分析済みURL
https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression
計測: 一昨日
AI-Readyスコア
86
/ 100
良好
/ 100
トークン削減量
HTMLトークン
10.478
Markdownトークン
2779
削減率
73%
スコア内訳
アクセシビリティ
88/100
AI発見可能性
69/100
構造化データ
93/100
セマンティックHTML
100/100
コンテンツ効率
86/100
新興プロトコル
6件中0件検出AIエージェントが探すwell-knownエンドポイント。検出されればエージェントが自動的にあなたのサービスを発見・接続できます。
-
OAuth Protected Resource RFC 9728
/.well-known/oauth-protected-resource -
OAuth Discovery RFC 8414
/.well-known/oauth-authorization-server -
MCP Server Card SEP-1649 draft
/.well-known/mcp/server-card.json -
A2A Agent Card A2A v1.0
/.well-known/agent-card.json -
API Catalog RFC 9727
/.well-known/api-catalog -
Agent Skills index Discovery RFC v0.2.0 draft
/.well-known/agent-skills/index.json
この数字は動きます。 モニタリングは開発中です。リストに登録すると公開時にお知らせします。
リストに登録されました！サービス開始時にお知らせします。
計測結果 No Markdown for Agents support detected
サイトがMarkdown for Agentsに対応していません。このCloudflare標準により、AIエージェントがmarkdown形式でコンテンツをリクエストでき、トークン使用量を約80%削減できます。
実装方法
以下の1つ以上を実装してください：(1) Accept: text/markdownにmarkdownコンテンツで応答。(2) .md URL（例：/page.md）を提供。(3) <link rel="alternate" type="text/markdown">タグを追加。(4) markdown検出用のLink HTTPヘッダーを追加。
コーディングエージェントに貼り付けて修正させる
計測結果 2/3 OG tags present
Open Graphタグが不足または不完全です。OGタグはAIエージェント（およびソーシャルプラットフォーム）がページのタイトル、説明、画像を理解するのに役立ちます。
実装方法
ページの<head>にog:title、og:description、og:imageメタタグを追加してください。
コーディングエージェントに貼り付けて修正させる
✓✓ Beats tuned baseline 2026
## Residual-only unbiased gradient compression
Usefulness7/10
Difficulty4/10
Novelty5/10
Source paper: [Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization](https://arxiv.org/abs/2608.06563) [arXiv:2608.06563](https://arxiv.org/abs/2608.06563) ⓘ · analyzed Aug 31, 2026
AI-generated research hypothesis, automatically tested. Not peer-reviewed.
## Idea description
Compress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control variate tracks the client gradient, the residual shrinks and the same communication budget produces less compression noise than direct gradient quantization.
## Formulas
$$\\mathbb E\\left\[g^t\\mid x^t,y^t\\right\]=\\nabla f(x^t).$$
$$\\widehat g\_m^t=h\_m^t+\\mathcal Q\\left(g\_m^t-h\_m^t\\right),\\qquad \\mathbb E\[\\mathcal Q(v)\]=v,\\qquad \\mathbb E\\|\\mathcal Q(v)-v\\|^2\\leq\\omega\\|v\\|^2.$$
$$\\mathbb E\_{\\mathcal Q}\\left\[\\|\\widehat g\_t\\|^2\\right\]\\leq\\frac{\\omega}{C^2}\\sum\_{m\\in S^t}\\|g\_m^t-h\_m^t\\|^2+\\left\\|\\frac{1}{C}\\sum\_{m\\in S^t}g\_m^t\\right\\|^2.$$
$$x^{t+1}=x^t-\\eta\\widehat g\_t,\\qquad h\_m^{t+1}=(1-\\alpha)h\_m^t+\\alpha g\_m^t.$$
## Mathematical statement
The method uses an unbiased compressor \\(\\mathcal Q\\) with variance parameter \\(\\omega\\), satisfying \\(\\mathbb E\[\\mathcal Q(v)\]=v\\) and typically \\(\\mathbb E\\|\\mathcal Q(v)-v\\|^2\\leq\\omega\\|v\\|^2\\). For client gradients \\(g\_m^t\\) and stored control variates \\(h\_m^t\\), the compressed estimator is \\(\\widehat g\_m^t=h\_m^t+\\mathcal Q(g\_m^t-h\_m^t)\\). The paper's second-moment calculation gives \\(\\mathbb E\_{\\mathcal Q}\\|\\widehat g\_t\\|^2\\leq\\frac{\\omega}{C^2}\\sum\_{m\\in S^t}\\|g\_m^t-h\_m^t\\|^2+\\|\\frac{1}{C}\\sum\_{m\\in S^t}g\_m^t\\|^2\\), where \\(S^t\\) is the selected client set, \\(C=|S^t|\\), and \\(\\widehat g\_t=C^{-1}\\sum\_{m\\in S^t}\\widehat g\_m^t\\). Therefore compression noise depends on residual norms rather than full-gradient norms. The control variate should be refreshed after communication or with an exponential update so that \\(h\_m^t\\) tracks the local gradient.
## Implementation notes
Integrate this at the client-to-server gradient or model-delta transmission operation in federated learning, or at the worker-to-worker all-reduce buffer in distributed training. Each client stores a full-precision vector \\(h\_m\\) with the same shape as the transmitted gradient and uses an unbiased compressor, such as stochastic uniform quantization, randomized sparsification, or unbiased blockwise int8 quantization. For each local minibatch, compute \\(g\_m=\\nabla f\_m(x\_m)\\), form the residual \\(r\_m=g\_m-h\_m\\), transmit \\(q\_m=\\mathcal Q(r\_m)\\), and reconstruct \\(\\widehat g\_m=h\_m+q\_m\\) at the server. Aggregate \\(\\widehat g=C^{-1}\\sum\_{m\\in S}\\widehat g\_m\\), update the global model \\(x\\leftarrow x-\\eta\\widehat g\\), and refresh memory with \\(h\_m\\leftarrow(1-\\alpha)h\_m+\\alpha g\_m\\) whenever client \\(m\\) participates. Use \\(\\alpha=1\\) after a full synchronization and \\(\\alpha\\in\[0.05,0.2\]\\) for sparse participation. The paper's bound predicts compression noise proportional to \\(\\sum\_m\\|g\_m-h\_m\\|^2\\), not \\(\\sum\_m\\|g\_m\\|^2\\); log both quantities to verify this mechanism. If exact unbiased stochastic quantization is inconvenient, implement per-block stochastic rounding and measure its empirical bias. First test on FEMNIST or CIFAR-10 with 16 simulated non-IID clients, comparing uncompressed FedAvg, direct 8-bit gradient compression, and residual-only 8-bit compression at identical transmitted bytes. Use a small CNN or ResNet-18 and report validation accuracy versus communicated bytes, gradient variance, and client-memory overhead. Success means lower gradient variance and at least 1.5x fewer bytes to reach the same accuracy, with no systematic compression bias and no divergence under client heterogeneity.
## Verification
Beats tuned baseline
Stage 1 — Mechanism check agent confidence 9/10
Built an unbiased random-k residual compressor with persistent client control variates and a deterministic heterogeneous federated quadratic experiment. The math checks passed: empirical compressor noise was within 0.09% of the exact variance, residual noise ratios matched squared residual/full-gradient ratios within 0.24%, and EMA steady-state residual norms matched ||u||/alpha to numerical precision across alpha=1.0 to 0.05. In the toy federated task, residual compression used 103,680 bytes and reached 3.7e-13 final loss, essentially matching uncompressed training, while direct compression at the same bytes plateaued at 0.753 loss with much larger noise; this is a clear mechanism and toy-task win, not evidence of general deep-learning superiority.
Agent confidence
9/10
Baseline
Direct random-k compression: final loss 0.752743, mean last-50 loss 0.764952, mean per-client compression noise 580.811, 103680 bytes.
Idea
Residual-only random-k with alpha=0.2: final loss 3.7267e-13, mean last-50 loss 1.7733e-10, mean per-client compression noise 7.8378e-10, 103680 bytes. Math: variance relative error 0.00087; residual-ratio max absolute error 0.00230; EMA residual relative error <=1.3e-13.
**Limitations:** Only a synthetic full-participation quadratic federated problem was tested; no FEMNIST/CIFAR-10, CNN, partial client participation, minibatch gradient noise, wall-clock communication implementation, true packed index/scale encoding, or multi-seed confidence intervals were evaluated. The toy compressor uses random-k sparsification rather than 8-bit stochastic quantization, and the stored control variate remains full precision.
**How to run:** `python3 experiment.py`
Stage 2 — Benchmark vs. tuned baseline Sep 1, 2026
Beats the tuned baseline by 61.2% (p=0.0327, wins 6 / 8 paired seeds; metric: lower is better).
Benchmark
Tabular regression (Friedman)
Model
mlp\_tiny
Paired seeds
8
Baseline mean
20.3734
Idea mean
7.9047
Effect (Δ)
\-12.4686 (−61.2%; negative = idea better)
Wins
6 / 8 paired seeds
p-value
0.0327 (permutation test, 20 000 shuffles)
Smallest detectable effect
±142.7%
Mechanism
Confirmed ✓
Practical effect
Helps
Baseline tuning
swept over 3 configs
**Limitations:**
Only the built-in tabular track and small mlp\_tiny model were tested. Random-k sparse tensors proxy communication rather than implementing packed transmission or stochastic int8; federated client participation, wall-clock bytes, control-variate memory overhead, and larger neural models were not tested. One baseline seed is a large outlier, so generalization beyond this benchmark is uncertain.
**How to run:** `python3 run_stage2.py`
Verdict computed by deterministic test code from paired-seed statistics — not by the language model.
Stage 2 — Benchmark Sep 1, 2026 latest Worked ✓
Agent confidence: 7/10
Residual-only unbiased random-k gradient compression was evaluated on the registered tabular track with the shared mlp\_tiny architecture. It achieved lower mean test MSE than the tuned direct-compression baseline (7.9047 vs 20.3734), with paired delta -12.4686 and permutation p=0.0327; the trained-model mechanism prediction was confirmed within 4.49% relative error.
