{"id":"d7c6c271-17c8-4212-bedd-9ed8f7363397","arxiv_id":"2505.19175","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":16,"one_line_summary":"A triangle-soup representation with a compact normalized window function is optimized end-to-end and beats Gaussian and convex splatting baselines on LPIPS while rendering at real-time rates.","lead":"This paper optimizes unstructured 3D triangles as differentiable splats for photorealistic novel-view rendering, instead of Gaussian blobs or neural fields. It reports better perceptual quality than 3D Gaussian Splatting on several benchmarks, roughly 100 FPS on an A100, and compatibility with ordinary game-engine renderers.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's own tables contradict its headline: 3DGS renders 134 FPS vs. Triangle Splatting's 97, and 2DGS trains in 29m vs. 39m; the 2,400 FPS figure comes from a separate annealed mesh pipeline with no quality metrics.","rationale":"The reader identified the MCMC densification as the weakest assumption. I agree that Section 3.2's MCMC framing is unsupported: no target distribution or transition kernel is defined, and 'probability of the state remains unchanged' is not a valid stationarity condition. However, the speed and throughput contradiction attacks the central claim directly: the paper's own tables falsify the superlative. Even if the MCMC heuristic were replaced by a standard heuristic densifier, the empirical results might stand; but if the FPS/training-time comparisons are incorrect or conflate different pipelines, the headline claim's quantitative content is wrong. The MCMC issue is a theoretical gap in a supporting mechanism; the speed issue is a factual gap in the claim itself. The paper remains conditionally acceptable because the core differentiable-triangle idea and LPIPS improvements are plausible and the issues are correctable with reruns and reworded claims.","tokens_in":16438,"tokens_out":10588,"duration_ms":77207,"concrete_test":"Obtain the released code and recompute Table 1 and Table 2 under the stated protocol on an A100: (1) verify whether the FPS column measures the differentiable splatting renderer for all methods; if so, the claim of higher rendering throughput than 3DGS is false. (2) Report training time to a fixed quality target (e.g., LPIPS=0.20) rather than total wall-clock; if Triangle Splatting needs more time than 2DGS to reach the target, the 'faster convergence' claim fails. (3) Run the annealed mesh-renderer pipeline on held-out views and compute PSNR/LPIPS against the splatting renderer's outputs; if LPIPS worsens by more than ~0.02, the '2,400 FPS' headline is for a degraded variant and should be labeled as such.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline claim—'surpassing 3DGS, 2DGS, and 3DCS in visual fidelity, training speed, and rendering throughput' (Abstract; Section 1)—is contradicted by the paper's own measurements. Table 1's average Mip-NeRF360 FPS is 134 for 3DGS and 97 for Triangle Splatting, so the differentiable splatting renderer is not faster than 3DGS. Table 2 lists 2DGS training as 29 min versus 39 min for Triangle Splatting, so training is not faster than 2DGS. The 2,400+ FPS figure (Section 1, Figure 2, Table 4) is for a different pipeline: after annealing opacity and sigma and zeroing SH in the final 5,000 iterations (Supplementary A.5), the triangles are rendered by an off-the-shelf mesh renderer, not by the differentiable splatting renderer used for the comparisons. No quality metrics are reported for this annealed mesh output, so its fidelity relative to the trained splatting model is unknown. The central claim thus bundles two different renderers and two different representations, and the 'surpassing 3DGS' portion is not supportable from the reported evidence.