Twelve-phase image-to-3-D project. The weight-space hypothesis (shapes are decoder weights) fails for image-conditioned generation: warm-started per-shape weights are ≥96% shared anchor, the ≤4% per-shape signal is too thin for diffusion to extract — mode collapse survives every ablation. The autoencoder rescue fails too (cos=0.997 yet broken meshes). The DeepSDF pivot constructs a 64-dim latent rather than extracting one, and works: perfect recall + category-appropriate OOD at 976 shapes. Code, 26GB dataset, live HF Space, 30-page thesis public.

Self-supervised part segmentation with no part labels — by clustering the activations of a trained DeepSDF decoder as it is queried across a shape. On 9 CSG shapes the activation clustering recovers the constructive components (ARI reported per shape). The paper is equally an account of what did not work: four separate attempts to reconstruct individual parts as standalone SDFs, and why each failed.

A compact reimplementation of SDF-SRN — recovering a neural signed-distance field from single-view 2-D silhouette supervision through a differentiable ray-marching renderer, with no 3-D ground truth. Trained on synthetic primitives (sphere, box, ellipsoid); the report covers the renderer, the training schedule, novel-view quality, and the configuration that made it converge.

A self-contained image-to-3-D pipeline — image conditioner, rectified-flow velocity network, SDF decoder, differentiable renderer — trained end-to-end on 2-D silhouette and RGB supervision with no 3-D data. The central diagnostic: 128-dim Gaussian noise has norm ~11.3 against SDF latent codes of norm ~0.42, so the flow minimises MSE by shrinking magnitude, not finding direction. Scaling source noise to the target's std fixed cosine similarity 0.08 → 0.95. Deliberately mirrors the Hunyuan3D component stack at small scale as a scaling recipe.

The standalone weight-space pipeline that the Topic-41 archive grew out of. 24 images per object become 24 image-SIRENs, then one per-object hypernetwork; its weights route — via a tiny mapper through a 128-dim weight-space autoencoder — into shape-SIREN weights and a mesh. Two findings carried forward: per-layer hypernetworks preserve genus-1 topology where monolithic ones destroy it even at MSE ~10⁻⁷; and warm-starting all shape-SIRENs from a shared anchor is necessary for coherent weight-space interpolation — the same property the archive later finds fatal at scale.

Mechanics of triplane representations (3 axis-aligned planes, bilinear sample, MLP, volume render) and the three-way comparison against Gaussian splats and VDB / FVDB. Triplane wins as the universal intermediate on storage (6–12 MB), editability, and lossless convertibility to either alternative. Mesh extraction is a separate downstream step, not part of rendering.

UODF stores three axis-aligned unsigned distance fields instead of a single SDF, giving interpolation-free surface extraction. 20–100× quality gain on open surfaces; triplane variant at 30–80 M points/s. The same axis-aligned principle the thesis-line Six-Plane Mesh and Hexplane AE use implicitly — UODF provides the theoretical justification.

Four-method survey (Splatter Image, GS-LRM, Triplane-Meets-Gaussian, Gamba) + three-way comparison (G-Splat vs VDB vs triplane). Triplane wins as universal intermediate. Gamba (Mamba over Gaussian-sequence tokens) is published validation of the MambaFlow3D substitution premise for sparse-cube tokens.

Summary of Li & He's x-prediction manifold-hypothesis argument and an extension showing the case is structurally stronger for 3-D geometry than for natural images. SDFs (eikonal constraint), sparse voxels (surface-band coherence), and triplanes all have algebraic constraints that ε-prediction destroys. Decides x / v-prediction for all thesis-line diffusion work.

Design specification for a flow-matching polyline generator that replaces PGN's autoregressive seq2seq DSL head. Padded fixed-length tensor with explicit length mask; Pure-Mamba backbone; flow-matching velocity prediction; added-embedding attribute conditioning. Three open architectural questions enumerated for the first training run.

Five-method survey identifies a structural field gap: no published method combines image input with parametric (procedural-CAD) output. The field bifurcates into image-input + raw-geometry-output (SparC3D, TRELLIS) and latent-input + parametric-output (CAPRI-Net, BrepGen, HoLa). The intersection is the thesis-line opportunity, operationalised by PGN and SculptNet.

From-first-principles pure-NumPy implementation of a character-level transformer block (multi-head causal self-attention, positional encoding, FFN, LayerNorm, residuals). The "hello world" run shows three occurrences of the letter l producing three distinct output vectors — the operational signature of context-dependent representation. Foundation study for the thesis-line transformer use.

Study of LDM (Stable Diffusion-class) decomposition: frozen VAE compressor + trained U-Net denoiser + frozen text encoder + scheduler. LCM distillation gives 25× sampling speed-up. Same VAE-U-Net decoupling structures the thesis-line 3-D-diffusion work — triplane encoder is the VAE-analogue, Mamba block is the U-Net-analogue.