Baseline
mean test MSE 20.37335467338562, std 33.97063256083515, best lr 0.0035, k\_fraction 0.125
Idea
mean test MSE 7.904710650444031, std 1.6384066086211326, lr 0.0035, alpha 0.2, k\_fraction 0.125
Benchmark result
Beats the tuned baseline by 61.2% (p=0.0327, wins 6 / 8 paired seeds; metric: lower is better).
Benchmark
Tabular regression (Friedman)
Model
mlp\_tiny
Paired seeds
8
Baseline mean
20.3734
Idea mean
7.9047
Effect (Δ)
\-12.4686 (−61.2%; negative = idea better)
Wins
6 / 8 paired seeds
p-value
0.0327 (permutation test, 20 000 shuffles)
Smallest detectable effect
±142.7%
Mechanism
Confirmed ✓
Practical effect
Helps
Baseline tuning
swept over 3 configs
**Limitations:**
Only the built-in tabular track and small mlp\_tiny model were tested. Random-k sparse tensors proxy communication rather than implementing packed transmission or stochastic int8; federated client participation, wall-clock bytes, control-variate memory overhead, and larger neural models were not tested. One baseline seed is a large outlier, so generalization beyond this benchmark is uncertain.
**How to run:** `python3 run_stage2.py`
## Artifacts
- 📊 [bench\_report.json](https://synthcore.org/code/721/bench_report.json) 6.6 KB [View](https://synthcore.org/code/721/bench_report.json) [Raw JSON](https://synthcore.org/raw/721/bench_report.json)
- 🐍 [experiment.py](https://synthcore.org/code/721/experiment.py) 5.1 KB [View](https://synthcore.org/code/721/experiment.py) [Raw JSON](https://synthcore.org/raw/721/experiment.py)
- 📄 [report.md](https://synthcore.org/code/721/report.md) 1.9 KB [View](https://synthcore.org/code/721/report.md)
- 📄 [report\_bench\_2026-09-01T010911.md](https://synthcore.org/code/721/report_bench_2026-09-01T010911.md) 3.7 KB [View](https://synthcore.org/code/721/report_bench_2026-09-01T010911.md)
- 📊 [results.json](https://synthcore.org/code/721/results.json) 2.7 KB [View](https://synthcore.org/code/721/results.json) [Raw JSON](https://synthcore.org/raw/721/results.json)
- 🐍 [run\_stage2.py](https://synthcore.org/code/721/run_stage2.py) 6.8 KB [View](https://synthcore.org/code/721/run_stage2.py) [Raw JSON](https://synthcore.org/raw/721/run_stage2.py)
Residual-only unbiased gradient compression — SynthCore [Skip to content](https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression#main)
[SynthCore](https://synthcore.org/)
✓✓ Beats tuned baseline 2026
# Residual-only unbiased gradient compression
Usefulness7/10
Difficulty4/10
Novelty5/10
[Memory](https://synthcore.org/category/memory) [Memory](https://synthcore.org/tag/solves/memory "What it solves")[Speedup](https://synthcore.org/tag/solves/speedup "What it solves")[Scalability](https://synthcore.org/tag/solves/scalability "What it solves")[Optimizer](https://synthcore.org/tag/ml/optimizer "ML area")[Federated](https://synthcore.org/tag/ml/federated "ML area")[Quantization](https://synthcore.org/tag/ml/quantization "ML area")[Memory](https://synthcore.org/tag/ml/memory "ML area")[Probability](https://synthcore.org/tag/math/probability "Math field")[Stochastic processes](https://synthcore.org/tag/math/stochastic-processes "Math field")[Optimization](https://synthcore.org/tag/math/optimization "Math field")[Linear algebra](https://synthcore.org/tag/math/linear-algebra "Math field")
Source paper: [Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization](https://arxiv.org/abs/2608.06563) [arXiv:2608.06563](https://arxiv.org/abs/2608.06563) ⓘ · analyzed Aug 31, 2026
AI-generated research hypothesis, automatically tested. Not peer-reviewed.
## Idea description
Compress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control variate tracks the client gradient, the residual shrinks and the same communication budget produces less compression noise than direct gradient quantization.
## Formulas
$$\\mathbb E\\left\[g^t\\mid x^t,y^t\\right\]=\\nabla f(x^t).$$
$$\\widehat g\_m^t=h\_m^t+\\mathcal Q\\left(g\_m^t-h\_m^t\\right),\\qquad \\mathbb E\[\\mathcal Q(v)\]=v,\\qquad \\mathbb E\\|\\mathcal Q(v)-v\\|^2\\leq\\omega\\|v\\|^2.$$
$$\\mathbb E\_{\\mathcal Q}\\left\[\\|\\widehat g\_t\\|^2\\right\]\\leq\\frac{\\omega}{C^2}\\sum\_{m\\in S^t}\\|g\_m^t-h\_m^t\\|^2+\\left\\|\\frac{1}{C}\\sum\_{m\\in S^t}g\_m^t\\right\\|^2.$$
$$x^{t+1}=x^t-\\eta\\widehat g\_t,\\qquad h\_m^{t+1}=(1-\\alpha)h\_m^t+\\alpha g\_m^t.$$
## Mathematical statement
The method uses an unbiased compressor \\(\\mathcal Q\\) with variance parameter \\(\\omega\\), satisfying \\(\\mathbb E\[\\mathcal Q(v)\]=v\\) and typically \\(\\mathbb E\\|\\mathcal Q(v)-v\\|^2\\leq\\omega\\|v\\|^2\\). For client gradients \\(g\_m^t\\) and stored control variates \\(h\_m^t\\), the compressed estimator is \\(\\widehat g\_m^t=h\_m^t+\\mathcal Q(g\_m^t-h\_m^t)\\). The paper's second-moment calculation gives \\(\\mathbb E\_{\\mathcal Q}\\|\\widehat g\_t\\|^2\\leq\\frac{\\omega}{C^2}\\sum\_{m\\in S^t}\\|g\_m^t-h\_m^t\\|^2+\\|\\frac{1}{C}\\sum\_{m\\in S^t}g\_m^t\\|^2\\), where \\(S^t\\) is the selected client set, \\(C=|S^t|\\), and \\(\\widehat g\_t=C^{-1}\\sum\_{m\\in S^t}\\widehat g\_m^t\\). Therefore compression noise depends on residual norms rather than full-gradient norms. The control variate should be refreshed after communication or with an exponential update so that \\(h\_m^t\\) tracks the local gradient.
## Implementation notes
Integrate this at the client-to-server gradient or model-delta transmission operation in federated learning, or at the worker-to-worker all-reduce buffer in distributed training. Each client stores a full-precision vector \\(h\_m\\) with the same shape as the transmitted gradient and uses an unbiased compressor, such as stochastic uniform quantization, randomized sparsification, or unbiased blockwise int8 quantization. For each local minibatch, compute \\(g\_m=\\nabla f\_m(x\_m)\\), form the residual \\(r\_m=g\_m-h\_m\\), transmit \\(q\_m=\\mathcal Q(r\_m)\\), and reconstruct \\(\\widehat g\_m=h\_m+q\_m\\) at the server. Aggregate \\(\\widehat g=C^{-1}\\sum\_{m\\in S}\\widehat g\_m\\), update the global model \\(x\\leftarrow x-\\eta\\widehat g\\), and refresh memory with \\(h\_m\\leftarrow(1-\\alpha)h\_m+\\alpha g\_m\\) whenever client \\(m\\) participates. Use \\(\\alpha=1\\) after a full synchronization and \\(\\alpha\\in\[0.05,0.2\]\\) for sparse participation. The paper's bound predicts compression noise proportional to \\(\\sum\_m\\|g\_m-h\_m\\|^2\\), not \\(\\sum\_m\\|g\_m\\|^2\\); log both quantities to verify this mechanism. If exact unbiased stochastic quantization is inconvenient, implement per-block stochastic rounding and measure its empirical bias. First test on FEMNIST or CIFAR-10 with 16 simulated non-IID clients, comparing uncompressed FedAvg, direct 8-bit gradient compression, and residual-only 8-bit compression at identical transmitted bytes. Use a small CNN or ResNet-18 and report validation accuracy versus communicated bytes, gradient variance, and client-memory overhead. Success means lower gradient variance and at least 1.5x fewer bytes to reach the same accuracy, with no systematic compression bias and no divergence under client heterogeneity.
## Verification
Beats tuned baseline
Stage 1 — Mechanism check agent confidence 9/10
Built an unbiased random-k residual compressor with persistent client control variates and a deterministic heterogeneous federated quadratic experiment. The math checks passed: empirical compressor noise was within 0.09% of the exact variance, residual noise ratios matched squared residual/full-gradient ratios within 0.24%, and EMA steady-state residual norms matched ||u||/alpha to numerical precision across alpha=1.0 to 0.05. In the toy federated task, residual compression used 103,680 bytes and reached 3.7e-13 final loss, essentially matching uncompressed training, while direct compression at the same bytes plateaued at 0.753 loss with much larger noise; this is a clear mechanism and toy-task win, not evidence of general deep-learning superiority.
Agent confidence
9/10
Baseline
Direct random-k compression: final loss 0.752743, mean last-50 loss 0.764952, mean per-client compression noise 580.811, 103680 bytes.
Idea
Residual-only random-k with alpha=0.2: final loss 3.7267e-13, mean last-50 loss 1.7733e-10, mean per-client compression noise 7.8378e-10, 103680 bytes. Math: variance relative error 0.00087; residual-ratio max absolute error 0.00230; EMA residual relative error <=1.3e-13.
**Limitations:** Only a synthetic full-participation quadratic federated problem was tested; no FEMNIST/CIFAR-10, CNN, partial client participation, minibatch gradient noise, wall-clock communication implementation, true packed index/scale encoding, or multi-seed confidence intervals were evaluated. The toy compressor uses random-k sparsification rather than 8-bit stochastic quantization, and the stored control variate remains full precision.
**How to run:** `python3 experiment.py`
Stage 2 — Benchmark vs. tuned baseline Sep 1, 2026
Beats the tuned baseline by 61.2% (p=0.0327, wins 6 / 8 paired seeds; metric: lower is better).
