{"id":"b883be0c-429c-485a-a7bd-93176ef5c5ee","arxiv_id":"2411.17392","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"NumGrad-Pull uses tri-plane feature grids, numerical gradients, progressive resolution increases, and complementary sampling to improve signed-distance-function surface reconstruction from point clouds.","lead":"This paper presents NumGrad-Pull, a method that reconstructs smooth 3D surfaces from unoriented point clouds using tri-plane features and numerical gradients instead of analytical ones. It reports lower reconstruction error and faster queries than previous neural approaches, which matters for 3D scanning, content creation, and robotics.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The core claim that numerical gradients outperform analytical gradients rests on an unspecified analytical-gradient baseline in Table 5 (Model C); given the paper's questionable description of bilinear interpolation as non-differentiable, the 331.84 CD may be an implementation artifact rather than…","rationale":"The reader's weakest-assumption concern is the nearest-neighbor proxy inherited from Neural-Pull. That is a real limitation, especially for noisy scans, but it is not specific to the paper's central novelty and does not threaten the internal comparison that establishes the method's main claim. The more load-bearing vulnerability is the analytical-gradient baseline used in the decisive ablation. The paper claims numerical gradients are essential because analytical gradients are unstable, yet it never defines the analytical-gradient computation. Its explanation that floor/ceil rounding makes the encoding non-differentiable is technically inaccurate for the piecewise-linear interpolation in Eq. 4, and it raises the possibility that the analytical baseline was implemented in a way that does not provide a meaningful gradient direction. Because the finite-difference gradient approaches the analytical gradient as epsilon shrinks, the dramatic difference in Table 5 cannot be taken at face value without knowing the exact stencil and implementation. This is a concrete, checkable issue: reimplementing the analytical gradient correctly and rerunning Model C will settle whether the paper's central mechanism is real. The paper otherwise has credible empirical support: ablations for each module, plausible speed improvements from the tri-plane representation, and results on multiple benchmarks. The code link, if functional, would enable the proposed check, but the paper text alone does not resolve the ambiguity. I therefore recommend maintaining a CONDITIONAL verdict, with the added condition that the analytical-gradient baseline be clarified and the Model C ablation be repeated with a correct autograd implementation; if the catastrophic failure disappears, the paper's central claim would need substantial revision.","tokens_in":12984,"tokens_out":15230,"duration_ms":157804,"concrete_test":"Independently rerun the Model C ablation on the FAMOUS dataset with the analytical gradient computed by full autograd through the tri-plane bilinear interpolation, keeping q on the autograd graph through the interpolation weights rather than through detached floor/ceil indices, and using the same training schedule and data as the paper; then compare the resulting CD against the reported 331.84 and the full model's 0.39. In parallel, inspect the released repository to determine whether the original Model C analytical-gradient path detaches the query or uses a non-differentiable index operation. If the corrected analytical-gradient CD falls to the same order as the full model, the claimed benefit of numerical gradients is an artifact of the baseline implementation.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central contribution is the claim that replacing analytical gradients with numerical gradients in a tri-plane pulling framework significantly improves training stability and convergence. The only direct evidence is Table 5, where the variant without numerical gradients (Model C) yields CD 331.84 versus 0.39 for the full model. This comparison is load-bearing, but the paper never specifies how the analytical gradient is computed in Model C. In Sec. 3.3, the authors justify the need for numerical gradients by saying the tri-plane forward pass 'involves non-differentiable rounding operations' such as floor and ceil, and that this makes the gradient 'inherently local.' That explanation is imprecise: Eq. 4 is piecewise-linear in the query coordinate q, with a well-defined derivative inside each grid cell; only the derivative at grid boundaries is discontinuous. If the Model C implementation computes the analytical gradient by detaching the floor/ceil indices or by treating them as non-differentiable integers, the gradient with respect to q can be zero or degenerate, and Eq. 1 would pull queries in arbitrary directions. The catastrophic failure at 331.84 would then reflect a faulty baseline, not the claimed locality of analytical gradients. Furthermore, for a fixed differentiable network, the central-difference gradient in Eq. 6 converges to the analytical gradient as epsilon tends to zero; the paper sets epsilon = 1/(2R) with no sensitivity analysis, so the dramatic qualitative gap between numerical and analytical gradients is surprising and needs verification. If the analytical baseline is corrected, the paper's central mechanistic claim may collapse or be substantially weakened, even if the overall SOTA numbers survive.