{"id":"d5bca75a-1765-4b42-a23c-94e30c6ad99a","arxiv_id":"2412.05517","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"An RNN-based super-resolution model sequentially predicts Fourier components, letting users trade quality against computation at test time by choosing the number of components.","lead":"This paper presents a super-resolution model that can change its quality and computational load at test time, without retraining, simply by choosing how many Fourier pieces the network produces. If it works as reported, it offers a practical way to adapt a single model to devices and situations with different computing power.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'cost' side of the cost-quality trade-off is never measured: no FLOPs, latency, or memory data appear in Section IV, so the central claim that reducing T lowers computational cost is asserted, not demonstrated.","rationale":"The reader's weakest assumption identifies exactly the load-bearing gap: T is used as a compute proxy without any measurement of compute. I agree with that diagnosis. The quality behavior is well supported by the monotonic PSNR trends in Tables 1-5, Fig. 8, and Table 6, so the 'quality' half of the trade-off is credible. But the paper's headline contribution is 'cost-and-quality' control; if T does not translate into meaningful compute savings, the contribution reduces to a quality knob rather than a cost-control mechanism. This concern is concrete and testable, and the missing measurement is not merely a stylistic issue because the abstract explicitly promises 'lower cost' with fewer recurrences. I do not see a fatal mathematical flaw in Eqs. 8-14; the RNN architecture is a reasonable way to make the component count variable, and the training strategy in Eq. 12 is coherent. The conditional verdict should stand: if the authors provide FLOPs/latency/memory measurements and release the model, the cost claim can be upgraded; if the measurements contradict linear scaling, the title and abstract need revision. The baseline-fairness issue noted by the reader is also worth attention, but the cost measurement is the more direct test of the paper's central promise.","tokens_in":15019,"tokens_out":6976,"duration_ms":74241,"concrete_test":"Obtain or reimplement the proposed model and benchmark it on DIV2K val with scale 4, using a fixed input size such as 1280x720 LR, on a single GPU. Measure FLOPs, wall-clock latency for batch size 1, and peak memory for T=4, 8, 16, 32, and 64, and separately time the EDSR feature extractor and feature unfolding. Plot total cost versus PSNR alongside the T axis. If the T=64 to T=4 latency improvement is much smaller than the reduction in RNN steps, or if the fixed extractor time is the dominant term, the abstract's cost claim should be qualified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that a single trained RNN can control both computational cost and SR quality by varying the number of recurrences T (Abstract, Eq. 11). The quality half is supported: Tables 1-5 and Fig. 8 show PSNR increasing with T. The cost half, however, is not supported by any measurement. Section IV reports only PSNR; there are no FLOPs, latency, memory, or energy numbers, and no code or weights are released to obtain them. The architecture makes T a plausible proxy: each recurrence adds a fixed per-pixel RNN pass through the Linear Transformer and FC estimators. But the total inference cost also includes the one-time EDSR feature extractor, feature unfolding, and bilinear upsampling, whose share of wall-clock time is never quantified. If that fixed part dominates, shrinking T from 64 to 4 would produce little real-world speedup while sacrificing several dB of PSNR, and the 'cost-control' half of the contribution would be misleading. Because the paper's title and abstract promise test-time cost control, the absence of any measured trade-off curve is a load-bearing gap, not a cosmetic omission.