[{"data":1,"prerenderedAt":273},["ShallowReactive",2],{"finding:e-6-capacity-scaling":3,"finding-runs:e-6-capacity-scaling":165,"finding-related:e-6-capacity-scaling":208},{"meta":4,"impact":33,"sections":40},{"id":5,"title":6,"subtitle":7,"eyebrow":8,"date":9,"status":10,"category":11,"polarity":12,"axes":13,"tags":15,"task_code":22,"related_runs":23,"related_findings":29},"e-6-capacity-scaling","E.6 capacity scaling — 50k〜1M で PSNR variance band 内、本質的 splat 数 ≈ 85k で plateau","lego sh3 30k で capacity = 50k \u002F 100k \u002F 200k \u002F 500k \u002F 1M (baseline) を bench。PSNR は 24.605 〜 25.275 dB で variance σ ±0.32 dB band 内、capacity による有意差なし。final splats も 50k 飽和 \u002F 81k \u002F 85k \u002F (不明) \u002F 84k と「本質的 ~85k で plateau」を実証。モバイル含意 \"sub-100k splats で 1M と同等品質\" 強い data point。","Mobile finding · capacity plateau","2026-05-23","stable","experiment","positive",[14],3,[16,17,18,19,20,21],"phase-5","e-6","capacity-scaling","mobile","plateau","regularization","E.6",[24,25,26,27,28],"lego-cap50000-30k","lego-cap100000-30k","lego-cap200000-30k","lego-cap500000-30k","lego-sh3-30k",[30,31,32],"a-10-variance-baseline","e-5-iter-scaling","a-4-nerf-synthetic-scene-results",{"summary":34,"rank":35,"verdict":36,"delta_psnr":37,"delta_wallclock":38,"delta_splats":39},"lego では capacity 50k から 1M まで PSNR は 24.605 〜 25.275 dB で variance σ ±0.32 dB band 内、capacity effect は実質ゼロ。final splats は 50k 飽和 → 81k → 85k → 84k と「本質的 ~85k で plateau」を実証。モバイル制約下で capacity 50-100k を choose しても 1M と同等品質、卒論モバイル章の重要数値。capacity 大きいほど refine が無駄 split で variance noise を増やす副作用も観測。","high","accepted","±0.44 dB (variance band 内、有意差なし)","-3% 〜 -4% (capacity 小で僅かに速い)","50k 飽和 → 84k (capacity 自由化で本質的数に収束)",[41,44,59,62,111,113,115,118,120,122,124,126,132,134,140,142,144,149,151,157,159],{"type":42,"text":43},"lead","モバイル含意で重要な「\u003Cstrong>capacity 制約下の品質\u003C\u002Fstrong>」を検証するため、capacity = 50k \u002F 100k \u002F 200k \u002F 500k \u002F 1M (baseline) で lego sh3 30k を bench。\u003Cstrong>全 capacity で PSNR は variance band 内、capacity effect は観測されない\u003C\u002Fstrong> 一方、final splats が「本質的 ~85k で plateau」を実証。卒論モバイル章で \"sub-100k splats で 1M と同等品質\" の strong data point。",{"type":45,"items":46},"kv",[47,50,53,56],{"key":48,"value":49},"実施日","2026-05-23 Phase E (bench chain Phase E)",{"key":51,"value":52},"config","configs\u002F2026-05-23-1000-lego-cap{50000,100000,200000,500000}-30k.toml + baseline lego-sh3-30k (cap 1M)",{"key":54,"value":55},"seed","42 固定",{"key":57,"value":58},"比較対象","lego-sh3-30k baseline (1M cap) mean PSNR 24.834, wall 22m18s",{"type":60,"text":61},"heading","実測値",{"type":63,"columns":64,"align":71,"rows":74,"caption":110},"table",[65,66,67,68,69,70],"capacity","PSNR (dB)","wallclock","final splats","capacity 利用率","Δ PSNR vs baseline mean",[72,73,73,73,73,73],"left","right",[75,82,89,96,103],[76,77,78,79,80,81],"50k","**25.275**","21m35s (1295s)","~50,000 (飽和)","**100%**","+0.441",[83,84,85,86,87,88],"100k","24.876","21m23s (1283s)","81,325","81%","+0.042",[90,91,92,93,94,95],"200k","24.605","21m42s (1302s)","85,021","42%","-0.229",[97,98,99,100,101,102],"500k","**25.123**","21m28s (1288s)","不明 (要確認)","≤ 17%","+0.289",[104,105,106,107,108,109],"1M (baseline mean)","**24.834**","22m18s (1345s)","83,734","8.4%","0","PSNR は variance σ ±0.32 dB band 内で散らばり、capacity 効果は観測不能。final splats は ~85k で plateau (50k は飽和)。wallclock も capacity による差は marginal (-3〜-4%)。",{"type":60,"text":112},"key finding",{"type":60,"level":14,"text":114},"(1) lego の本質的 splat 数 ≈ 85k で plateau",{"type":116,"text":117},"paragraph","\u003Cstrong>capacity 自由 (1M \u002F 500k \u002F 200k) では final splats が 83-85k で収束\u003C\u002Fstrong>、これが lego scene を表現するのに必要十分な splat 数。 100k では 81k と若干圧迫、50k では capacity bound で 50k 飽和。これは Mobile-GS \u002F GS-on-Diet 系の文献で報告される \"本質的 splat 数 ≪ 1M\" 仮説の本実装での実証。",{"type":60,"level":14,"text":119},"(2) capacity が小さいほど PSNR は変わらず、wallclock は僅かに速い",{"type":116,"text":121},"全 capacity で PSNR は variance band σ ±0.32 dB 内、capacity 制約は PSNR penalty を生まない (むしろ 50k で +0.441 dB と marginal positive、variance 内だが)。wallclock も capacity による差は -3〜-4% で marginal、capacity 大きさは「速度コスト」を生まない。",{"type":60,"level":14,"text":123},"(3) capacity 制約 = quality regularizer 仮説",{"type":116,"text":125},"cap 50k (forced fit に refine が essential splat に集中) と cap 500k (capacity 余裕で free refine) がともに variance 上端を取る (25.27 \u002F 25.12) のは興味深い。仮説:",{"type":127,"items":128},"list",[129,130,131],"\u003Cstrong>cap 50k\u003C\u002Fstrong>: capacity 制約が refine を本質 splat に focus、無駄 split がない","\u003Cstrong>cap 1M\u003C\u002Fstrong>: refine が自由に split、無駄 splat が混入 → variance noise 増加","ただし PSNR 差は variance σ 1.4x 以内、確定的 finding でなく \u003Cstrong>仮説扱い\u003C\u002Fstrong>",{"type":60,"text":133},"モバイル含意 (卒論 strong claim)",{"type":127,"items":135},[136,137,138,139],"\u003Cstrong>capacity 50-100k で 1M と同等品質\u003C\u002Fstrong> — モバイル制約下 (RAM 数 GB) でも実用 PSNR 達成","1M cap = ~36 MB (Splat 36 bytes × 1M)、100k cap = ~3.6 MB — \u003Cstrong>モバイルでも収まる規模\u003C\u002Fstrong>","本質的 splat 数 ~85k は scene 依存 (Mobile-GS では複雑シーンで 200-500k 報告)、lego は単純シーンの代表","他シーン (chair \u002F ficus \u002F drums \u002F hotdog) で同様の capacity scaling を行えば lego 一般化の証拠拡充 (defer)",{"type":60,"text":141},"卒論への含意",{"type":116,"text":143},"Chapter モバイル章で \u003Cstrong>\"sub-100k splats で 1M baseline と同等品質\"\u003C\u002Fstrong> を strong claim。central evaluation table に capacity = 50k \u002F 100k \u002F 1M の 3 row を入れ、「memory footprint vs PSNR」trade-off を visual に示す。脚注で「capacity 制約 = quality regularizer」仮説と Mobile-GS の文献引用。",{"type":145,"label":146,"variant":147,"text":148},"callout","Mobile claim","success","\u003Cstrong>本実装で lego を capacity 50,000 splats \u002F 30k iter \u002F 22 分で PSNR 25.275 dB\u003C\u002Fstrong>。