{"id":"205f736c-b464-44d4-8277-dc6207aacdf3","arxiv_id":"2607.08379","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"low","formal_verification":"none","parameter_count":4,"one_line_summary":"Tuned HOG nearly matches the best frozen deep features for mirror-symmetry scoring (~0.03 skill gap) at ~300× lower CPU cost; discrimination lives in mid-scale oriented features.","lead":"A benchmark of 13 methods for scoring how mirror-symmetric an image is about a given axis finds that a tuned classical HOG descriptor nearly matches the best frozen deep-network features while running ~300× faster on CPU. The result matters for anyone who needs a practical symmetry score in aesthetics, medical imaging, or design.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The paper's strongest claim is an empirical ranking under a carefully controlled discrimination protocol, not a claim that relative ranking is the only quantity applications ever need. The Discussion already flags the absolute-degree gap, the frozen-only scope, and the open question of task-trained scorers. The protocol controls (fixed-extent crops, multi-axis preservation of ranking, global-vs-local stratification, direction-inference bias quantified) and the mid-scale principle (independent stage and cell-size ablations) give the ranking independent support. The reader's weakest_assumption is therefore a real boundary but not a load-bearing threat to the claim as written. No stronger technical concern (e.g., crop-geometry leakage, unacknowledged tuning leakage, or bootstrap-unit inflation that would reverse the top-three ordering) survives the paper's own checks. Verdict remains ACCEPT; no adjustment needed.","tokens_in":21520,"tokens_out":473,"duration_ms":4862,"concrete_test":"Re-run the single-axis leaderboard (Table 4) after replacing the coarser-half negatives with the full perturbation ladder (including 0.5–2% / 0.5–2°) and recompute the DeepFeat–HOG paired difference; if the Holm-adjusted significance of the +0.031 gap disappears or the ordering reverses, the magnitude-selection choice would have been load-bearing.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (frozen deep features offer little over tuned HOG for measuring mirror symmetry under the stated protocol) is well-supported by the reflection-exact harness, paired bootstrap with Holm correction, fixed-extent and multi-axis controls, stage/cell ablations, and the open imgsym release. The reader's weakest_assumption correctly notes that the metric is relative within-image discrimination rather than calibrated cross-image degree of symmetry, but the paper states this boundary explicitly in the Discussion and scopes the claim to ranking skill among existing (frozen) methods. That scoping is not a soft spot that undermines the ranking or the cost–skill map; it is an honest limit. No internal inconsistency, unstated assumption, or protocol artifact appears load-bearing enough to move the verdict.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper presents the first head-to-head benchmark of thirteen mirror-symmetry scoring methods (nine from the literature, four introduced or adapted here), spanning intensity, binary-shape, gradient, spectral, oriented-filter, patch-correspondence, and frozen deep-feature families. All methods are cast as instances of a common representation–comparison–aggregation template and evaluated under a reflection-exact crop protocol with chance-anchored discrimination skill (2·AUC−1), paired bootstrap significance testing, fixed-extent and multi-axis controls, and local-versus-global negative stratification across four single-axis and five multi-axis datasets (~3950 axis units). The central empirical claim is that a tuned classical HOG descriptor trails the best frozen deep readout (DeepFeat) by only +0.031 skill (Holm-adjusted p=0.044), is not statistically separable from AlexNet-C2, and runs ~300× faster on CPU; ablations locate discrimination in mid-scale unsigned oriented features. The scorers and harness are released as the open toolkit imgsym.","tokens_in":21688,"tokens_out":1287,"duration_ms":29099,"significance":"If the ranking and cost–skill map hold, the result is immediately actionable for any application that consumes a scalar symmetry score about a given axis (aesthetics, medical asymmetry indices, developmental biology). The mid-scale oriented-feature principle is of independent scientific interest and is supported by two independent routes (network stage and HOG cell size) plus a columnar-ViT control. Strengths that raise the contribution above a routine bake-off include: the reflection-exact extraction with fixed-extent control, chance-anchored within-image skill with paired bootstrap and Holm correction, explicit multi-axis generalization including DENDI, transparent quantification of protocol artifacts (direction inference, crop geometry, axis-count cap), and the full open release of scorers, harness, and analysis scripts. The paper also states its scope boundary clearly: relative within-image ranking, not calibrated cross-image degree of symmetry, and frozen rather than task-trained deep scorers.","major_comments":[{"comment":"§5.1–5.2 and Table 4: On the multi-axis protocol, absolute skill levels fall substantially (DeepFeat 0.83→0.70; HOG 0.80→0.65), and on DENDI the best methods reach only ~0.5. The relative ranking and the HOG–DeepFeat gap are preserved, but the practical claim that HOG is a near-substitute for frozen deep features should be caveated more explicitly for hard multi-axis / in-the-wild settings where absolute discrimination remains modest for every method. A short quantitative