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"NumGrad-Pull proposes a hybrid tri-plane/MLP signed distance function for surface reconstruction from unoriented point clouds, trained with a pulling loss. The three claimed contributions are (i) replacing analytical gradients with finite-difference numerical gradients in the pulling operation to stabilize tri-plane training, (ii) a progressive tri-plane resolution expansion schedule, and (iii) a complementary sampling strategy that augments near-surface query points with points from the unit cube. The method is evaluated on ShapeNet, ABC, FAMOUS, and the SRB scans, reporting Chamfer and Hausdorff distances that beat or match prior work (e.g., ShapeNet average CD 0.020 vs. 0.032 for IF), with faster per-iteration training. Ablations on FAMOUS show that removing numerical gradients leads to a catastrophic CD of 331.84 (scaled by 10^4) versus 0.39 for the full model, which the paper interprets as evidence for the central claim.","tokens_in":13325,"tokens_out":4791,"duration_ms":45757,"significance":"If the central claim is valid, the paper would show that a simple and cheap modification (finite-difference gradients) resolves a real training instability in grid-based SDF learning, which is a practically important problem. The paper ships code and evaluates on several standard benchmarks, which is a clear strength. However, the evidence for the central claim currently rests on a single ablation table with an unspecified analytical-gradient baseline, so the significance of the numerical-gradient contribution is not yet established. The progressive expansion and complementary sampling appear to be useful engineering additions, and the speed gains are credible, but these are secondary to the main claim. The overall approach is plausible and the benchmark results are encouraging, but the load-bearing evidence needs to be made rigorous before the paper's conclusions can be accepted.","major_comments":[{"comment":"The justification for numerical gradients is based on an incorrect characterization of bilinear interpolation. Equation (4) is a continuous, piecewise-linear function of the query coordinate q; the floor and ceil indices are constant within each grid cell, and the interpolation coefficients are linear in the fractional parts. The function is differentiable almost everywhere, and the standard analytical gradient of the tri-plane feature with respect to q is well defined. The paper's statement that \"the gradient of the tri-plane encoding is inherently local\" because of \"non-differentiable rounding operations\" conflates non-differentiability at grid boundaries with the well-defined derivative inside each cell. This matters because it is the stated motivation for the central contribution. The authors should either provide a precise derivation of what the analytical gradient is and why it is problematic, or correct the explanation.","section":"§3.3 and Eq. (4)-(6)"},{"comment":"The ablation study that carries the central claim (Model C, 'w/o NumGrad', CD 331.84 vs. 0.39 for the full model) never specifies how the analytical gradient is computed in Model C. The text only says that analytical gradients 'only propagate supervision to local grids'. If the analytical-gradient baseline is implemented by detaching the floor/ceil indices or by taking the gradient of the interpolated feature with respect to the parameters only for the four corners in the current cell, then the comparison is not a clean test of numerical versus analytical gradients; it is a test of a particular—and possibly degenerate—implementation. The manuscript must state precisely the computation used for Model C, provide the relevant code or pseudocode, and verify that the catastrophic failure is not an artifact of that implementation (e.g., a zero or arbitrarily directed gradient). Without this, the headline ablation does not support the paper's central claim.","section":"Table 5 and §4.4.2"},{"comment":"The perturbation size is set to epsilon = 1/(2R), where R is the current tri-plane resolution, but no sensitivity analysis is reported. Since the numerical gradient in Eq. (6) is the mechanism supposed to stabilize training, the paper should show results for at least two alternative epsilon values (e.g., epsilon = 1/R and epsilon = 1/(4R)) and for a fixed epsilon while the resolution expands, to establish that the choice is not fine-tuned for the reported ablations. Additionally, the claim that numerical gradients improve over analytical gradients should be supported by training curves (loss or CD over iterations) rather than only a single endpoint metric.","section":"§3.4 and Eq. (6)"},{"comment":"The ablation table is internally inconsistent with the text. The text defines Model A as 'full model without our data sampling strategy,' but the row for Model A in Table 5 shows a ✗ under 'w/o Data', implying data sampling is present, and a ✓ under 'w/o Tri-plane', 'w/o NumGrad', and 'w/o Progressive', which cannot be correct for a 'full model without one component'. The checkmark encoding is either reversed or misaligned. This must be fixed, because the table is the primary quantitative evidence for the contribution of each module. All ablation numbers are also single-run; the central comparison (0.39 vs. 331.84) would be more convincing if