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Triangle Splatting, a differentiable renderer that optimizes an unstructured soup of 3D triangles for novel-view synthesis. Each triangle is projected to screen space and rendered with a normalized window function based on the exact signed distance field of its 2D projection; vertex positions, opacity, sharpness, and spherical-harmonic colors are optimized end-to-end. An adaptive pruning and densification routine, presented as MCMC-inspired, controls the number of triangles. Experiments on Mip-NeRF360 and Tanks and Temples report LPIPS, PSNR, SSIM, training time, rendering FPS, and memory usage, along with an annealed mesh-renderer pipeline where the authors claim over 2,400 FPS on the Garden scene. The central claim is that Triangle Splatting surpasses 3DGS, 2DGS, and 3DCS in visual fidelity, training speed, and rendering throughput.","tokens_in":16775,"tokens_out":8204,"duration_ms":48089,"significance":"If the empirical results hold, the method is a useful step toward optimizing triangle primitives directly for radiance-field-style rendering. The window function in Eq. (1) is compact, has a formal depth-invariance proof in Eq. (4), and the ablations in Table 3 isolate the contributions of the main loss terms. The reported LPIPS improvements over 2DGS and 3DCS, and the competitive performance on indoor Mip-NeRF360 scenes, suggest that triangle-based primitives are a viable alternative to Gaussian and convex primitives. However, the headline comparative claims are not supported by the paper's own measurements, the MCMC framing of densification is not formalized, and the high-FPS mesh pipeline is not evaluated for quality. The core primitive and window function are valuable, but the presentation overstates the results.","major_comments":[{"comment":"The headline claim that Triangle Splatting surpasses 3DGS, 2DGS, and 3DCS in visual fidelity, training speed, and rendering throughput is contradicted by the paper's own numbers: Table 1 reports 134 FPS for 3DGS versus 97 FPS for Triangle Splatting on Mip-NeRF360, and Table 2 reports 29 minutes for 2DGS versus 39 minutes for Triangle Splatting. The Speed & Memory paragraph states that Triangle Splatting achieves \"faster training and rendering,\" which is also inconsistent with the 29m versus 39m row. Please revise the abstract, Section 1, and the Speed & Memory discussion to state precisely which methods are improved on which axes, and add convergence curves or per-iteration metrics before claiming faster convergence.","section":"Abstract; Section 1; Tables 1 and 2"},{"comment":"The MCMC-based densification is not specified. The text asserts that the transition \"preserves the probability of the state\" and that splitting a triangle into four is a move between equally probable samples, but it never defines the state distribution, the transition kernel, an acceptance rule, or how the probability is computed after the number of primitives changes. Since the state space changes dimension under split-by-four, the claim requires a reversible-jump or explicit hierarchical construction to be meaningful. The alternating Bernoulli sampling based on inverse sigma and opacity is not a substitute for a formal acceptance rule. Please either provide these details or present the densification as a heuristic and remove the MCMC interpretation; the current text leaves the adaptive-density mechanism, which is central to the method's coverage behavior, underspecified.","section":"Section 3.2"},{"comment":"The 2,400+ FPS result is measured with a different renderer and a different representation than the one used in the quantitative comparisons. After annealing opacity and sigma and zeroing SH in the final 5,000 iterations, the triangles are rendered by an off-the-shelf mesh renderer; no PSNR, SSIM, or LPIPS is reported for this annealed mesh output. The paper therefore does not establish that the mesh-rendered result preserves the fidelity of the trained splatting model, and the throughput claim in the abstract and Section 1 conflates two pipelines. Please report quality metrics for the annealed mesh output on the same test views, or clearly separate the two claims and avoid attributing the mesh-renderer FPS to the differentiable splatting renderer.","section":"Section 5, Table 4; Supplementary A.5"}],"minor_comments":[{"comment":"The aggregated Mip-NeRF360 columns omit average PSNR and SSIM, even though per-scene values are given in Tables 9 and 10; please report the averages in the main table so that readers can compare all three standard metrics at a glance.","section":"Table 1"},{"comment":"The mesh-renderer FPS numbers are inconsistent: the abstract and Table 4 say \"over 2,400 FPS\" for Garden, while Supplementary A.5 reports 3,000 FPS; please clarify the configuration for each measurement and why they differ.","section":"Abstract; Section 5; Supplementary A.5"},{"comment":"The paper does not explain how gradients are computed through the non-smooth max in Eq. (1); since the method is described as differentiable