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a test-time cost-and-quality (CQ) controllable arbitrary-scale super-resolution method. It uses an RNN to sequentially estimate Fourier components (amplitude and frequency), and reconstructs the SR image by summing the contributions of the selected number of components T (Eq. 11). The RNN is trained with a variable number of recurrences (Eq. 12) to generalize across different T at test time. Experiments on DIV2K, BSD100, and Urban100 show that PSNR degrades gracefully as T is reduced, whereas truncated fixed-length baselines (LTE, CiaoSR, CLIT) drop sharply. The paper claims to be the first to enable test-time CQ control in arbitrary-scale SR without retraining.","tokens_in":15278,"tokens_out":5121,"duration_ms":52060,"significance":"The idea of using an RNN for variable-length Fourier-component prediction is novel and directly addresses a real deployment need: adapting SR quality and compute to varying resource constraints. The training strategy with uniformly sampled T is simple and appears effective; Figure 8 provides a clear ablation showing the benefit of random-length training. If the cost-saving claim is substantiated, this would be a practical contribution to edge and streaming SR applications. However, the paper currently lacks any measurement of computational cost, and its comparison to modified baselines is not a fair test of CQ controllability. The quality-side results are solid and reproducible in principle, but the central cost-control claim remains unverified.","major_comments":[{"comment":"The central claim of test-time cost-and-quality control is only validated on the quality axis. The abstract, introduction, and Figure 1 explicitly state that fewer recurrences lead to lower computational cost, but Section IV reports no FLOPs, latency, memory, or energy measurements. The total inference cost includes the EDSR feature extractor, feature unfolding, and bilinear upsampling, which are independent of T; if these dominate, the actual savings from reducing T may be small. Please provide a measured cost-quality trade-off curve (e.g., FLOPs or wall-clock time per image vs PSNR) for T in {1..64}, and explicitly report the fixed-cost share. Without this, the cost-control half of the contribution is unsupported.","section":"Section IV (Results)"},{"comment":"The baseline comparison is not a fair evaluation of CQ controllability. LTE, CiaoSR, and CLIT are trained with a fixed number of Fourier components (K=64) and only at test time have their last FC layer removed and a subset of components selected. Because they are never trained with a variable-length objective like Eq. (12), the large PSNR drops at T<64 are an expected consequence of train-test mismatch. To support the claim of \"lower PSNR drop than other state-of-the-art methods,\" the baselines should either be retrained with the same variable-length training strategy (preserving their architectures) or the comparison should be explicitly framed as \"naive truncation of fixed-length models\" rather than as a CQ-controllable baseline comparison.","section":"Section IV-B (Comparison with SoTA methods)"},{"comment":"The \"Random\" selection procedure for the modified baselines is not a cost-control method. It averages the output over 100 random subsets, which multiplies the inference cost by 100, so it does not correspond to any meaningful operating point on a cost-quality curve. The paper should report only the deterministic \"Descending\" selection for the baseline comparisons, or provide cost measurements for all variants so that the cost-quality trade-off can be compared fairly.","section":"Section IV-B (Random selection)"}],"minor_comments":[{"comment":"Equation (14) has mismatched parentheses in the cosine and sine arguments; the arguments should read cos(πFtδ + hp(c, At, Ft)) and sin(πFtδ + hp(c, At, Ft)).","section":"Equation (14)"},{"comment":"The text describes F_t as a \"frequency matrix\" but Eq. (11) treats it as a vector in R^2; please clarify the dimension and use a dot product notation such as πF_t · δ.","section":"Section III-B"},{"comment":"The dataset name \"Urban109\" appears to be a typo for \"Urban100\", matching the reference [51].","section":"Section IV-B"},{"comment":"The sentence \"we plan to explore autoregressive models [] instead of RNNs\" contains an empty citation; please fill it in or remove the bracket.","section":"Section V (Conclusion)"},{"comment":"In Figure 8, the x-axis extends to 128 Fourier components, but Tmax is 64; clarify whether a model trained with Tmax=64 is being evaluated beyond its training range (which would degrade) or whether an additional model is used.","section":"Figure 8"},{"comment":"The abbreviation \"SPE\" is used without definition; please spell out \"Sinusoidal Positional Encoding\" or whatever the intended expansion is when it first appears.","section":"Section IV-C (Position Encoding)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript addresses a relevant and timely topic. The main risk is that the cost-control claim, which is central to the title and abstract, is never measured; this must be addressed