Benchmark
Tabular regression (Friedman)
Model
mlp\_tiny
Paired seeds
8
Baseline mean
20.3734
Idea mean
7.9047
Effect (Δ)
\-12.4686 (−61.2%; negative = idea better)
Wins
6 / 8 paired seeds
p-value
0.0327 (permutation test, 20 000 shuffles)
Smallest detectable effect
±142.7%
Mechanism
Confirmed ✓
Practical effect
Helps
Baseline tuning
swept over 3 configs
**Limitations:**
Only the built-in tabular track and small mlp\_tiny model were tested. Random-k sparse tensors proxy communication rather than implementing packed transmission or stochastic int8; federated client participation, wall-clock bytes, control-variate memory overhead, and larger neural models were not tested. One baseline seed is a large outlier, so generalization beyond this benchmark is uncertain.
**How to run:** `python3 run_stage2.py`
Verdict computed by deterministic test code from paired-seed statistics — not by the language model.
Stage 2 — Benchmark Sep 1, 2026 latest Worked ✓
Agent confidence: 7/10
Residual-only unbiased random-k gradient compression was evaluated on the registered tabular track with the shared mlp\_tiny architecture. It achieved lower mean test MSE than the tuned direct-compression baseline (7.9047 vs 20.3734), with paired delta -12.4686 and permutation p=0.0327; the trained-model mechanism prediction was confirmed within 4.49% relative error.
Baseline
mean test MSE 20.37335467338562, std 33.97063256083515, best lr 0.0035, k\_fraction 0.125
Idea
mean test MSE 7.904710650444031, std 1.6384066086211326, lr 0.0035, alpha 0.2, k\_fraction 0.125
Benchmark result
Beats the tuned baseline by 61.2% (p=0.0327, wins 6 / 8 paired seeds; metric: lower is better).
Benchmark
Tabular regression (Friedman)
Model
mlp\_tiny
Paired seeds
8
Baseline mean
20.3734
Idea mean
7.9047
Effect (Δ)
\-12.4686 (−61.2%; negative = idea better)
Wins
6 / 8 paired seeds
p-value
0.0327 (permutation test, 20 000 shuffles)
Smallest detectable effect
±142.7%
Mechanism
Confirmed ✓
Practical effect
Helps
Baseline tuning
swept over 3 configs
**Limitations:**
Only the built-in tabular track and small mlp\_tiny model were tested. Random-k sparse tensors proxy communication rather than implementing packed transmission or stochastic int8; federated client participation, wall-clock bytes, control-variate memory overhead, and larger neural models were not tested. One baseline seed is a large outlier, so generalization beyond this benchmark is uncertain.
**How to run:** `python3 run_stage2.py`
## Artifacts
[⬇ Download all as ZIP](https://synthcore.org/download/721) 6 files · code, reports and structured results
- 📊 [bench\_report.json](https://synthcore.org/code/721/bench_report.json) 6.6 KB [View](https://synthcore.org/code/721/bench_report.json) [Raw JSON](https://synthcore.org/raw/721/bench_report.json)
- 🐍 [experiment.py](https://synthcore.org/code/721/experiment.py) 5.1 KB [View](https://synthcore.org/code/721/experiment.py) [Raw JSON](https://synthcore.org/raw/721/experiment.py)
- 📄 [report.md](https://synthcore.org/code/721/report.md) 1.9 KB [View](https://synthcore.org/code/721/report.md)
- 📄 [report\_bench\_2026-09-01T010911.md](https://synthcore.org/code/721/report_bench_2026-09-01T010911.md) 3.7 KB [View](https://synthcore.org/code/721/report_bench_2026-09-01T010911.md)
- 📊 [results.json](https://synthcore.org/code/721/results.json) 2.7 KB [View](https://synthcore.org/code/721/results.json) [Raw JSON](https://synthcore.org/raw/721/results.json)
- 🐍 [run\_stage2.py](https://synthcore.org/code/721/run_stage2.py) 6.8 KB [View](https://synthcore.org/code/721/run_stage2.py) [Raw JSON](https://synthcore.org/raw/721/run_stage2.py)
このファイルをサーバーの/idea/1899/residual-only-unbiased-gradient-compression.mdとしてアップロードし、AIエージェントがページのクリーンなバージョンにアクセスできるようにしましょう。Accept: text/markdownコンテンツネゴシエーションを設定して自動的に配信することもできます。
推奨内容
# SynthCore > Compress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control variate tracks the client gradient, the residual shrinks and the same communication budget produces less compression noise than direct… ## Documentation - [report.md](https://synthcore.org/code/721/report.md) - [report_bench_2026-09-01T010911.md](https://synthcore.org/code/721/report_bench_2026-09-01T010911.md) ## Main - [Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization](https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression): Compress only the difference between the current client gradient and a persistent control variate, rather than compress… - [About](https://synthcore.org/about) - [SynthCore](https://synthcore.org/) - [Ideas](https://synthcore.org/ideas) - [Categories](https://synthcore.org/categories) - [Tags](https://synthcore.org/tags) - [Papers](https://synthcore.org/papers) - [API](https://synthcore.org/api) - [Memory](https://synthcore.org/category/memory) - [Memory](https://synthcore.org/tag/solves/memory)
完全なllms.txtにはドメイン全体の分析が必要です（近日公開）
このファイルをドメインのルートにhttps://synthcore.org/llms.txtとしてアップロードしてください。ChatGPT、Claude、PerplexityなどのAIエージェントはこのファイルを確認してサイト構造を理解します。
このサイトにはすでにllms.txtファイルがあります。
有効な形式# SynthCore
> Autonomous pipeline that extracts ML ideas from arXiv mathematics papers and empirically tests them (mechanism check, then benchmark vs tuned baseline over 8 paired seeds; verdicts computed by deterministic test code).
- Ideas: https://synthcore.org/ideas
- Verified ideas (beat a tuned baseline): https://synthcore.org/ideas?status=beats_baseline
- Mechanism-confirmed ideas: https://synthcore.org/ideas?status=mechanism_works
- About: https://synthcore.org/about
- Analyzed papers: https://synthcore.org/papers
- Categories: https://synthcore.org/categories
- Tags: https://synthcore.org/tags
- Structured data: /api/idea/{id}.json and JSON-LD on every idea page
- JSON API (filter and page the whole corpus programmatically, no rate limit): https://synthcore.org/api
Corpus: 8700 analyzed papers, 1845 ideas, 96 benchmark-verified.
Every idea is an AI-generated hypothesis, automatically tested. Not peer-reviewed.
## Benchmark-verified ideas (selection)
- [Derivative-conditioned fine-scale corrector](https://synthcore.org/idea/1850/derivative-conditioned-fine-scale-corrector) — usefulness 8/10, category architecture
- [Power-Balanced Modular Neural Block](https://synthcore.org/idea/1829/power-balanced-modular-neural-block) — usefulness 8/10, category architecture
- [Commutant-gated spectral loss](https://synthcore.org/idea/1815/commutant-gated-spectral-loss) — usefulness 8/10, category regularization
- [Active-Set Reduced Differentiable QP Layer](https://synthcore.org/idea/1778/active-set-reduced-differentiable-qp-layer) — usefulness 8/10, category optimization
- [Caustic-Aware Hamiltonian Feedback Layer](https://synthcore.org/idea/1777/caustic-aware-hamiltonian-feedback-layer) — usefulness 8/10, category dynamics
- [Jacobian Tube Training](https://synthcore.org/idea/1711/jacobian-tube-training) — usefulness 8/10, category dynamics
- [Zonotope-Bounded Latent State Space](https://synthcore.org/idea/1704/zonotope-bounded-latent-state-space) — usefulness 8/10, category dynamics
- [Stable Rotating-Memory State Space](https://synthcore.org/idea/1631/stable-rotating-memory-state-space) — usefulness 8/10, category architecture
- [Jacobian-Free Short-Trace Backpropagation](https://synthcore.org/idea/1624/jacobian-free-short-trace-backpropagation) — usefulness 8/10, category training
- [Directional Conformal Residual Sets for Neural Dynamics](https://synthcore.org/idea/1593/directional-conformal-residual-sets-for-neural-dynamics) — usefulness 8/10, category regularization
- [Heterogeneity-Calibrated Hopf RNN](https://synthcore.org/idea/1527/heterogeneity-calibrated-hopf-rnn) — usefulness 8/10, category dynamics
- [Trajectory-Certified Contractive RNN](https://synthcore.org/idea/1436/trajectory-certified-contractive-rnn) — usefulness 8/10, category dynamics
- [Defect-and-Jacobian Residual Dynamics](https://synthcore.org/idea/1358/defect-and-jacobian-residual-dynamics) — usefulness 8/10, category dynamics
- [Conditional-Transport Discrete Reverse Diffusion](https://synthcore.org/idea/1342/conditional-transport-discrete-reverse-diffusion) — usefulness 8/10, category sampling
- [Trajectory-Learned Actuator-Aware Funnel Network](https://synthcore.org/idea/1339/trajectory-learned-actuator-aware-funnel-network) — usefulness 8/10, category dynamics
- [Lattice Error-Feedback Residual Blocks](https://synthcore.org/idea/1318/lattice-error-feedback-residual-blocks) — usefulness 8/10, category architecture
- [Dephasing-Controlled Transport Layer](https://synthcore.org/idea/1272/dephasing-controlled-transport-layer) — usefulness 8/10, category dynamics
- [Backward-Equivalent Quotient GNN](https://synthcore.org/idea/1121/backward-equivalent-quotient-gnn) — usefulness 8/10, category architecture
- [Conservative Chapman–Enskog Neural Layer](https://synthcore.org/idea/1067/conservative-chapman-enskog-neural-layer) — usefulness 8/10, category architecture
- [Kesten–Stigum Attenuated Message Passing](https://synthcore.org/idea/1020/kesten-stigum-attenuated-message-passing) — usefulness 8/10, category architecture
アクセシビリティ
JavaScript不要でコンテンツ利用可能
(100/100)
Content available without JavaScript
HTML内でコンテンツが早い位置に配置
(50/100)
Main content starts at 46% of HTML
適切なページサイズ
(100/100)
Page size: 37KB
AI発見可能性
robots.txtがAIボットを許可
(80/100)
1/5 AI search bots blocked: Amazonbot
Markdown for Agentsサポート
(0/100)
✗ Accept: text/markdown
✗ .md URL
✗ <link> tag
✗ Link header
sitemap.xmlあり
(100/100)
Sitemap found
robots.txtファイルあり
(100/100)
robots.txt exists
llms.txtファイルあり
(100/100)
llms.txt exists and is valid
Content-Signalあり（robots.txtまたはHTTPヘッダー）
(60/100)
✓ robots.txt
✗ HTTP header
✓ Policy
構造化データ
Schema.org / JSON-LDあり
(100/100)
JSON-LD found: Organization, SoftwareApplication, WebSite, WebPage, BreadcrumbList, DefinedTermSet, DefinedTermSet, DefinedTermSet, ScholarlyArticle, TechArticle
Open Graphタグあり
(67/100)
2/3 OG tags present
メタディスクリプションあり
(100/100)
Meta description: 157 chars
正規URLあり
(100/100)
Canonical URL present
lang属性あり
(100/100)
lang="en"
セマンティックHTML
適切な見出し階層
(100/100)
Clean heading hierarchy
articleまたはmain要素を使用
(100/100)