and the window function is a core contribution, please state the subgradient or relaxed rule used in the implementation.","section":"Section 3.1, Eq. (1)"},{"comment":"No error bars or standard deviations are reported for the LPIPS, PSNR, and SSIM averages, and several differences (e.g., Triangle Splatting versus 3DCS on Mip-NeRF360 LPIPS) are small; adding variation across random seeds or multiple runs would strengthen the comparisons.","section":"Section 4.1; Tables 8-10"},{"comment":"The claim that the LogSumExp approximation means \"only one of the three vertices has any influence on the final shape\" is stated without supporting evidence; please provide a plot or quantitative comparison if it is used to justify the exact max choice.","section":"Section 3.1"}],"recommendation":"major_revision","confidential_remarks":"The contradictory speed and training claims are the central issue; they are fixable by rewording the abstract and Section 1, but they currently misrepresent the paper's own tables. The MCMC framing should be either formalized or explicitly downgraded to a heuristic. I do not see an irreparable flaw in the core triangle-splatting idea, so a major revision with corrected claims and a clarified densification description would be appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the window function is genuinely new and the LPIPS results are credible; the speed and training claims are not, as the paper's own tables contradict them.\n\nThe core contribution is a compact normalized window function over projected triangle coordinates: 1 at the incenter, 0 on the boundary and outside, with a single smoothness parameter that is scale-invariant under projection. That is a clean, useful primitive for differentiable rendering, and the paper shows it beats sigmoid-window convexes both in principle and in the ablations. Directly optimizing an unstructured triangle soup from SfM points, with midpoint subdivision and opacity-based pruning, is a sensible pipeline, and the ablations give each loss term a fair shake. The LPIPS improvements over 3DGS, 2DGS, and 3DCS on Mip-NeRF360 and Tanks and Temples are consistent and meaningful; the per-scene tables show the wins are not a single outlier.\n\nThe soft spots are real but mostly about framing. The abstract and introduction claim Triangle Splatting surpasses 3DGS, 2DGS, and 3DCS in visual fidelity, training speed, and rendering throughput. Table 2 shows 3DGS at 134 FPS against 97 for Triangle Splatting, and 2DGS training at 29 minutes against 39. So two of the three legs of that claim are contradicted by the paper's own numbers. The 2,400 FPS figure comes from a different pipeline—after annealing opacity and sigma and zeroing SH, rendered with an off-the-shelf mesh renderer—and no quality metrics are reported for that output. It is a neat byproduct, but it should not be bundled into the same sentence as the differentiable splatting results.\n\nThe MCMC densification section is the weakest part of the writing. The paper says the split/clone transition preserves the probability of the state, but never defines the state distribution or the transition kernel, so the claim is not checkable. In practice it reads as a reasonable heuristic, and it should be described as one unless the probabilistic formalism is actually supplied.\n\nMissing code, error bars, and convergence curves are standard pre-release complaints; they are minor given the benchmark coverage, but they matter for a method whose main advantage is perceptual quality. I'd like to see aggregate PSNR/SSIM in the main table too.\n\nBottom line: the central idea is sound and the paper deserves a serious referee. It needs recalibrated claims, a clarified two-pipeline story, and ideally code before acceptance.","headline":"Genuinely new compact triangle window function with credible LPIPS wins, but the paper's speed and training claims are contradicted by its own tables.","tokens_in":17345,"tokens_out":2944,"would_cite":true,"duration_ms":26848,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Triangle Splatting claims that an unstructured soup of triangles, rendered through a compact normalized window function, can be optimized end-to-end and outdo Gaussian and convex primitives in visual quality, training speed, and rendering…","keywords":["triangle splatting","differentiable rendering","radiance fields","novel view synthesis","3D Gaussian Splatting","window