statement of residual error rates (or of how often the true axis is not ranked first) would make the cost–skill recommendation more usable.","section":null},{"comment":"§4 and §5.3: Exactly two methods (HOG cell/bins/sign and DeepFeat backbone/stage) were selected on single-axis ablation subsets of the same public data used for the leaderboard. The paper shows held-out generalization and treats both methods symmetrically, which is good practice, but the abstract and conclusion phrasing “a classical HOG descriptor” / “among existing methods” slightly understates that the competitive classical entry is a re-engineered, benchmark-tuned formulation rather than an off-the-shelf literature default. A one-sentence clarification in the abstract and §7 that the HOG result is for the tuned configuration introduced here would keep the claim precise without weakening it.","section":null}],"minor_comments":[{"comment":"§3.5: The direction-inference step (inferring score polarity from evaluation data) is quantified (~0.8 SE inflation for near-chance methods) and is irrelevant for the leaders, but it would be cleaner to fix polarity a priori from each method’s definition and report any residual flips as a diagnostic.","section":null},{"comment":"Figure 2 / Table 4: Whiskers show per-dataset range rather than bootstrap CIs; adding the paired-bootstrap intervals (or a small table of them) next to the means would make the non-separation claims easier to read without consulting the text.","section":null},{"comment":"§5.3 / Appendix A: The hard-subset backbone ordering is correctly flagged as unstable (n=40, overlapping intervals). Consider moving the full per-backbone table to the main text or a short supplementary figure so readers do not over-read the point estimates.","section":null},{"comment":"§5.4.1: CPU-only timings are appropriate for the classical methods; a single GPU number for DeepFeat / AlexNet-C2 (even as a footnote) would complete the cost map for readers who will run the deep scorers on accelerators.","section":null},{"comment":"§2.2 / Table 1: The exclusion of SSIM-style quality indices, per-pixel symmetry maps, and pure shape scores is justified in the text; a one-line note in the table caption would make the pool boundary self-contained.","section":null},{"comment":"Typos / polish: “reflection” vs “reflection” is consistent in the PDF but mixed in some arXiv metadata; “Somers’ D (Gini)” is fine but a parenthetical pointer to the rank-correlation literature would help non-stats readers. The Acknowledgments AI-use statement is clear and appropriate.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is unusually careful for a benchmark paper: protocol controls, significance testing, and open release are all above the field average. I see no novelty or citation-pattern concerns. Fit for a methods/benchmark venue in computer vision or computational aesthetics is strong; if the journal prioritizes purely theoretical novelty over rigorous empirical consolidation, that is an editorial scope call rather than a scientific defect. The two major comments are clarifications, not threats to the central claim."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is the first proper common-protocol ranking of mirror-symmetry scorers, and the takeaway is practical: a tuned HOG trails the best frozen deep readout by only ~0.03 skill, is not separable from AlexNet-C2, and is ~300x faster on CPU. Discrimination lives in mid-scale unsigned oriented features—two independent ablations (network stage and HOG cell size) land on the same place.\n\nWhat is new is the harness, not the individual scorers. Reflection-exact crops, chance-anchored skill (2·AUC−1), paired bootstrap with Holm correction, fixed-extent and multi-axis controls, local-vs-global stratification, and the imgsym release make the ranking usable. The paper scopes itself honestly: frozen features only, relative within-image ranking not calibrated absolute degree, task-trained scorers left open. Tables and figures match the claims; citations cover the scattered literature without padding.\n\nSoft spots are ordinary and stated. HOG cell/bins and DeepFeat stage were selected on single-axis subsets (they check hold-out behavior). Multi-axis bootstrap is axis-level (cluster bootstrap only mildly widens intervals). Main results use coarser perturbations (≥3%/3°). None of that moves the ranking or the cost–skill map. The evaluation target is relative discrimination; applications that need a cross-image absolute score will still need calibration, which the Discussion flags.\n\nThis is for people who score symmetry axes (aesthetics, medical asymmetry, detection pipelines) and want a default method plus an open toolkit. Math and stats are standard and carefully applied; data are public competition and perception sets. I would send it to peer review without hesitation and would cite the ranking and the mid-scale finding. Engage with it.","headline":"Solid first head-to-head of symmetry scorers: frozen deep features barely beat tuned HOG, with a clean mid-scale story and open code.","tokens_in":22321,"tokens_out":459,"would_cite":true,"duration_ms":5245,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"A tuned classical HOG nearly matches frozen deep networks at measuring mirror symmetry, at roughly 300× lower CPU cost.","keywords":["symmetry scoring","mirror symmetry","reflection symmetry","symmetry axis discrimination","histogram of oriented gradients","deep features","benchmark"],"falsifier":"Train a deep scorer end-to-end for axis discrimination on the same protocol and show a large, significant skill gain over HOG that survives multi-axis