before acceptance. The baseline comparison also needs to be reframed or the baselines retrained with variable-length objectives. The quality-side results are encouraging, but the current evidence is insufficient to support the full CQ-controllability claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What's actually new here is the mechanism: an RNN that sequentially emits a variable number of Fourier components, summed to reconstruct the SR image, with random-length training so the model behaves sensibly at any test-time truncation. That is not in LTE (fixed K=64) or BACON (fixed sequential order), and the random-length training strategy is a sensible addition. The quality half of the paper is honestly supported. Tables 1-5 show graceful PSNR degradation as T drops from 64 to 4, versus baselines that collapse, and Figure 8 demonstrates that variable-length training is essential. The paper also fairly admits that LTE beats it at full T=64, which makes the comparison more credible.\n\nThe load-bearing gap is exactly what the stress-test note identifies: the cost half is never measured. There are no FLOPs, latency, or memory numbers anywhere in Section IV. The architecture makes T a plausible proxy for compute, but the fixed EDSR feature extractor and bilinear upsampling may dominate wall-clock time, and the paper gives no evidence. Since the title and abstract promise test-time cost control, this is not cosmetic.\n\nThe baseline comparison is also weaker than it looks. LTE, CiaoSR, and CLIT are modified after training and then their Fourier components are selected randomly or by amplitude norm. Those models were trained with a fixed-length decoder, so they are not designed to use a partial subset; selecting components post-hoc is a real handicap. To make a strong claim of superiority at low T, the baselines should be retrained with variable-length targets (or the comparison reframed as 'our training strategy works better than ad hoc truncation'). This does not sink the paper, but it does make the 'state-of-the-art comparison' less definitive.\n\nMinor issues: no error bars or statistical tests on the PSNR differences; no code or weights released; 'Urban109' in Table 5 should be Urban100. The paper is otherwise clearly written and the Fourier-sum construction is explicit.\n\nBottom line: this is a useful contribution for people working on efficient SR or adaptive inference, and it deserves a serious referee. The mechanism is novel, the quality evidence is real, and the paper is honest about its limitations. But the cost-control claim must be backed by measurements, and the baselines should be given a fairer chance, before the headline claim is accepted as stated.","headline":"A clever RNN-based Fourier component mechanism gives real test-time quality scaling, but the cost-control half of the claim needs actual FLOPs/latency numbers and less handicapped baselines before it holds up.","tokens_in":15771,"tokens_out":2043,"would_cite":true,"duration_ms":19828,"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":"The paper proposes a single arbitrary-scale super-resolution network in which a recurrent neural network sequentially outputs Fourier components, so that choosing how many recurrences to run at test time trades computational cost against…","keywords":["arbitrary-scale super-resolution","cost-quality control","recurrent neural network","Fourier components","test-time control","variable-length training","single-image super-resolution","PSNR"],"falsifier":"Run the released model at $T=4,8,16,32,64$ on the same hardware and measure end-to-end latency and FLOPs; if total compute is nearly flat across $T$, or PSNR stops increasing with $T$ on held-out datasets, the claimed cost-and-quality controllability fails.","tokens_in":14780,"feed_emoji":"🖼️","tokens_out":5930,"duration_ms":60379,"temperature":0.7,"pith_summary":"This paper tries to establish that arbitrary-scale super-resolution can be made cost-and-quality controllable in a single trained model by casting reconstruction as a sum of Fourier components that a recurrent network emits one at a time. The key claim is that the number of RNN recurrences $T$ can be chosen at inference: fewer components cost less and degrade gracefully, more components improve PSNR, and the same weights serve every budget. This matters because previous arbitrary-scale SR methods either fix the number of Fourier components in a fully connected layer or require retraining a new model for each complexity level, which prevents end users from trading quality