function","mesh-based rendering"],"falsifier":"Measure the log-probability of a triangle configuration before and after a midpoint-subdivision or clone-with-noise step under the sampling distribution used in the densification section (built from opacity and $\\sigma^{-1}$). If the ratio is not 1, or if no well-defined distribution exists, the MCMC premise fails; a simpler check is to ablate the specific split/clone moves against uniform or random densification with the same triangle budget and see whether LPIPS on Mip-NeRF360 changes materially.","tokens_in":16179,"feed_emoji":"🔺","tokens_out":7082,"duration_ms":59595,"temperature":0.7,"pith_summary":"Triangle Splatting seeks to bring the triangle back as the core primitive for photorealistic 3D reconstruction from photos. The authors propose a differentiable renderer that optimizes an unstructured soup of triangles directly from image gradients, using a compact window function that confines each triangle's influence to its own projected footprint. They report that this representation beats 3D and 2D Gaussian Splatting and 3D Convex Splatting in visual fidelity, training time, and rendering speed, and matches or exceeds the perceptual quality of the implicit field Zip-NeRF on indoor scenes. Because the optimized output is an ordinary triangle mesh, it renders in standard game engines at thousands of frames per second, closing the gap between neural radiance-field training and conventional graphics pipelines.","feed_headline":"Triangles beat Gaussian splats in radiance-field rendering","feed_subtitle":"A bounded window function keeps each triangle inside its footprint, enabling 2,400+ FPS in standard game engines.","key_machinery":"The load-bearing mechanism is the window function $I(p)=\\mathrm{ReLU}(\\phi(p)/\\phi(s))^\\sigma$, defined from the signed distance field $\\phi$ of the projected triangle, the incenter $s$, and a learned smoothness $\\sigma$. Unlike sigmoid-based windows used in prior convex splatting, this function is exactly 1 at the incenter, exactly 0 at the boundary and outside, so a triangle never bleeds beyond its vertices; the normalization also makes the same $\\sigma$ work at every depth because uniform scaling cancels in the ratio. This window is what makes an unstructured triangle soup optimizable: compact support gives tight gradients to vertex positions, and the $\\sigma$ exponent controls how solid or soft each triangle is, which in turn drives the adaptive densification that samples new triangles where coverage is sparse.","core_discovery":"On its own terms, the paper's central claim is that a triangle soup—unstructured, disconnected triangles—can be optimized end-to-end for novel-view synthesis and outperform both volumetric (3D Gaussian Splatting and convex splatting) and planar (2D Gaussian Splatting) primitives. The key to making triangles trainable is a normalized window function $I(p)=\\mathrm{ReLU}(\\phi(p)/\\phi(s))^\\sigma$, which is 1 at the triangle's incenter, 0 at the boundary and outside, and controlled by a single smoothness parameter $\\sigma$. This bounded, depth-invariant falloff lets gradients flow to vertex positions while keeping each primitive's support tightly inside its projected geometry, so the optimizer moves vertices instead of inflating soft shapes. The authors claim this yields sharper reconstructions, lower LPIPS than 2DGS, BBSplat, 3DGS, and 3DCS on Mip-NeRF360, and higher perceptual quality than Zip-NeRF on indoor scenes, with the final triangle soup renderable unmodified in mesh pipelines at over 2,400 FPS.","pith_inferences":["I would test whether the MCMC framing is doing real work: if densification is run with the same budget but without the split-into-four/clone-and-noise moves, and the quality gap is small, then the method's gains come from the window function and loss terms, not from the sampling story.","The bounded-support window function is a general recipe: replacing the triangle SDF with the SDF of a quad or tetrahedron should extend the same 'normalized peak, zero at boundary' scheme to other primitive families.","The paper's own meshing section is thin, but the representation makes connected-mesh extraction more natural than Gaussian splatting because vertices are already explicit and coplanar; a direct triangulation or vertex-merge step could turn the soup into a watertight mesh.","The consistently lower PSNR alongside better LPIPS suggests