Has both <article> and <main>
セマンティックHTML要素を使用
(100/100)
17 semantic elements, 26 divs (ratio: 40%)
意味のある画像alt属性
(100/100)
No images found
低いdivネスト深度
(100/100)
Avg div depth: 0.3, max: 1
コンテンツ効率
良好なトークン削減率
(80/100)
73% token reduction (HTML→Markdown)
良好なコンテンツ対ノイズ比
(80/100)
Content ratio: 24.1% (9051 content chars / 37518 HTML bytes)
適切なページ重量
(100/100)
HTML size: 37KB
最小限のインラインスタイル
(100/100)
0/326 elements with inline styles (0.0%)
{
"url": "https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression",
"timestamp": 1788215231935,
"fetch": {
"mode": "simple",
"timeMs": 168,
"htmlSizeBytes": 37518,
"supportsMarkdown": false,
"markdownAgents": {
"contentNegotiation": false,
"mdUrl": {
"found": false,
"url": null
},
"linkTag": {
"found": false,
"url": null
},
"linkHeader": {
"found": false,
"url": null
},
"responseHeaders": {
"contentSignal": null,
"xMarkdownTokens": null,
"vary": null
},
"frontmatter": {
"present": false,
"fields": [],
"level": "none"
},
"level": "none"
},
"statusCode": 200
},
"extraction": {
"title": "Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization",
"excerpt": "Compress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control…",
"byline": null,
"siteName": "SynthCore",
"lang": "en",
"contentLength": 9051,
"metadata": {
"description": "Compress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control…",
"ogTitle": "Residual-only unbiased gradient compression — SynthCore",
"ogDescription": "Compress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control…",
"ogImage": null,
"ogType": "article",
"canonical": "https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression",
"lang": "en",
"schemas": [
{
"@id": "https://synthcore.org/#organization",
"@type": "Organization",
"description": "Autonomous research project: an LLM-driven pipeline turns arXiv mathematics papers into concrete machine-learning ideas and verifies them empirically.",
"name": "SynthCore",
"url": "https://synthcore.org/"
},
{
"@id": "https://synthcore.org/#pipeline",
"@type": "SoftwareApplication",
"applicationCategory": "ResearchAutomation",
"author": {
"@id": "https://synthcore.org/#organization"
},
"description": "Autonomous multi-agent pipeline: paper triage, idea extraction, stage-1 mechanism implementation, stage-2 benchmark against a tuned baseline over paired seeds.",
"name": "SynthCore pipeline",
"operatingSystem": "Linux"
},
{
"@id": "https://synthcore.org/#website",
"@type": "WebSite",
"description": "Autonomous research pipeline: extracts machine-learning ideas from arXiv mathematics papers and empirically tests them.",
"inLanguage": "en",
"name": "SynthCore",
"potentialAction": {
"@type": "SearchAction",
"query-input": "required name=search_term_string",
"target": "https://synthcore.org/ideas?q={search_term_string}"
},
"publisher": {
"@id": "https://synthcore.org/#organization"
},
"url": "https://synthcore.org/"
},
{
"@id": "https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression#webpage",
"@type": "WebPage",
"about": {
"@id": "https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression#article"
},
"breadcrumb": {
"@id": "https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression#breadcrumb"
},
"inLanguage": "en",
"isPartOf": {
"@id": "https://synthcore.org/#website"
},
"name": "Residual-only unbiased gradient compression",
"url": "https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression"
},
{
"@id": "https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression#breadcrumb",
"@type": "BreadcrumbList",
"itemListElement": [
{
"@type": "ListItem",
"item": "https://synthcore.org/",
"name": "Home",
"position": 1
},
{
"@type": "ListItem",
"item": "https://synthcore.org/ideas",
"name": "Ideas",
"position": 2
},
{
"@type": "ListItem",
"name": "Residual-only unbiased gradient compression",
"position": 3
}
]
},
{
"@id": "https://synthcore.org/tags#termset-math",
"@type": "DefinedTermSet",
"name": "Mathematical fields behind SynthCore ideas",
"url": "https://synthcore.org/tags"
},
{
"@id": "https://synthcore.org/tags#termset-ml",
"@type": "DefinedTermSet",
"name": "Machine-learning areas of SynthCore ideas",
"url": "https://synthcore.org/tags"
},
{
"@id": "https://synthcore.org/tags#termset-solves",
"@type": "DefinedTermSet",
"name": "Problem goals addressed by SynthCore ideas",
"url": "https://synthcore.org/tags"
},
{
"@id": "https://arxiv.org/abs/2608.06563",
"@type": "ScholarlyArticle",
"datePublished": "2026",
"headline": "Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization",
"inLanguage": "en",
"isAccessibleForFree": true,
"sameAs": "https://arxiv.org/abs/2608.06563",
"url": "https://arxiv.org/abs/2608.06563"
},
{
"@id": "https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression#article",
"@type": "TechArticle",
"about": [
{
"@id": "https://synthcore.org/tag/math/probability#term",
"@type": "DefinedTerm",
"inDefinedTermSet": {
"@id": "https://synthcore.org/tags#termset-math"
},
"name": "Probability theory",
"sameAs": [
"https://en.wikipedia.org/wiki/Probability_theory",
"https://www.wikidata.org/wiki/Q5862903"
],
"termCode": "probability",
"url": "https://synthcore.org/tag/math/probability"
},
{
"@id": "https://synthcore.org/tag/math/stochastic-processes#term",
"@type": "DefinedTerm",
"inDefinedTermSet": {
"@id": "https://synthcore.org/tags#termset-math"
},
"name": "Stochastic process",
"sameAs": [
"https://en.wikipedia.org/wiki/Stochastic_process",
"https://www.wikidata.org/wiki/Q176737"
],
"termCode": "stochastic-processes",
"url": "https://synthcore.org/tag/math/stochastic-processes"
},
{
"@id": "https://synthcore.org/tag/math/optimization#term",
"@type": "DefinedTerm",
"inDefinedTermSet": {
"@id": "https://synthcore.org/tags#termset-math"
},
"name": "Mathematical optimization",
"sameAs": [
"https://en.wikipedia.org/wiki/Mathematical_optimization",
"https://www.wikidata.org/wiki/Q141495"
],
"termCode": "optimization",
"url": "https://synthcore.org/tag/math/optimization"
},
{
"@id": "https://synthcore.org/tag/math/linear-algebra#term",
"@type": "DefinedTerm",
"inDefinedTermSet": {
"@id": "https://synthcore.org/tags#termset-math"
},
"name": "Linear algebra",
"sameAs": [
"https://en.wikipedia.org/wiki/Linear_algebra",
"https://www.wikidata.org/wiki/Q82571"
],
"termCode": "linear-algebra",
"url": "https://synthcore.org/tag/math/linear-algebra"
},
{
"@id": "https://synthcore.org/tag/ml/optimizer#term",
"@type": "DefinedTerm",
"inDefinedTermSet": {
"@id": "https://synthcore.org/tags#termset-ml"
},
"name": "Gradient descent",
"sameAs": [
"https://en.wikipedia.org/wiki/Gradient_descent",
"https://www.wikidata.org/wiki/Q1199743"
],
"termCode": "optimizer",
"url": "https://synthcore.org/tag/ml/optimizer"
},
{
"@id": "https://synthcore.org/tag/ml/federated#term",
"@type": "DefinedTerm",
"inDefinedTermSet": {
"@id": "https://synthcore.org/tags#termset-ml"
},
"name": "Federated learning",
"sameAs": [
"https://en.wikipedia.org/wiki/Federated_learning",
"https://www.wikidata.org/wiki/Q50818671"
],
"termCode": "federated",
"url": "https://synthcore.org/tag/ml/federated"
},
{
"@id": "https://synthcore.org/tag/ml/quantization#term",
"@type": "DefinedTerm",
"inDefinedTermSet": {
"@id": "https://synthcore.org/tags#termset-ml"
},
"name": "Quantization",
"termCode": "quantization",
"url": "https://synthcore.org/tag/ml/quantization"
},
{
"@id": "https://synthcore.org/tag/ml/memory#term",
"@type": "DefinedTerm",
"inDefinedTermSet": {
"@id": "https://synthcore.org/tags#termset-ml"
},
"name": "Computer memory",
"sameAs": [
"https://en.wikipedia.org/wiki/Computer_memory",
"https://www.wikidata.org/wiki/Q5830907"
],
"termCode": "memory",
"url": "https://synthcore.org/tag/ml/memory"
},
{
"@id": "https://synthcore.org/tag/solves/memory#term",
"@type": "DefinedTerm",
"inDefinedTermSet": {
"@id": "https://synthcore.org/tags#termset-solves"
},
"name": "Computer memory",
"sameAs": [
"https://en.wikipedia.org/wiki/Computer_memory",
"https://www.wikidata.org/wiki/Q5830907"
],
"termCode": "memory",
"url": "https://synthcore.org/tag/solves/memory"
},
{
"@id": "https://synthcore.org/tag/solves/speedup#term",
"@type": "DefinedTerm",
"inDefinedTermSet": {
"@id": "https://synthcore.org/tags#termset-solves"
},
"name": "Speedup",
"sameAs": [
"https://en.wikipedia.org/wiki/Speedup",
"https://www.wikidata.org/wiki/Q1549489"
],
"termCode": "speedup",
"url": "https://synthcore.org/tag/solves/speedup"
},
{
"@id": "https://synthcore.org/tag/solves/scalability#term",
"@type": "DefinedTerm",
"inDefinedTermSet": {
"@id": "https://synthcore.org/tags#termset-solves"
},
"name": "Scalability",
"sameAs": [
"https://en.wikipedia.org/wiki/Scalability",
"https://www.wikidata.org/wiki/Q727490"
],
"termCode": "scalability",
"url": "https://synthcore.org/tag/solves/scalability"
}
],
"additionalProperty": [
{
"@type": "PropertyValue",
"name": "verification_status",
"value": "beats_baseline"
},
{
"@type": "PropertyValue",
"name": "peer_reviewed",
"value": false
},
{
"@type": "PropertyValue",
"name": "usefulness",
"value": 7
},
{
"@type": "PropertyValue",
"name": "difficulty",
"value": 4
},
{
"@type": "PropertyValue",
"name": "novelty",
"value": 5
},
{
"@type": "PropertyValue",
"name": "mechanism_tested",
"value": true
},
{
"@type": "PropertyValue",
"name": "mechanism_confirmed",
"value": true
},
{
"@type": "PropertyValue",
"name": "beats_tuned_baseline",
"value": true
},
{
"@type": "PropertyValue",
"name": "benchmark",
"value": "Tabular regression (Friedman)"
},
{
"@type": "PropertyValue",
"name": "paired_seeds",
"value": 8
},
{
"@type": "PropertyValue",
"name": "p_value",
"value": 0.0327
},
{
"@type": "PropertyValue",
"name": "practical_verdict",
"value": "helps"
},
{
"@type": "PropertyValue",
"name": "limitations_stage1",
"value": "Only a synthetic full-participation quadratic federated problem was tested; no FEMNIST/CIFAR-10, CNN, partial client participation, minibatch gradient noise, wall-clock communication implementation, true packed index/scale encoding, or multi-seed confidence intervals were evaluated. The toy compressor uses random-k sparsification rather than 8-bit stochastic quantization, and the stored control variate remains full precision."