for compute after deployment. Experiments on DIV2K, BSD100, and Urban100 report that PSNR rises monotonically with $T$ and that at reduced $T$ the method outperforms state-of-the-art baselines modified for variable component counts.","feed_headline":"One super-resolution model dials quality to any compute budget","feed_subtitle":"An RNN emits Fourier components one by one; stopping earlier saves compute while PSNR degrades gracefully.","key_machinery":"The central object is the recurrent Fourier predictor, an implicit function that starts from a latent code $z$ and local offset $\\delta$, runs an RNN cell for $T$ steps, and at each step estimates an amplitude vector $A_t\\in\\mathbb{R}^2$, a frequency matrix $F_t\\in\\mathbb{R}^2$, and phase information $h_p(c,A_t,F_t)$. The additive identity that the pixel value is the sum of the individual Fourier contributions is the mechanism that allows variable-length output with fixed weights, since no fully connected decoder with fixed input width is involved. The second machine is random-length training, which samples $T\\sim U(1,T_{\\max})$ each iteration and forces the early recurrences to carry the most dominant Fourier information, making truncation graceful rather than catastrophic.","core_discovery":"On the paper's own terms, the discovery is that the additive nature of Fourier components lets a recurrent predictor turn super-resolution into a controllable, progressive reconstruction. Instead of decoding a fixed set of Fourier components through a final layer, an RNN estimates one amplitude--frequency pair (with phase) per recurrence, and the SR pixel value is simply the sum over recurrences, written as $I^{HR}(x_q)=\\sum_{t=1}^{T} A_t \\cdot [\\cos(\\pi F_t \\delta + h_p(c,A_t,F_t)),\\ \\sin(\\pi F_t \\delta + h_p(c,A_t,F_t))]$. Because the number of recurrences $T$ is chosen at test time, one network spans a quality--cost curve. The paper also establishes that this only works if training draws $T$ uniformly from $1$ to $T_{\\max}$; training only at $T_{\\max}$ makes test-time truncation unstable. In the reported comparison, at $T=64$ the LTE baseline has a slightly higher PSNR, but across $T=4,\\dots,32$ the proposed method keeps substantially higher PSNR than the modified baselines, with PSNR growing monotonically as $T$ increases.","pith_inferences":["The paper's cost claim rests on the unmeasured assumption that total inference cost scales with $T$; a direct FLOP and latency measurement across $T$ values would turn the stated quality--cost trade-off into a quantitative curve, which the paper leaves open.","The recurrence order likely encodes a learned coarse-to-fine decomposition, so probing which spatial frequencies are added at each step could test whether early recurrences carry low-frequency content and motivate progressive SR for streaming.","Because the reconstruction is a pure sum, one could decode a shared prefix of components at multiple scales or continue the recurrence to refine an existing SR image, both of which the paper does not explore.","Random-length training may transfer to other additive output representations such as wavelets or Laplacian pyramids, an implication the paper only hints at through its Fourier choice."],"forward_implications":["A single trained SR model can cover multiple deployment budgets: an end user picks $T$ at inference and gets a monotonically ordered PSNR without downloading or switching to another network.","The training procedure suggests a general recipe for recurrent generative models whose outputs are additive: random-length training makes truncation tolerable, so the model can be used at any prefix length.","Because test quality peaks near the training maximum $T_{\\max}$, the deployment target can be chosen by training with the largest budget that will actually be used, and then any $T\\le T_{\\max}$ remains available.","The comparison implies that fixed fully connected Fourier decoders are not safely truncatable, so a recurrent additive decoder is a design choice rather than an optional refinement.","Relative position encoding materially improves low-$T$ performance, indicating that relations learned among early recurrences transfer to later recurrences and help sparse reconstructions."],"supporting_citations":[{"why":"Supplies the LIIF implicit-function formulation over latent codes that the proposed method builds on.","marker":"[14]"},{"why":"Provides the LTE Fourier-component SR formulation that the RNN generalizes from a fixed number $K$ to a variable number $T$.","marker":"[15]"},{"why":"Serves