System design pitch for real-time 3-D reconstruction (DPT depth → NICER-SLAM pose → TSDF fusion → Rerun.io browser viewer; 10 fps end-to-end target). WTFund ₹20 L grant application declined ("PoC needed"). The pitch's "real-time, on a laptop, no server" framing is the consumer-hardware throughline that shapes every later thesis-line architecture decision.

From-scratch DDPM: 3 M-param MLP denoiser with sinusoidal timestep embedding, 100-step linear β schedule, ε-prediction MSE loss, single-image training on a 16×16 red square. Trains in ~5 min on M2 CPU; reverse-pass reconstruction MSE < 0.01. The 0.8 s sampling cost on the toy seeds the flow-matching switch in the later thesis-line work.

Foundational SDF study. Structured comparison (point cloud vs mesh vs SDF), analytic sphere / cuboid SDFs with closed-form CSG operators (union = min, intersection = max, difference = max(a, −b)), and a brief abandoned GAN-SDF exploration. Decisions made here propagate forward: Hexplane AE's continuous-feature pivot, the diffusion-over-GAN preference, the UODF cross-reference.

Matched-parameter MNIST validation across three sequence backbones with identical FM head + training schedule. Hybrid wins loss (0.080) but Pure Mamba ties on visual sample quality and is 1.44× faster per step. Pure Transformer produces noise at 50-epoch budget. Decision rule (set ex ante) picks Pure Mamba — the backbone choice that carries into MambaFlow3D.

Architecture spec for single-image-to-3-D substituting Pure-Mamba state-space blocks for transformer attention (vs SparC3D / TRELLIS) and flow matching for DDPM sampling. PointNet++ → 10 Mamba blocks (d_model=256, d_state=128) → FM head → FoldingNet, 7.25 M parameters. Speed-up budget: 2–3× training, 5–12× end-to-end inference. ModelNet10 Phase-2 bring-up with the PointNet++ +3-channel trap diagnostic.

Reproduction of LTH14/JiT (ViT-B/16 + x-prediction, ImageNet-256) on 2 × RTX 3060 12 GB. Documents the hardware-adaptation table (1024 → 32 effective batch, 80 % → 55 % memory, ~1 h → ~6 h per epoch) and a five-failure debugging cascade (MKL ITT, ImageNet flat dirs, "hang" diagnostic, DataLoader OOM, pos_embed shape mismatch). Epoch-0 FID 281.24; crash at start of epoch 1 in sampling pass.

Diagnoses a structural failure mode of VAEs trained on binary hexplane occupancy: continuous-Gaussian distributional assumption is violated, reconstruction term converges to degenerate mean solution, posterior collapses regardless of KL schedule. Fix is at input representation, not loss schedule. Pivot to deterministic AE with continuous depth+normals features eliminates the failure.

Four-stage coarse-to-fine pipeline (block → shape → detail → compose) over five named primitives (box, cylinder, cone, sphere, wedge) with independent face/cap deformation. PartNeXt-trained via a Houdini Python SOP geometric classifier. ~1.3 cm Hausdorff on chair benchmark (2.6% of bounding diagonal). No executor gap — primitives are continuous parametric geometry.

N + 1 triplane sets — one per semantic part in a local frame, one coarser global for spatial context. Shared SDF decoder conditioned on part-id embedding. Structural fix to the EG3D / SparC3D inter-part occlusion failure mode. ~6× storage, ~2× inference, fidelity 4.8% → 1.9% Hausdorff on chair benchmark.

Inverts six axis-aligned orthographic depth maps into a single watertight 3D triangle mesh. Six-stage pipeline (foreground → cluster → contour → simplify → triangulate → stitch) compresses 352K input pixels to ~454 vertices on the sphere benchmark; minimal-polygon vs cloth-grid trade-off characterised.

Routing a single street-view photo through six orthographic elevations → marching-squares contours → depth clustering → earcut triangulation → watertight stitched mesh. Compresses 352K source pixels to ~454 vertices / ~332 triangles.

Seq2seq transformer mapping polylines with semantic boundary attributes to executable DSL programs that construct USD bridge scenes. 15-pair training corpus, dual-loss curriculum, analysis of the non-differentiable executor gap.

CNN system mapping freehand building sketches to CityEngine CGA grammar programs. 95–99% accuracy on synthetic data; domain-gap analysis between synthetic edges and human sketches; differentiable rendering gradient analysis.

Re-implementation of Merrell's graph grammar from scratch — half-edge boundary strings, 3D extension, Python prototype generating chairs / tables with detected symmetry rules. Path toward neural rule prediction outlined.