},
{
"@type": "PropertyValue",
"name": "how_to_run_stage1",
"value": "python3 experiment.py"
},
{
"@type": "PropertyValue",
"description": "baseline",
"name": "stage1_metric_baseline",
"value": "Direct random-k compression: final loss 0.752743, mean last-50 loss 0.764952, mean per-client compression noise 580.811, 103680 bytes."
},
{
"@type": "PropertyValue",
"description": "idea",
"name": "stage1_metric_idea",
"value": "Residual-only random-k with alpha=0.2: final loss 3.7267e-13, mean last-50 loss 1.7733e-10, mean per-client compression noise 7.8378e-10, 103680 bytes. Math: variance relative error 0.00087; residual-ratio max absolute error 0.00230; EMA residual relative error <=1.3e-13."
},
{
"@type": "PropertyValue",
"name": "limitations_stage2",
"value": "Only the built-in tabular track and small mlp_tiny model were tested. Random-k sparse tensors proxy communication rather than implementing packed transmission or stochastic int8; federated client participation, wall-clock bytes, control-variate memory overhead, and larger neural models were not tested. One baseline seed is a large outlier, so generalization beyond this benchmark is uncertain."
},
{
"@type": "PropertyValue",
"name": "how_to_run_stage2",
"value": "python3 run_stage2.py"
}
],
"articleSection": "Memory",
"author": {
"@id": "https://synthcore.org/#pipeline"
},
"citation": {
"@id": "https://arxiv.org/abs/2608.06563"
},
"dateModified": "2026-09-01",
"datePublished": "2026-08-31",
"description": "Compress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control variate tracks the client gradient, the residual shrinks and the same communication budget produces less compression noise than direct…",
"headline": "Residual-only unbiased gradient compression",
"inLanguage": "en",
"isAccessibleForFree": true,
"isBasedOn": {
"@id": "https://arxiv.org/abs/2608.06563"
},
"keywords": [
"memory",
"speedup",
"scalability",
"optimizer",
"federated",
"quantization",
"memory",
"probability",
"stochastic-processes",
"optimization",
"linear-algebra"
],
"mainEntityOfPage": {
"@id": "https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression#webpage"
},
"publisher": {
"@id": "https://synthcore.org/#organization"
},
"subjectOf": [
{
"@id": "https://synthcore.org/code/721/bench_report.json#data",
"@type": "Dataset",
"creator": {
"@type": "Organization",
"name": "SynthCore",
"url": "https://synthcore.org"
},
"description": "Benchmark report for the idea «Residual-only unbiased gradient compression»: per-seed metrics of the idea against the tuned baseline with paired-seed statistical test output.",
"distribution": {
"@type": "DataDownload",
"contentSize": "6.6 KB",
"contentUrl": "https://synthcore.org/raw/721/bench_report.json",
"encodingFormat": "application/json"
},
"name": "bench_report.json"
},
{
"@id": "https://synthcore.org/code/721/experiment.py#code",
"@type": "SoftwareSourceCode",
"associatedMedia": {
"@type": "DataDownload",
"contentSize": "5.1 KB",
"contentUrl": "https://synthcore.org/raw/721/experiment.py",
"encodingFormat": "text/x-python"
},
"creator": {
"@type": "Organization",
"name": "SynthCore",
"url": "https://synthcore.org"
},
"description": "Reference Python implementation of the idea «Residual-only unbiased gradient compression»: runnable experiment code for the mechanism check and benchmark stages.",
"name": "experiment.py",
"programmingLanguage": "Python",
"url": "https://synthcore.org/code/721/experiment.py"
},
{
"@id": "https://synthcore.org/code/721/report.md#report",
"@type": "CreativeWork",
"associatedMedia": {
"@type": "DataDownload",
"contentSize": "1.9 KB",
"contentUrl": "https://synthcore.org/raw/721/report.md",
"encodingFormat": "text/markdown"
},
"creator": {
"@type": "Organization",
"name": "SynthCore",
"url": "https://synthcore.org"
},
"description": "Human-readable report of the verification experiment for the idea «Residual-only unbiased gradient compression».",
"encodingFormat": "text/markdown",
"name": "report.md",
"url": "https://synthcore.org/code/721/report.md"
},
{
"@id": "https://synthcore.org/code/721/report_bench_2026-09-01T010911.md#report",
"@type": "CreativeWork",
"associatedMedia": {
"@type": "DataDownload",
"contentSize": "3.7 KB",
"contentUrl": "https://synthcore.org/raw/721/report_bench_2026-09-01T010911.md",
"encodingFormat": "text/markdown"
},
"creator": {
"@type": "Organization",
"name": "SynthCore",
"url": "https://synthcore.org"
},
"description": "Human-readable report of the verification experiment for the idea «Residual-only unbiased gradient compression».",
"encodingFormat": "text/markdown",
"name": "report_bench_2026-09-01T010911.md",
"url": "https://synthcore.org/code/721/report_bench_2026-09-01T010911.md"
},
{
"@id": "https://synthcore.org/code/721/results.json#data",
"@type": "Dataset",
"creator": {
"@type": "Organization",
"name": "SynthCore",
"url": "https://synthcore.org"
},
"description": "Machine-readable JSON artifact of the verification experiment for the idea «Residual-only unbiased gradient compression».",
"distribution": {
"@type": "DataDownload",
"contentSize": "2.7 KB",
"contentUrl": "https://synthcore.org/raw/721/results.json",
"encodingFormat": "application/json"
},
"name": "results.json"
},
{
"@id": "https://synthcore.org/code/721/run_stage2.py#code",
"@type": "SoftwareSourceCode",
"associatedMedia": {
"@type": "DataDownload",
"contentSize": "6.8 KB",
"contentUrl": "https://synthcore.org/raw/721/run_stage2.py",
"encodingFormat": "text/x-python"
},
"creator": {
"@type": "Organization",
"name": "SynthCore",
"url": "https://synthcore.org"
},
"description": "Reference Python implementation of the idea «Residual-only unbiased gradient compression»: runnable experiment code for the mechanism check and benchmark stages.",
"name": "run_stage2.py",
"programmingLanguage": "Python",
"url": "https://synthcore.org/code/721/run_stage2.py"
},
{
"@id": "https://synthcore.org/download/721#zip",
"@type": "DataDownload",
"contentUrl": "https://synthcore.org/download/721",
"encodingFormat": "application/zip",
"name": "All experiment files (ZIP)"
}
],
"url": "https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression"
}
],
"robotsMeta": null,
"author": null,
"generator": null,
"markdownAlternateHref": null
}
},
"markdown": "✓✓ Beats tuned baseline 2026\n\n## Residual-only unbiased gradient compression\n\nUsefulness7/10\n\nDifficulty4/10\n\nNovelty5/10\n\nSource paper: [Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization](https://arxiv.org/abs/2608.06563) [arXiv:2608.06563](https://arxiv.org/abs/2608.06563) ⓘ · analyzed Aug 31, 2026\n\nAI-generated research hypothesis, automatically tested. Not peer-reviewed.\n\n## Idea description\n\nCompress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control variate tracks the client gradient, the residual shrinks and the same communication budget produces less compression noise than direct gradient quantization.\n\n## Formulas\n\n$$\\\\mathbb E\\\\left\\[g^t\\\\mid x^t,y^t\\\\right\\]=\\\\nabla f(x^t).$$\n\n$$\\\\widehat g\\_m^t=h\\_m^t+\\\\mathcal Q\\\\left(g\\_m^t-h\\_m^t\\\\right),\\\\qquad \\\\mathbb E\\[\\\\mathcal Q(v)\\]=v,\\\\qquad \\\\mathbb E\\\\|\\\\mathcal Q(v)-v\\\\|^2\\\\leq\\\\omega\\\\|v\\\\|^2.$$\n\n$$\\\\mathbb E\\_{\\\\mathcal Q}\\\\left\\[\\\\|\\\\widehat g\\_t\\\\|^2\\\\right\\]\\\\leq\\\\frac{\\\\omega}{C^2}\\\\sum\\_{m\\\\in S^t}\\\\|g\\_m^t-h\\_m^t\\\\|^2+\\\\left\\\\|\\\\frac{1}{C}\\\\sum\\_{m\\\\in S^t}g\\_m^t\\\\right\\\\|^2.$$\n\n$$x^{t+1}=x^t-\\\\eta\\\\widehat g\\_t,\\\\qquad h\\_m^{t+1}=(1-\\\\alpha)h\\_m^t+\\\\alpha g\\_m^t.$$\n\n## Mathematical statement\n\nThe method uses an unbiased compressor \\\\(\\\\mathcal Q\\\\) with variance parameter \\\\(\\\\omega\\\\), satisfying \\\\(\\\\mathbb E\\[\\\\mathcal Q(v)\\]=v\\\\) and typically \\\\(\\\\mathbb E\\\\|\\\\mathcal Q(v)-v\\\\|^2\\\\leq\\\\omega\\\\|v\\\\|^2\\\\). For client gradients \\\\(g\\_m^t\\\\) and stored control variates \\\\(h\\_m^t\\\\), the compressed estimator is \\\\(\\\\widehat g\\_m^t=h\\_m^t+\\\\mathcal Q(g\\_m^t-h\\_m^t)\\\\). The paper's second-moment calculation gives \\\\(\\\\mathbb E\\_{\\\\mathcal Q}\\\\|\\\\widehat g\\_t\\\\|^2\\\\leq\\\\frac{\\\\omega}{C^2}\\\\sum\\_{m\\\\in S^t}\\\\|g\\_m^t-h\\_m^t\\\\|^2+\\\\|\\\\frac{1}{C}\\\\sum\\_{m\\\\in S^t}g\\_m^t\\\\|^2\\\\), where \\\\(S^t\\\\) is the selected client set, \\\\(C=|S^t|\\\\), and \\\\(\\\\widehat g\\_t=C^{-1}\\\\sum\\_{m\\\\in S^t}\\\\widehat g\\_m^t\\\\). Therefore compression noise depends on residual norms rather than full-gradient norms. The control variate should be refreshed after communication or with an exponential update so that \\\\(h\\_m^t\\\\) tracks the local gradient.