that pixel-wise metrics punish sharp solid primitives; if this holds, the field's ranking of smooth versus sharp representations may need to lean more heavily on perceptual metrics."],"forward_implications":["If the claim holds, any radiance-field scene can be trained as a triangle soup and then rendered without conversion in off-the-shelf mesh engines, with the paper reporting 2,400+ FPS at 1280x720 on the Garden scene on an RTX 4090.","Perceptual quality on Mip-NeRF360 indoor scenes would put a primitive-based, non-volumetric method ahead of the implicit Zip-NeRF in LPIPS, an outcome that would shift comparison standards away from PSNR.","Because each pixel only evaluates signed distances to three edges, triangle splatting would be strictly cheaper per pixel than convex splatting's six edges, yielding the reported 4x faster inference over 3DCS.","The depth-invariant window function removes the manual depth-scaling of smoothness that convex splatting needs, simplifying the optimizer and stabilizing coverage in sparse regions."],"supporting_citations":[{"why":"Supplies the baseline primitive representation and rendering equation that triangle splatting extends and compares against.","marker":"[21]"},{"why":"Supplies the closest convex-primitive baseline and the sigmoid window function that the paper replaces.","marker":"[14]"},{"why":"Supplies the planar-primitive baseline and the distortion and normal losses reused in training.","marker":"[15]"},{"why":"Supplies the probabilistic densification framework that the paper adapts to triangles.","marker":"[22]"},{"why":"Provides the main benchmark dataset and the baseline results the paper compares against.","marker":"[2]"},{"why":"Provides the implicit baseline whose indoor perceptual quality the paper claims to match or exceed.","marker":"[3]"},{"why":"Provides the implicit baseline for the 10x rendering speed comparison.","marker":"[32]"},{"why":"Supplies the sparse point cloud used to initialize triangles.","marker":"[36]"}],"fun_headline_variants":["Triangle splats outperform Gaussian splats in radiance fields","Triangles return to radiance field rendering with splatting","2,400 FPS triangle splatting for real-time radiance fields","Radiance fields: triangles trump Gaussians via splatting"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that splitting one triangle into four (or cloning and jittering it) keeps the whole triangle configuration exactly as probable as before, so densification can be described as sampling from one stable distribution; if that probability equality does not hold, the density control is a heuristic and the reported quality may rest on hand-tuned details rather than on a principled sampler.","fun_headline_variants_meta":{"raw":{"variants":["Triangle splats outperform Gaussian splats in radiance fields","Triangles return to radiance field rendering with splatting","2,400 FPS triangle splatting for real-time radiance fields","Radiance fields: triangles trump Gaussians via splatting"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0005,"raw_usage":{"total_tokens":2480,"prompt_tokens":1015,"completion_tokens":1465,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":631,"completion_tokens_details":{"reasoning_tokens":1392}},"tokens_in":631,"tokens_out":1465,"duration_ms":10971,"temperature":1.0,"reasoning_tokens":1392,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:20:06.241521+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the log-probability of a triangle configuration before and after a midpoint-subdivision or clone-with-noise step under the sampling distribution used in the densification section (built from opacity and $\\sigma^{-1}$). If the ratio is not 1, or if no well-defined distribution exists, the MCMC premise fails; a simpler check is to ablate the specific split/clone moves against uniform or random densification with the same triangle budget and see whether LPIPS on Mip-NeRF360 changes materially.","supporting_citations":[{"cited_title":"3D convex splatting: Radiance field rendering with 3D smooth convexes","cited_arxiv_id":null,"evidence_quote":"Supplies the closest convex-primitive baseline and the sigmoid window function that the paper replaces."},{"cited_title":"3D Gaussian splatting as Markov chain Monte Carlo","cited_arxiv_id":null,"evidence_quote":"Supplies the probabilistic densification framework that the paper adapts to triangles."}],"review_version":1}