and domain-transfer checks; or re-run the benchmark on native medical volumes and show domain asymmetry indices overtake HOG and frozen deep readouts.","tokens_in":22386,"feed_emoji":"🪞","tokens_out":1004,"duration_ms":11994,"temperature":0.7,"pith_summary":"This paper asks a practical question that the field has never answered head-to-head: among existing methods, which ones actually measure how mirror-symmetric an image is about a given axis, and at what cost? The authors put thirteen scorers—from raw pixel correlation through oriented filters to frozen deep-network readouts—on the same reflection-exact discrimination task across nine public datasets, scoring each method by how well it ranks a true axis above controlled wrong ones. Deep mid-stage features lead, but a carefully tuned histogram-of-oriented-gradients descriptor trails by only a small skill margin, is statistically inseparable from a classical CNN-filter measure, and runs hundreds of times faster on CPU. Two independent ablations (network stage and HOG cell size) converge on the same mechanism: discrimination lives in mid-scale, unsigned, oriented structure. The result is an actionable cost–skill map and an open toolkit, while leaving open whether scorers trained specifically for the task could widen the gap.","feed_headline":"Classical HOG nearly matches deep nets for mirror symmetry","feed_subtitle":"A mid-scale oriented descriptor trails frozen features by 0.03 skill and runs ~300× faster on CPU","key_machinery":"A single representation–comparison–aggregation template, s(I) = A(C(T(I), T(MI))), evaluated under a reflection-exact crop protocol with chance-anchored discrimination skill (2·AUC − 1) and paired-bootstrap significance testing. The representation T is the decisive variable; mid-scale unsigned oriented structure is the operative signal.","core_discovery":"Among existing methods, frozen deep features offer little over a tuned classical HOG descriptor for measuring mirror symmetry. DeepFeat leads at mean single-axis skill 0.83; HOG trails by only 0.031 (significant but small), is not statistically separable from AlexNet-C2 at 0.81, and runs about 300× faster on CPU. Discrimination concentrates in mid-scale unsigned oriented features: deep backbones peak at a low or mid stage, HOG peaks at a mid cell size, and columnar Vision Transformers without spatial hierarchy fall behind.","pith_inferences":["The mid-scale oriented principle may transfer to other bilateral-structure tasks (figure-ground, aesthetic balance) that currently default to deep features without checking classical baselines.","A natural extension is to drive axis search with HOG first, then refine with a mid-stage deep readout only on hard candidates—hybrid detection that the paper leaves open.","If annotation noise at the finest perturbations is the true floor, future benchmarks need inter-rater axis spread, not only consensus labels.","Medical and industrial domains that already use domain-specific indices may still prefer those methods; the natural-image ranking should not be assumed universal without re-benchmarking."],"forward_implications":["For most practical scoring, a tuned mid-cell HOG is the default: near-top skill at ~0.5 ms per crop on CPU.","Deep frozen readouts are justified only when the final ~0.03 skill justifies two orders of magnitude more compute, or as part of a complementary ensemble with HOG.","Detection pipelines that wrap a scorer around candidate axes can substitute a cheap mid-scale oriented scorer without large accuracy loss.","Architecture choice for frozen scoring matters less than stage: low/mid hierarchical features win; single-resolution tokenizers underperform.","Whether task-trained deep scorers can beat this classical ceiling remains the open next experiment."],"fun_headline_variants":["HOG nearly matches frozen deep nets on mirror symmetry skill","Classical HOG trails best deep readout by just 0.03 skill","Tuned HOG rivals deep features for mirror symmetry, 300× faster","Deep scorers offer little over mid-scale HOG for symmetry","Frozen nets peak mid-stage; HOG matches them on oriented features"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"That ranking the true axis above controlled wrong axes within an image is the right test of what applications need, rather than a calibrated score of how symmetric an image is that can be compared across images.","fun_headline_variants_meta":{"raw":{"variants":["HOG nearly matches frozen deep nets on mirror symmetry skill","Classical HOG trails best deep readout by just 0.03 skill","Tuned HOG rivals deep features for mirror symmetry, 300× faster","Deep scorers offer little over mid-scale HOG for symmetry","Frozen nets peak mid-stage; HOG matches them on oriented features"]},"model":"grok-4.5","effort":"low","cost_usd":0.006432,"raw_usage":{"total_tokens":1686,"prompt_tokens":825,"num_sources_used":0,"completion_tokens":95,"cost_in_usd_ticks":64320000,"prompt_tokens_details":{"text_tokens":825,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":766,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":825,"tokens_out":95,"duration_ms":6452,"temperature":1.0,"reasoning_tokens":766,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-10T08:24:35.649904+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Train a deep scorer end-to-end for axis discrimination on the same protocol and show a large, significant skill gain over HOG that survives multi-axis and domain-transfer checks; or re-run the benchmark on native medical volumes and show domain asymmetry indices overtake HOG and frozen deep readouts.","supporting_citations":[],"review_version":1}