\n\n## Implementation notes\n\nIntegrate this at the client-to-server gradient or model-delta transmission operation in federated learning, or at the worker-to-worker all-reduce buffer in distributed training. Each client stores a full-precision vector \\\\(h\\_m\\\\) with the same shape as the transmitted gradient and uses an unbiased compressor, such as stochastic uniform quantization, randomized sparsification, or unbiased blockwise int8 quantization. For each local minibatch, compute \\\\(g\\_m=\\\\nabla f\\_m(x\\_m)\\\\), form the residual \\\\(r\\_m=g\\_m-h\\_m\\\\), transmit \\\\(q\\_m=\\\\mathcal Q(r\\_m)\\\\), and reconstruct \\\\(\\\\widehat g\\_m=h\\_m+q\\_m\\\\) at the server. Aggregate \\\\(\\\\widehat g=C^{-1}\\\\sum\\_{m\\\\in S}\\\\widehat g\\_m\\\\), update the global model \\\\(x\\\\leftarrow x-\\\\eta\\\\widehat g\\\\), and refresh memory with \\\\(h\\_m\\\\leftarrow(1-\\\\alpha)h\\_m+\\\\alpha g\\_m\\\\) whenever client \\\\(m\\\\) participates. Use \\\\(\\\\alpha=1\\\\) after a full synchronization and \\\\(\\\\alpha\\\\in\\[0.05,0.2\\]\\\\) for sparse participation. The paper's bound predicts compression noise proportional to \\\\(\\\\sum\\_m\\\\|g\\_m-h\\_m\\\\|^2\\\\), not \\\\(\\\\sum\\_m\\\\|g\\_m\\\\|^2\\\\); log both quantities to verify this mechanism. If exact unbiased stochastic quantization is inconvenient, implement per-block stochastic rounding and measure its empirical bias. First test on FEMNIST or CIFAR-10 with 16 simulated non-IID clients, comparing uncompressed FedAvg, direct 8-bit gradient compression, and residual-only 8-bit compression at identical transmitted bytes. Use a small CNN or ResNet-18 and report validation accuracy versus communicated bytes, gradient variance, and client-memory overhead. Success means lower gradient variance and at least 1.5x fewer bytes to reach the same accuracy, with no systematic compression bias and no divergence under client heterogeneity.\n\n## Verification\n\nBeats tuned baseline\n\nStage 1 — Mechanism check agent confidence 9/10\n\nBuilt an unbiased random-k residual compressor with persistent client control variates and a deterministic heterogeneous federated quadratic experiment. The math checks passed: empirical compressor noise was within 0.09% of the exact variance, residual noise ratios matched squared residual/full-gradient ratios within 0.24%, and EMA steady-state residual norms matched ||u||/alpha to numerical precision across alpha=1.0 to 0.05. In the toy federated task, residual compression used 103,680 bytes and reached 3.7e-13 final loss, essentially matching uncompressed training, while direct compression at the same bytes plateaued at 0.753 loss with much larger noise; this is a clear mechanism and toy-task win, not evidence of general deep-learning superiority.\n\nAgent confidence\n\n9/10\n\nBaseline\n\nDirect random-k compression: final loss 0.752743, mean last-50 loss 0.764952, mean per-client compression noise 580.811, 103680 bytes.\n\nIdea\n\nResidual-only random-k with alpha=0.2: final loss 3.7267e-13, mean last-50 loss 1.7733e-10, mean per-client compression noise 7.8378e-10, 103680 bytes. Math: variance relative error 0.00087; residual-ratio max absolute error 0.00230; EMA residual relative error <=1.3e-13.\n\n**Limitations:** Only a synthetic full-participation quadratic federated problem was tested; no FEMNIST/CIFAR-10, CNN, partial client participation, minibatch gradient noise, wall-clock communication implementation, true packed index/scale encoding, or multi-seed confidence intervals were evaluated. The toy compressor uses random-k sparsification rather than 8-bit stochastic quantization, and the stored control variate remains full precision.\n\n**How to run:** `python3 experiment.py`\n\nStage 2 — Benchmark vs. tuned baseline Sep 1, 2026\n\nBeats the tuned baseline by 61.2% (p=0.0327, wins 6 / 8 paired seeds; metric: lower is better).\n\nBenchmark\n\nTabular regression (Friedman)\n\nModel\n\nmlp\\_tiny\n\nPaired seeds\n\n8\n\nBaseline mean\n\n20.3734\n\nIdea mean\n\n7.9047\n\nEffect (Δ)\n\n\\-12.4686 (−61.2%; negative = idea better)\n\nWins\n\n6 / 8 paired seeds\n\np-value\n\n0.0327 (permutation test, 20 000 shuffles)\n\nSmallest detectable effect\n\n±142.7%\n\nMechanism\n\nConfirmed ✓\n\nPractical effect\n\nHelps\n\nBaseline tuning\n\nswept over 3 configs\n\n**Limitations:**\n\nOnly the built-in tabular track and small mlp\\_tiny model were tested. Random-k sparse tensors proxy communication rather than implementing packed transmission or stochastic int8; federated client participation, wall-clock bytes, control-variate memory overhead, and larger neural models were not tested. One baseline seed is a large outlier, so generalization beyond this benchmark is uncertain.\n\n**How to run:** `python3 run_stage2.py`\n\nVerdict computed by deterministic test code from paired-seed statistics — not by the language model.\n\nStage 2 — Benchmark Sep 1, 2026 latest Worked ✓\n\nAgent confidence: 7/10\n\nResidual-only unbiased random-k gradient compression was evaluated on the registered tabular track with the shared mlp\\_tiny architecture. It achieved lower mean test MSE than the tuned direct-compression baseline (7.9047 vs 20.3734), with paired delta -12.4686 and permutation p=0.0327; the trained-model mechanism prediction was confirmed within 4.49% relative error.\n\nBaseline\n\nmean test MSE 20.37335467338562, std 33.97063256083515, best lr 0.0035, k\\_fraction 0.125\n\nIdea\n\nmean test MSE 7.904710650444031, std 1.6384066086211326, lr 0.0035, alpha 0.2, k\\_fraction 0.125\n\nBenchmark result\n\nBeats the tuned baseline by 61.2% (p=0.0327, wins 6 / 8 paired seeds; metric: lower is better).\n\nBenchmark\n\nTabular regression (Friedman)\n\nModel\n\nmlp\\_tiny\n\nPaired seeds\n\n8\n\nBaseline mean\n\n20.3734\n\nIdea mean\n\n7.9047\n\nEffect (Δ)\n\n\\-12.4686 (−61.2%; negative = idea better)\n\nWins\n\n6 / 8 paired seeds\n\np-value\n\n0.0327 (permutation test, 20 000 shuffles)\n\nSmallest detectable effect\n\n±142.7%\n\nMechanism\n\nConfirmed ✓\n\nPractical effect\n\nHelps\n\nBaseline tuning\n\nswept over 3 configs\n\n**Limitations:**\n\nOnly the built-in tabular track and small mlp\\_tiny model were tested. Random-k sparse tensors proxy communication rather than implementing packed transmission or stochastic int8; federated client participation, wall-clock bytes, control-variate memory overhead, and larger neural models were not tested. One baseline seed is a large outlier, so generalization beyond this benchmark is uncertain.\n\n**How to run:** `python3 run_stage2.py`\n\n## Artifacts\n\n- 📊 [bench\\_report.json](https://synthcore.org/code/721/bench_report.json) 6.6 KB [View](https://synthcore.org/code/721/bench_report.json) [Raw JSON](https://synthcore.org/raw/721/bench_report.json)\n- 🐍 [experiment.py](https://synthcore.org/code/721/experiment.py) 5.1 KB [View](https://synthcore.org/code/721/experiment.py) [Raw JSON](https://synthcore.org/raw/721/experiment.py)\n- 📄 [report.md](https://synthcore.org/code/721/report.md) 1.9 KB [View](https://synthcore.org/code/721/report.md)\n- 📄 [report\\_bench\\_2026-09-01T010911.md](https://synthcore.org/code/721/report_bench_2026-09-01T010911.md) 3.7 KB [View](https://synthcore.org/code/721/report_bench_2026-09-01T010911.md)\n- 📊 [results.json](https://synthcore.org/code/721/results.json) 2.7 KB [View](https://synthcore.org/code/721/results.json) [Raw JSON](https://synthcore.org/raw/721/results.json)\n- 🐍 [run\\_stage2.py](https://synthcore.org/code/721/run_stage2.py) 6.8 KB [View](https://synthcore.org/code/721/run_stage2.py) [Raw JSON](https://synthcore.org/raw/721/run_stage2.py)\n",