reported over repeated runs with variance.","section":"Table 5 checkmark encoding"}],"minor_comments":[{"comment":"The complementary sampling strategy is described as 'randomly sampling points in a unit cube [−1,1]^3', but the number of such points per training step or per surface point is not specified. This is needed for reproducibility.","section":"§3.5"},{"comment":"The row for 'Ours' in Table 3 appears as a run-together string of numbers in the provided version (e.g., '0.0511.1940.0410.113...'), making the results unreadable. Please ensure the table formatting is correct in the camera-ready version.","section":"Table 3"},{"comment":"There is a typo: 'exploys' should be 'employs'.","section":"§2.3"},{"comment":"The speed comparison reports 'iter/s' without specifying how many forward/backward passes each iteration comprises. Since the numerical-gradient variant performs six additional forward evaluations per query, a per-iteration comparison overstates the practical speed advantage. Clarify this in the text.","section":"§4.4.1 and Table 4"},{"comment":"The sentence 'we are pioneering the exploration of hybrid explicit–implicit representations [5] for fundamental surface reconstruction problems' overstates novelty, as several tri-plane or grid-based SDF works exist (e.g., Grid-Pull [8] and Neuralangelo [23]). Please temper the claim and cite the relevant prior art.","section":"§2.3"}],"recommendation":"major_revision","confidential_remarks":"The paper's main novelty reduces to replacing analytical gradients with central differences in a tri-plane pulling framework. This is a small change, and the paper's own explanation of why it helps is technically shaky (the differentiability claim about bilinear interpolation). The reviewer should require the authors to document the analytical-gradient baseline precisely before accepting the central claim. The benchmark results are competitive, but the lack of variance reporting in ablations and the inconsistency in Table 5 are concerning. The paper cites several of the authors' own prior works (e.g., [9], [10], [11], [12], [39]) in the related work and background; this is not inappropriate, but the 'pioneering' language in §2.3 should be softened. Overall, the work may be publishable after a revision that addresses the control of the analytical-gradient baseline and the epsilon sensitivity."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I read NumGrad-Pull last night. The short version: it's a legitimate extension of the Neural-Pull line, with consistent benchmark improvements and an ablation that mostly supports the design. The main weakness is exactly where the stress-test note points: the paper's headline claim about numerical gradients over analytical gradients is only as strong as Table 5's Model C, and that comparison is not adequately specified.\n\nWhat's genuinely new: combining a tri-plane SDF representation with the pulling objective, finite-difference gradients, progressive plane expansion, and complementary sampling. Individually those pieces exist; the combination is new and it works. The numbers are credible: ShapeNet average CD 0.020 vs. IF's 0.032, similar margins on ABC and FAMOUS, and a 5.4x iteration speedup over IF. The SRB results are also competitive. Credit where due: the paper evaluates on external benchmarks, provides ablations for each module, and says code is available.\n\nThe soft spots are real but not disqualifying. First, the explanation for why analytical gradients fail is imprecise. The paper says bilinear interpolation involves 'non-differentiable rounding operations,' which is misleading: inside each cell the function is differentiable; only at cell boundaries is it non-differentiable. That alone doesn't explain a collapse to CD 331.84. The stress-test note is right that Model C's analytical gradient may have been computed with detached indices, giving zero or degenerate gradients for half the query points. The authors need to state exactly how Model C's gradient is computed. Without that, the central mechanistic claim is under-verified.\n\nSecond, the ablation table header is confusing: the columns say 'w/o Data,' 'w/o Tri-plane,' etc., but the checkmarks appear to indicate presence of the component. A reader shouldn't have to reverse-engineer that. Third, all results are single-run numbers with no variance or significance tests. On a method that is supposed to improve stability, showing run-to-run variance is important. Fourth, epsilon is set to 1/(2R) with no sensitivity analysis; since the benefit of numerical gradients is the whole point, that's a gap.\n\nThe nearest-neighbor proxy assumption is inherited from Neural-Pull and is load-bearing, but the paper doesn't pretend otherwise; it's a known limitation of the pulling paradigm. The paper's own future-work section admits high-frequency noise at higher resolutions, which is honest.