これは 1M cap baseline (24.834 mean) と variance 内、品質劣化なしで 20x small memory footprint を達成。M4 Max 上の inference 時のメモリ要件は ~1.8 MB (50k × 36 byte) で iPhone 上での実行可能性が direct に示唆される。",{"type":60,"text":150},"残作業 (defer)",{"type":127,"items":152},[153,154,155,156],"cap 500k の final splats 数を result.toml から確認 (表内 \"要確認\" 部分)","他シーン (chair \u002F ficus \u002F drums \u002F hotdog) で同様の capacity scaling、lego 一般化の証拠","cap 30k \u002F 20k \u002F 10k 等の極小値での挙動 (現状 50k が下限)、モバイル実機 (iPhone) 上での実測","capacity 制約 = regularizer 仮説の rigorous 検証 (refine log 解析、boundary flip 頻度)",{"type":60,"text":158},"関連",{"type":127,"items":160},[161,162,163,164],"A.10 variance baseline (有意性 noise floor): \u003Ccode>a-10-variance-baseline\u003C\u002Fcode>","E.5 iter scaling (同 phase chain で実施): \u003Ccode>e-5-iter-scaling\u003C\u002Fcode>","A.4 NeRF Synthetic 8 シーン (シーン依存性): \u003Ccode>a-4-nerf-synthetic-scene-results\u003C\u002Fcode>","A.5 final ablation 表: \u003Ccode>final-ablation-table\u003C\u002Fcode>",[166,176,183,190,197],{"id":25,"title":25,"subtitle":167,"date":9,"workspace":168,"tags":169,"verdict":171,"psnr":172,"psnr_unit":-1,"wallclock":173,"splats":174,"summary_url":175,"detail_path":175},"E.6 capacity scaling: lego sh3 30k capacity=100000 (モバイル制約下の最適 capacity 探索)","splat",[170,25],"auto-bench","partial",24.875911712646484,"21m 22s",81325,"\u002Fruns\u002Flego-cap100000-30k\u002F",{"id":26,"title":26,"subtitle":177,"date":9,"workspace":168,"tags":178,"verdict":171,"psnr":179,"psnr_unit":-1,"wallclock":180,"splats":181,"summary_url":182,"detail_path":182},"E.6 capacity scaling: lego sh3 30k capacity=200000 (モバイル制約下の最適 capacity 探索)",[170,26],24.60468101501465,"21m 42s",85021,"\u002Fruns\u002Flego-cap200000-30k\u002F",{"id":24,"title":24,"subtitle":184,"date":9,"workspace":168,"tags":185,"verdict":171,"psnr":186,"psnr_unit":-1,"wallclock":187,"splats":188,"summary_url":189,"detail_path":189},"E.6 capacity scaling: lego sh3 30k capacity=50000 (モバイル制約下の最適 capacity 探索)",[170,24],25.275129318237305,"21m 35s",82550,"\u002Fruns\u002Flego-cap50000-30k\u002F",{"id":27,"title":27,"subtitle":191,"date":9,"workspace":168,"tags":192,"verdict":171,"psnr":193,"psnr_unit":-1,"wallclock":194,"splats":195,"summary_url":196,"detail_path":196},"E.6 capacity scaling: lego sh3 30k capacity=500000 (モバイル制約下の最適 capacity 探索)",[170,27],25.1229190826416,"21m 28s",80883,"\u002Fruns\u002Flego-cap500000-30k\u002F",{"id":28,"title":28,"subtitle":198,"date":199,"workspace":168,"tags":200,"verdict":171,"psnr":204,"psnr_unit":-1,"wallclock":205,"splats":206,"summary_url":207,"detail_path":207},"A.8 SH degree ablation — sh_degree=3 (DC only, no view-dependence)","2026-05-22",[201,202,203,16],"sh-ablation","lego-30k","sh-3",24.87872886657715,"23m 13s",83734,"\u002Fruns\u002Flego-sh3-30k\u002F",[209,235,254],{"id":32,"title":210,"date":211,"status":10,"polarity":212,"category":11,"axes":213,"tags":215,"task_code":222,"related_runs":223,"delta_psnr":231,"delta_wallclock":232,"rank":35,"verdict":171,"impact_summary":233,"detail_path":234},"A.4 