"fullPageMarkdown": "Residual-only unbiased gradient compression — SynthCore [Skip to content](https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression#main)\n\n[SynthCore](https://synthcore.org/)\n\n✓✓ Beats tuned baseline 2026\n\n# Residual-only unbiased gradient compression\n\nUsefulness7/10\n\nDifficulty4/10\n\nNovelty5/10\n\n[Memory](https://synthcore.org/category/memory) [Memory](https://synthcore.org/tag/solves/memory \"What it solves\")[Speedup](https://synthcore.org/tag/solves/speedup \"What it solves\")[Scalability](https://synthcore.org/tag/solves/scalability \"What it solves\")[Optimizer](https://synthcore.org/tag/ml/optimizer \"ML area\")[Federated](https://synthcore.org/tag/ml/federated \"ML area\")[Quantization](https://synthcore.org/tag/ml/quantization \"ML area\")[Memory](https://synthcore.org/tag/ml/memory \"ML area\")[Probability](https://synthcore.org/tag/math/probability \"Math field\")[Stochastic processes](https://synthcore.org/tag/math/stochastic-processes \"Math field\")[Optimization](https://synthcore.org/tag/math/optimization \"Math field\")[Linear algebra](https://synthcore.org/tag/math/linear-algebra \"Math field\")\n\nSource paper: [Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization](https://arxiv.org/abs/2608.06563) [arXiv:2608.06563](https://arxiv.org/abs/2608.06563) ⓘ · analyzed Aug 31, 2026\n\nAI-generated research hypothesis, automatically tested. Not peer-reviewed.\n\n## Idea description\n\nCompress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control variate tracks the client gradient, the residual shrinks and the same communication budget produces less compression noise than direct gradient quantization.\n\n## Formulas\n\n$$\\\\mathbb E\\\\left\\[g^t\\\\mid x^t,y^t\\\\right\\]=\\\\nabla f(x^t).$$\n\n$$\\\\widehat g\\_m^t=h\\_m^t+\\\\mathcal Q\\\\left(g\\_m^t-h\\_m^t\\\\right),\\\\qquad \\\\mathbb E\\[\\\\mathcal Q(v)\\]=v,\\\\qquad \\\\mathbb E\\\\|\\\\mathcal Q(v)-v\\\\|^2\\\\leq\\\\omega\\\\|v\\\\|^2.$$\n\n$$\\\\mathbb E\\_{\\\\mathcal Q}\\\\left\\[\\\\|\\\\widehat g\\_t\\\\|^2\\\\right\\]\\\\leq\\\\frac{\\\\omega}{C^2}\\\\sum\\_{m\\\\in S^t}\\\\|g\\_m^t-h\\_m^t\\\\|^2+\\\\left\\\\|\\\\frac{1}{C}\\\\sum\\_{m\\\\in S^t}g\\_m^t\\\\right\\\\|^2.$$\n\n$$x^{t+1}=x^t-\\\\eta\\\\widehat g\\_t,\\\\qquad h\\_m^{t+1}=(1-\\\\alpha)h\\_m^t+\\\\alpha g\\_m^t.$$\n\n## Mathematical statement\n\nThe method uses an unbiased compressor \\\\(\\\\mathcal Q\\\\) with variance parameter \\\\(\\\\omega\\\\), satisfying \\\\(\\\\mathbb E\\[\\\\mathcal Q(v)\\]=v\\\\) and typically \\\\(\\\\mathbb E\\\\|\\\\mathcal Q(v)-v\\\\|^2\\\\leq\\\\omega\\\\|v\\\\|^2\\\\). For client gradients \\\\(g\\_m^t\\\\) and stored control variates \\\\(h\\_m^t\\\\), the compressed estimator is \\\\(\\\\widehat g\\_m^t=h\\_m^t+\\\\mathcal Q(g\\_m^t-h\\_m^t)\\\\). The paper's second-moment calculation gives \\\\(\\\\mathbb E\\_{\\\\mathcal Q}\\\\|\\\\widehat g\\_t\\\\|^2\\\\leq\\\\frac{\\\\omega}{C^2}\\\\sum\\_{m\\\\in S^t}\\\\|g\\_m^t-h\\_m^t\\\\|^2+\\\\|\\\\frac{1}{C}\\\\sum\\_{m\\\\in S^t}g\\_m^t\\\\|^2\\\\), where \\\\(S^t\\\\) is the selected client set, \\\\(C=|S^t|\\\\), and \\\\(\\\\widehat g\\_t=C^{-1}\\\\sum\\_{m\\\\in S^t}\\\\widehat g\\_m^t\\\\). Therefore compression noise depends on residual norms rather than full-gradient norms. The control variate should be refreshed after communication or with an exponential update so that \\\\(h\\_m^t\\\\) tracks the local gradient.\n\n## Implementation notes\n\nIntegrate this at the client-to-server gradient or model-delta transmission operation in federated learning, or at the worker-to-worker all-reduce buffer in distributed training. Each client stores a full-precision vector \\\\(h\\_m\\\\) with the same shape as the transmitted gradient and uses an unbiased compressor, such as stochastic uniform quantization, randomized sparsification, or unbiased blockwise int8 quantization. For each local minibatch, compute \\\\(g\\_m=\\\\nabla f\\_m(x\\_m)\\\\), form the residual \\\\(r\\_m=g\\_m-h\\_m\\\\), transmit \\\\(q\\_m=\\\\mathcal Q(r\\_m)\\\\), and reconstruct \\\\(\\\\widehat g\\_m=h\\_m+q\\_m\\\\) at the server. Aggregate \\\\(\\\\widehat g=C^{-1}\\\\sum\\_{m\\\\in S}\\\\widehat g\\_m\\\\), update the global model \\\\(x\\\\leftarrow x-\\\\eta\\\\widehat g\\\\), and refresh memory with \\\\(h\\_m\\\\leftarrow(1-\\\\alpha)h\\_m+\\\\alpha g\\_m\\\\) whenever client \\\\(m\\\\) participates. Use \\\\(\\\\alpha=1\\\\) after a full synchronization and \\\\(\\\\alpha\\\\in\\[0.05,0.2\\]\\\\) for sparse participation. The paper's bound predicts compression noise proportional to \\\\(\\\\sum\\_m\\\\|g\\_m-h\\_m\\\\|^2\\\\), not \\\\(\\\\sum\\_m\\\\|g\\_m\\\\|^2\\\\); log both quantities to verify this mechanism. If exact unbiased stochastic quantization is inconvenient, implement per-block stochastic rounding and measure its empirical bias. First test on FEMNIST or CIFAR-10 with 16 simulated non-IID clients, comparing uncompressed FedAvg, direct 8-bit gradient compression, and residual-only 8-bit compression at identical transmitted bytes. Use a small CNN or ResNet-18 and report validation accuracy versus communicated bytes, gradient variance, and client-memory overhead. Success means lower gradient variance and at least 1.5x fewer bytes to reach the same accuracy, with no systematic compression bias and no divergence under client heterogeneity.\n\n## Verification\n\nBeats tuned baseline\n\nStage 1 — Mechanism check agent confidence 9/10\n\nBuilt an unbiased random-k residual compressor with persistent client control variates and a deterministic heterogeneous federated quadratic experiment. The math checks passed: empirical compressor noise was within 0.09% of the exact variance, residual noise ratios matched squared residual/full-gradient ratios within 0.24%, and EMA steady-state residual norms matched ||u||/alpha to numerical precision across alpha=1.0 to 0.05. In the toy federated task, residual compression used 103,680 bytes and reached 3.7e-13 final loss, essentially matching uncompressed training, while direct compression at the same bytes plateaued at 0.753 loss with much larger noise; this is a clear mechanism and toy-task win, not evidence of general deep-learning superiority.\n\nAgent confidence\n\n9/10\n\nBaseline\n\nDirect random-k compression: final loss 0.752743, mean last-50 loss 0.764952, mean per-client compression noise 580.811, 103680 bytes.\n\nIdea\n\nResidual-only random-k with alpha=0.2: final loss 3.7267e-13, mean last-50 loss 1.7733e-10, mean per-client compression noise 7.8378e-10, 103680 bytes. Math: variance relative error 0.00087; residual-ratio max absolute error 0.00230; EMA residual relative error <=1.3e-13.\n\n**Limitations:** Only a synthetic full-participation quadratic federated problem was tested; no FEMNIST/CIFAR-10, CNN, partial client participation, minibatch gradient noise, wall-clock communication implementation, true packed index/scale encoding, or multi-seed confidence intervals were evaluated. The toy compressor uses random-k sparsification rather than 8-bit stochastic quantization, and the stored control variate remains full precision.\n\n**How to run:** `python3 experiment.py`\n\nStage 2 — Benchmark vs. tuned baseline Sep 1, 2026\n\nBeats the tuned baseline by 61.2% (p=0.0327, wins 6 / 8 paired seeds; metric: lower is better).\n\nBenchmark\n\nTabular regression (Friedman)\n\nModel\n\nmlp\\_tiny\n\nPaired seeds\n\n8\n\nBaseline mean\n\n20.3734\n\nIdea mean\n\n7.9047\n\nEffect (Δ)\n\n\\-12.4686 (−61.2%; negative = idea better)\n\nWins\n\n6 / 8 paired seeds\n\np-value\n\n0.0327 (permutation test, 20 000 shuffles)\n\nSmallest detectable effect\n\n±142.7%\n\nMechanism\n\nConfirmed ✓\n\nPractical effect\n\nHelps\n\nBaseline tuning\n\nswept over 3 configs\n\n**Limitations:**\n\nOnly the built-in tabular track and small mlp\\_tiny model were tested. Random-k sparse tensors proxy communication rather than implementing packed transmission or stochastic int8; federated client participation, wall-clock bytes, control-variate memory overhead, and larger neural models were not tested. One baseline seed is a large outlier, so generalization beyond this benchmark is uncertain.