compare the distributions of validation accuracy; if the intervals overlap on every configuration, the claim of consistent improvement is unsupported. A companion check is to freeze or randomly initialize the $p_i$ weights and see whether the gains persist, which would show whether the learned adaptation is the active ingredient.","supporting_citations":[{"cited_title":", author Perelygin, A","cited_arxiv_id":null,"evidence_quote":"This reference provides the SST-2 sentiment dataset used for one NLP fine-tuning evaluation."},{"cited_title":", author Singh, A","cited_arxiv_id":null,"evidence_quote":"This reference provides the CoLA acceptability dataset used for the other NLP fine-tuning evaluation."}],"review_version":1}