as a state-of-the-art baseline modified for cost-and-quality control in the comparison.","marker":"[17]"},{"why":"Serves as a second state-of-the-art baseline modified for cost-and-quality control in the comparison.","marker":"[18]"},{"why":"Motivates periodic Fourier representations by showing how sinusoidal activations address spectral bias.","marker":"[21]"},{"why":"Motivates sequentially estimating Fourier components from low to high frequency, a principle the RNN recurrence exploits.","marker":"[23]"},{"why":"Provides the pretrained EDSR backbone used as the feature extractor for latent codes.","marker":"[1]"},{"why":"Supplies the Linear Transformer implementation used as the RNN cell.","marker":"[47]"},{"why":"Supplies the relative position encoding shown to improve performance with fewer Fourier components.","marker":"[48]"}],"fun_headline_variants":["Super-resolution quality dialed by Fourier component count","Progressive Fourier SR: stop anytime, degrade gracefully","RNN emits Fourier pairs to trade compute for SR fidelity","One super-resolution net, any quality-cost trade-off"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the number of RNN recurrences $T$ is a faithful proxy for computational cost: the paper reports no FLOPs, latency, or memory measurements, so if the fixed feature extractor or per-step overhead dominates inference, cutting $T$ may not save the user meaningful cost.","fun_headline_variants_meta":{"raw":{"variants":["Super-resolution quality dialed by Fourier component count","Progressive Fourier SR: stop anytime, degrade gracefully","RNN emits Fourier pairs to trade compute for SR fidelity","One super-resolution net, any quality-cost trade-off"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000266,"raw_usage":{"total_tokens":1638,"prompt_tokens":998,"completion_tokens":640,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":614,"completion_tokens_details":{"reasoning_tokens":577}},"tokens_in":614,"tokens_out":640,"duration_ms":7769,"temperature":1.0,"reasoning_tokens":577,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T20:39:07.778207+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the released model at $T=4,8,16,32,64$ on the same hardware and measure end-to-end latency and FLOPs; if total compute is nearly flat across $T$, or PSNR stops increasing with $T$ on held-out datasets, the claimed cost-and-quality controllability fails.","supporting_citations":[{"cited_title":"Learning continuous image repre- sentation with local implicit image function,","cited_arxiv_id":null,"evidence_quote":"Supplies the LIIF implicit-function formulation over latent codes that the proposed method builds on."},{"cited_title":"Local texture estimator for implicit repre- sentation function,","cited_arxiv_id":null,"evidence_quote":"Provides the LTE Fourier-component SR formulation that the RNN generalizes from a fixed number $K$ to a variable number $T$."},{"cited_title":"Ciaosr: Continuous implicit attention- in-attention network for arbitrary-scale image super-resolution,","cited_arxiv_id":null,"evidence_quote":"Serves as a state-of-the-art baseline modified for cost-and-quality control in the comparison."},{"cited_title":"Cascaded local implicit transformer for arbitrary-scale super-resolution,","cited_arxiv_id":null,"evidence_quote":"Serves as a second state-of-the-art baseline modified for cost-and-quality control in the comparison."},{"cited_title":"Implicit neural representations with periodic activation functions,","cited_arxiv_id":null,"evidence_quote":"Motivates periodic Fourier representations by showing how sinusoidal activations address spectral bias."},{"cited_title":"Bacon: Band- limited coordinate networks for multiscale scene representation,","cited_arxiv_id":null,"evidence_quote":"Motivates sequentially estimating Fourier components from low to high frequency, a principle the RNN recurrence exploits."},{"cited_title":"Enhanced deep resid- ual networks for single image super-resolution,","cited_arxiv_id":null,"evidence_quote":"Provides the pretrained EDSR backbone used as the feature extractor for latent codes."},{"cited_title":"Transformers are rnns: Fast autoregressive transformers with linear attention,","cited_arxiv_id":null,"evidence_quote":"Supplies the Linear Transformer implementation used as the RNN cell."},{"cited_title":"Linearized relative positional encoding,","cited_arxiv_id":null,"evidence_quote":"Supplies the relative position encoding shown to improve performance with fewer Fourier components."}],"review_version":1}