\n\nBottom line: this is a solid engineering paper for the surface-reconstruction subfield. It deserves a serious referee, but the referee should require the authors to clarify the analytical-gradient baseline, add error bars, and fix the ablation table. If the numerical-gradient advantage survives that scrutiny, it's a worthwhile contribution. I'd send it to review with those conditions.","headline":"A solid, incremental tri-plane pulling system with real benchmark gains, but the central numerical-gradient claim rests on an under-specified ablation that needs pinning down before I'd trust it.","tokens_in":13874,"tokens_out":1958,"would_cite":false,"duration_ms":20717,"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":"NumGrad-Pull's central claim is that finite-difference numerical gradients, not analytical ones, make tri-plane-based signed-distance learning stable enough to reconstruct accurate surfaces from unoriented point clouds.","keywords":["signed distance function","surface reconstruction","point clouds","tri-plane representation","numerical gradients","neural pulling","progressive resolution expansion","unoriented point clouds"],"falsifier":"Reproduce the paper's Model C ablation on FAMOUS: the same tri-plane pipeline with numerical gradients swapped back to analytical gradients, keeping all other modules fixed; the paper reports a collapse to CD 331.84 versus 0.39 ($\\times10^{-4}$). If that run trains stably, or fails for a different reason such as merely missing progressive expansion, the claim that numerical gradients are the stabilizing mechanism would be falsified. A complementary check on synthetic clouds with deliberately shifted nearest-neighbor targets would test the load-bearing pulling assumption directly.","tokens_in":12823,"feed_emoji":"🧊","tokens_out":8792,"duration_ms":74122,"temperature":0.7,"pith_summary":"NumGrad-Pull aims to reconstruct a clean continuous surface from a bare 3D point cloud, with no point normals, by learning a signed distance function whose zero set is the surface. The paper's central claim is that a tri-plane representation—three orthogonal feature grids with a small neural decoder—can learn such a function faster and with finer detail than deep networks alone, provided the training signal is changed. Instead of back-propagating through the analytical gradient of the network, the method estimates gradients by finite differences, which spreads each update across neighboring grid cells and stabilizes training. It adds a coarse-to-fine tri-plane expansion and a sampling mix that guides both surface-near and distant regions. On ShapeNet, ABC, FAMOUS, and real scans, the authors report lower chamfer distances (a surface error measure) than prior pulling-based methods while running several times faster.","feed_headline":"Numerical gradients stabilize tri-plane surface reconstruction","feed_subtitle":"Training runs up to 5.4x faster per iteration than the previous best while keeping finer detail.","key_machinery":"The load-bearing object is the tri-plane feature grid (three axis-aligned $N\\times N$ feature planes with bilinear interpolation, summed and decoded by a shallow MLP into a signed distance), and the load-bearing mechanism is the finite-difference gradient estimator used inside the pulling update. The mechanism's job is to replace the analytically computed gradient, which through the rounding operations of interpolation touches only the four corner features of one grid cell, with a computation that evaluates the SDF at six neighboring points and thereby back-propagates to multiple grid regions at once; this is what the paper credits for training stability.","core_discovery":"The paper's central discovery is that the instability of tri-plane SDF training is caused by the locality of analytical gradients: bilinear interpolation with rounding means back-propagation touches only the four corner features of one grid cell. Replacing the analytical gradient in the pulling update with a central finite difference, $\\nabla_x\\Phi(q) = [\\Phi(q+\\epsilon_x)-\\Phi(q-\\epsilon_x)]/(2\\epsilon)$ and similarly for the other axes, makes each gradient computation involve six nearby evaluations, so supervision reaches adjacent grid entities simultaneously. With that change, plus progressive resolution expansion and a complementary uniform-cube sampling strategy, the tri-plane signed distance function converges stably and produces reconstructions that the paper reports as more accurate than previous methods.","pith_inferences":["If the locality diagnosis is right, the same finite-difference trick should transfer to other grid-based implicit representations such as hash grids or octrees, where analytical gradients are also local; testing NumGrad-style gradients in those settings is a natural extension the paper does not make.","The numerical gradient couples three extra query evaluations, so the reported speed advantage is partly offset by more forward passes; a fairer efficiency comparison would hold total network evaluations constant, not just iterations per second.","The nearest-neighbor pulling target remains the weak link: on noisy scans, correcting targets (e.g., via local plane fitting) before pulling could combine with numerical gradients to improve robustness, an option the paper does not explore.","The method's robustness claims are demonstrated on object-level scans; applying it to scene-level data with larger scale and varying density is the paper's stated future work and would test whether tri-plane resolution expansion generalizes."],"forward_implications":["The reported FAMOUS chamfer distance drops from 11.35e-4 (baseline Neural-Pull) to 0.39e-4, meaning fine surface detail such as the hand's fingers is preserved rather than smoothed away.","Because finite-difference gradients couple neighboring grid cells, training converges without collapsing even when the tri-plane starts at 8x8 and expands through 16x16 