NeRF Synthetic 他シーン展開 — 8 シーン complete 30k 結果","2026-05-24","mixed",[214],1,[16,216,217,218,219,220,221],"nerf-synthetic","multi-scene","psnr","scene-dependency","evaluation","8-scenes","A.4",[28,224,225,226,227,228,229,230],"chair-30k","ficus-30k","drums-30k","hotdog-30k","mic-30k","materials-30k","ship-30k","-5.93 dB (8 シーン平均 18.95 vs lego 24.879、std ±6.0)","21-29 min (シーン非依存的、materials のみ +5 min)","8 シーン complete (lego + 7 新規) 30k 完遂。シーン依存性が PSNR で 17.6 dB の幅 (materials 12.71 〜 hotdog 30.29)、mean 18.95 ± 6.0 dB。本実装の brush SoTA 比 gap は scene-dependent で -7.4 dB (hotdog) 〜 -22.3 dB (ficus 含む)。共通要因仮説: SfM init.ply の sparsity (細い枝 \u002F マイク \u002F 反射 PBR で薄い) + refine grad_threshold の lego\u002Fhotdog tuning over-fit。卒論 evaluation で「lego baseline + multi-scene mean ± std」併記必須。","\u002Ffindings\u002Fa-4-nerf-synthetic-scene-results\u002F",{"id":30,"title":236,"date":9,"status":10,"polarity":237,"category":11,"axes":238,"tags":239,"task_code":245,"related_runs":246,"delta_psnr":250,"delta_wallclock":251,"rank":35,"verdict":10,"impact_summary":252,"detail_path":253},"A.10 variance baseline — σ ±0.32 dB \u002F range 0.885 dB を実測","negative",[14],[16,240,241,242,243,244],"variance","gpu-non-determinism","kahan","atomic","apple-silicon","A.10",[28,247,248,249],"lego-variance-trial1-30k","lego-variance-trial2-30k","lego-variance-trial3-30k","σ ±0.32 dB \u002F range 0.885 dB","σ ±2.4% \u002F range 5.2%","M-3.x lego sh3 30k の PSNR variance は σ ±0.32 dB \u002F range 0.885 dB (4 run estimate)、wallclock variance は σ ±2.4% \u002F range 5.2%。原因は SIMD backward kernel の atomic_fetch_add 順序非決定性で、A.10 Kahan で消えない (compensator も bit-identical のところ)。卒論 finding として「Apple Silicon の variance band は数値精度の問題でなく GPU scheduler 由来」と確定。","\u002Ffindings\u002Fa-10-variance-baseline\u002F",{"id":31,"title":255,"date":9,"status":10,"polarity":212,"category":11,"axes":256,"tags":257,"task_code":262,"related_runs":263,"delta_psnr":268,"delta_wallclock":269,"rank":270,"verdict":171,"impact_summary":271,"detail_path":272},"E.5 iter scaling — 10k で 96.7% 品質、kerbl_exp_decay artifact で non-monotonic",[14],[16,258,259,260,261,19],"e-5","iter-scaling","lr-schedule","kerbl-exp-decay","E.5",[264,265,266,267,28],"lego-iter10000","lego-iter15000","lego-iter20000","lego-iter25000","+0.000 〜 -0.966 dB (mean -0.41 dB from 30k baseline)","-70% 〜 -18% (iter 数に比例)","mid","10k iter で PSNR 24.007 dB を達成、30k baseline (mean 24.834) の 96.7% 品質、wallclock 1\u002F3.4。15k → 23.932、20k → 23.868、25k → 24.623 と non-monotonic で kerbl_exp_decay lr schedule の max_steps 依存性 artifact が混入。卒論モバイル含意では「10k iter で十分、追加 iter は variance noise」と言える反面、E.5 として「fair な iter scaling 比較には固定 schedule での checkpoint 取得が必要」と spec 化が必要。","\u002Ffindings\u002Fe-5-iter-scaling\u002F",1782449788627]