to 32x32; the authors claim this is what makes the progressive expansion viable.","The same architecture at 32x32 runs roughly 1.8x faster than Neural-Pull and 5.4x faster than IF in iterations per second, a direct consequence of the O(1) tri-plane interpolation.","Each proposed component is necessary in the authors' ablation: removing numerical gradients is the most destructive (Model C, CD 331.84e-4), and removing progressive expansion or complementary sampling also degrades results.","On ShapeNet, the paper reports an average chamfer distance of 0.020 versus 0.032 for the strongest prior method, with the best result in six of eight categories."],"supporting_citations":[{"why":"Defines the pulling operation and the squared-distance pulling loss that NumGrad-Pull inherits; also the primary baseline for stability and speed comparisons.","marker":"[27]"},{"why":"Introduces the tri-plane explicit–implicit representation that the paper adapts as its SDF backbone.","marker":"[5]"},{"why":"Most recent state-of-the-art pulling SDF method; supplies the main accuracy baseline and evaluation protocol on ShapeNet, ABC, and FAMOUS.","marker":"[22]"},{"why":"Grid-based pulling baseline that motivates using explicit grids for scalability and is a key speed and quality comparison point.","marker":"[8]"},{"why":"Divergence-guided pulling method the paper compares against and builds on for pulling-target constraints.","marker":"[2]"},{"why":"Provides the geometric network initialization used to initialize the SDF decoder toward a sphere.","marker":"[14]"},{"why":"Supplies the ABC and FAMOUS datasets, splits, and evaluation protocol used in the main comparisons.","marker":"[13]"},{"why":"Supplies the ShapeNet test split and categories used for the main benchmark.","marker":"[6]"}],"fun_headline_variants":["Numerical gradients beat analytic ones for tri-plane SDF reconstruction","Finite differences speed up tri-plane surface learning by 5.4x","Stable tri-plane SDF training via numerical gradient pulling","Tri-plane point cloud reconstruction with numerical gradient SDFs"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method's pulling targets are chosen as the nearest input point to each query, so the whole pipeline assumes that nearest neighbor in the sampled cloud is a trustworthy stand-in for the true closest point on the surface; on sparse, noisy, or incomplete scans that proxy can be wrong and drag the learned field to a biased surface.","fun_headline_variants_meta":{"raw":{"variants":["Numerical gradients beat analytic ones for tri-plane SDF reconstruction","Finite differences speed up tri-plane surface learning by 5.4x","Stable tri-plane SDF training via numerical gradient pulling","Tri-plane point cloud reconstruction with numerical gradient SDFs"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000949,"raw_usage":{"total_tokens":4027,"prompt_tokens":899,"completion_tokens":3128,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":515,"completion_tokens_details":{"reasoning_tokens":3056}},"tokens_in":515,"tokens_out":3128,"duration_ms":21911,"temperature":1.0,"reasoning_tokens":3056,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:10:28.067732+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Reproduce the paper's Model C ablation on FAMOUS: the same tri-plane pipeline with numerical gradients swapped back to analytical gradients, keeping all other modules fixed; the paper reports a collapse to CD 331.84 versus 0.39 ($\\times10^{-4}$). If that run trains stably, or fails for a different reason such as merely missing progressive expansion, the claim that numerical gradients are the stabilizing mechanism would be falsified. A complementary check on synthetic clouds with deliberately shifted nearest-neighbor targets would test the load-bearing pulling assumption directly.","supporting_citations":[{"cited_title":"Neural-pull: Learning signed distance function from point clouds by learning to pull space onto surface","cited_arxiv_id":null,"evidence_quote":"Defines the pulling operation and the squared-distance pulling loss that NumGrad-Pull inherits; also the primary baseline for stability and speed comparisons."},{"cited_title":"Efficient geometry-aware 3d generative adversarial networks","cited_arxiv_id":null,"evidence_quote":"Introduces the tri-plane explicit–implicit representation that the paper adapts as its SDF backbone."},{"cited_title":"Implicit filtering for learning neural signed distance functions from 3d point clouds","cited_arxiv_id":null,"evidence_quote":"Most recent state-of-the-art pulling SDF method; supplies the main accuracy baseline and evaluation protocol on ShapeNet, ABC, and FAMOUS."},{"cited_title":"Gridpull: To- wards scalability in learning implicit representations from 3d point clouds","cited_arxiv_id":null,"evidence_quote":"Grid-based pulling baseline that motivates using explicit grids for scalability and is a key speed and quality comparison point."},{"cited_title":"Digs: Divergence guided shape implicit neu- ral representation for unoriented point clouds","cited_arxiv_id":null,"evidence_quote":"Divergence-guided pulling method the paper compares against and builds on for pulling-target constraints."},{"cited_title":"Mitra, and Michael Wimmer","cited_arxiv_id":null,"evidence_quote":"Supplies the ABC and FAMOUS datasets, splits, and evaluation protocol used in the main comparisons."}],"review_version":1}