\n\n**How to run:** `python3 run_stage2.py`\n\nVerdict computed by deterministic test code from paired-seed statistics — not by the language model.\n\nStage 2 — Benchmark Sep 1, 2026 latest Worked ✓\n\nAgent confidence: 7/10\n\nResidual-only unbiased random-k gradient compression was evaluated on the registered tabular track with the shared mlp\\_tiny architecture. It achieved lower mean test MSE than the tuned direct-compression baseline (7.9047 vs 20.3734), with paired delta -12.4686 and permutation p=0.0327; the trained-model mechanism prediction was confirmed within 4.49% relative error.\n\nBaseline\n\nmean test MSE 20.37335467338562, std 33.97063256083515, best lr 0.0035, k\\_fraction 0.125\n\nIdea\n\nmean test MSE 7.904710650444031, std 1.6384066086211326, lr 0.0035, alpha 0.2, k\\_fraction 0.125\n\nBenchmark result\n\nBeats the tuned baseline by 61.2% (p=0.0327, wins 6 / 8 paired seeds; metric: lower is better).\n\nBenchmark\n\nTabular regression (Friedman)\n\nModel\n\nmlp\\_tiny\n\nPaired seeds\n\n8\n\nBaseline mean\n\n20.3734\n\nIdea mean\n\n7.9047\n\nEffect (Δ)\n\n\\-12.4686 (−61.2%; negative = idea better)\n\nWins\n\n6 / 8 paired seeds\n\np-value\n\n0.0327 (permutation test, 20 000 shuffles)\n\nSmallest detectable effect\n\n±142.7%\n\nMechanism\n\nConfirmed ✓\n\nPractical effect\n\nHelps\n\nBaseline tuning\n\nswept over 3 configs\n\n**Limitations:**\n\nOnly the built-in tabular track and small mlp\\_tiny model were tested. Random-k sparse tensors proxy communication rather than implementing packed transmission or stochastic int8; federated client participation, wall-clock bytes, control-variate memory overhead, and larger neural models were not tested. One baseline seed is a large outlier, so generalization beyond this benchmark is uncertain.\n\n**How to run:** `python3 run_stage2.py`\n\n## Artifacts\n\n[⬇ Download all as ZIP](https://synthcore.org/download/721) 6 files · code, reports and structured results\n\n- 📊 [bench\\_report.json](https://synthcore.org/code/721/bench_report.json) 6.6 KB [View](https://synthcore.org/code/721/bench_report.json) [Raw JSON](https://synthcore.org/raw/721/bench_report.json)\n- 🐍 [experiment.py](https://synthcore.org/code/721/experiment.py) 5.1 KB [View](https://synthcore.org/code/721/experiment.py) [Raw JSON](https://synthcore.org/raw/721/experiment.py)\n- 📄 [report.md](https://synthcore.org/code/721/report.md) 1.9 KB [View](https://synthcore.org/code/721/report.md)\n- 📄 [report\\_bench\\_2026-09-01T010911.md](https://synthcore.org/code/721/report_bench_2026-09-01T010911.md) 3.7 KB [View](https://synthcore.org/code/721/report_bench_2026-09-01T010911.md)\n- 📊 [results.json](https://synthcore.org/code/721/results.json) 2.7 KB [View](https://synthcore.org/code/721/results.json) [Raw JSON](https://synthcore.org/raw/721/results.json)\n- 🐍 [run\\_stage2.py](https://synthcore.org/code/721/run_stage2.py) 6.8 KB [View](https://synthcore.org/code/721/run_stage2.py) [Raw JSON](https://synthcore.org/raw/721/run_stage2.py)\n",
"markdownStats": {
"images": 0,
"links": 18,
"tables": 0,
"codeBlocks": 0,
"headings": 7
},
"tokens": {
"htmlTokens": 10478,
"markdownTokens": 2779,
"reduction": 7699,
"reductionPercent": 73
},
"score": {
"score": 86,
"grade": "B",
"rubricVersion": 3,
"dimensions": {
"accessibility": {
"score": 88,
"weight": 30,
"grade": "B",
"checks": {
"content_without_js": {
"score": 100,
"weight": 55,
"evidence": "proven",
"details": "Content available without JavaScript"
},
"fast_content_position": {
"score": 50,
"weight": 25,
"evidence": "plausible",
"details": "Main content starts at 46% of HTML"
},
"reasonable_page_size": {
"score": 100,
"weight": 20,
"evidence": "plausible",
"details": "Page size: 37KB"
}
}
},
"aiDiscoverability": {
"score": 69,
"weight": 25,
"grade": "C",
"checks": {
"robots_allows_ai_bots": {
"score": 80,
"weight": 35,
"evidence": "proven",
"details": "1/5 AI search bots blocked: Amazonbot"
},
"supports_markdown_negotiation": {
"score": 0,
"weight": 20,
"evidence": "plausible",
"details": "No Markdown for Agents support detected"
},
"has_sitemap": {
"score": 100,
"weight": 15,
"evidence": "plausible",
"details": "Sitemap found"
},
"has_robots_txt": {
"score": 100,
"weight": 10,
"evidence": "plausible",
"details": "robots.txt exists"
},
"has_llms_txt": {
"score": 100,
"weight": 10,
"evidence": "speculative",
"details": "llms.txt exists and is valid"
},
"has_content_signals": {
"score": 60,
"weight": 10,
"evidence": "speculative",
"details": "robots.txt: search=yes, ai-train=no | Policy included",
"mechanisms": {
"robotsTxt": true,
"httpHeader": false,
"policy": true
}
}
}
},
"structuredData": {
"score": 93,
"weight": 20,
"grade": "A",
"checks": {
"has_schema_org": {
"score": 100,
"weight": 35,
"evidence": "proven",
"details": "JSON-LD found: Organization, SoftwareApplication, WebSite, WebPage, BreadcrumbList, DefinedTermSet, DefinedTermSet, DefinedTermSet, ScholarlyArticle, TechArticle"
},
"has_open_graph": {
"score": 67,
"weight": 20,
"evidence": "plausible",
"details": "2/3 OG tags present"
},
"has_meta_description": {
"score": 100,
"weight": 20,
"evidence": "plausible",
"details": "Meta description: 157 chars"
},
"has_canonical_url": {
"score": 100,
"weight": 15,
"evidence": "plausible",
"details": "Canonical URL present"
},
"has_lang_attribute": {
"score": 100,
"weight": 10,
"evidence": "plausible",
"details": "lang=\"en\""
}
}
},
"semanticHtml": {
"score": 100,
"weight": 15,
"grade": "A",
"checks": {
"proper_heading_hierarchy": {
"score": 100,
"weight": 30,
"evidence": "plausible",
"details": "Clean heading hierarchy"
},
"uses_article_or_main": {
"score": 100,
"weight": 25,
"evidence": "plausible",
"details": "Has both <article> and <main>"
},
"semantic_elements": {
"score": 100,
"weight": 20,
"evidence": "plausible",
"details": "17 semantic elements, 26 divs (ratio: 40%)"
},
"meaningful_alt_texts": {
"score": 100,
"weight": 15,
"evidence": "plausible",
"details": "No images found"
},
"low_div_nesting": {
"score": 100,
"weight": 10,
"evidence": "speculative",
"details": "Avg div depth: 0.3, max: 1"
}
}
},
"contentEfficiency": {
"score": 86,
"weight": 10,
"grade": "B",
"checks": {
"token_reduction_ratio": {
"score": 80,
"weight": 40,
"evidence": "speculative",
"details": "73% token reduction (HTML→Markdown)"
},
"content_to_noise_ratio": {
"score": 80,
"weight": 30,
"evidence": "speculative",
"details": "Content ratio: 24.1% (9051 content chars / 37518 HTML bytes)"
},
"reasonable_page_weight": {
"score": 100,
"weight": 20,
"evidence": "speculative",
"details": "HTML size: 37KB"
},
"minimal_inline_styles": {
"score": 100,
"weight": 10,
"evidence": "speculative",
"details": "0/326 elements with inline styles (0.0%)"
}
}
}
}
},
"recommendations": [
{
"id": "add_markdown_negotiation",
"priority": "critical",
"category": "aiDiscoverability",
"titleKey": "rec.add_markdown_negotiation.title",
"descriptionKey": "rec.add_markdown_negotiation.description",
"howToKey": "rec.add_markdown_negotiation.howto",
"howToStepKeys": null,
"effort": "significant",
"estimatedImpact": 5,
"maxImpact": 5,
"evidence": "plausible",
"checkScore": 0,
"checkDetails": "No Markdown for Agents support detected"
},
{
"id": "add_open_graph",
"priority": "medium",
"category": "structuredData",
"titleKey": "rec.add_open_graph.title",
"descriptionKey": "rec.add_open_graph.description",
"howToKey": "rec.add_open_graph.howto",
"howToStepKeys": null,
"effort": "quick-win",
"estimatedImpact": 1.3,
"maxImpact": 4,
"evidence": "plausible",
"checkScore": 67,
"checkDetails": "2/3 OG tags present"
}
],
"llmsTxtPreview": "# SynthCore\n\n> Compress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control variate tracks the client gradient, the residual shrinks and the same communication budget produces less compression noise than direct…\n\n## Documentation\n- [report.md](https://synthcore.org/code/721/report.md)\n- [report_bench_2026-09-01T010911.md](https://synthcore.org/code/721/report_bench_2026-09-01T010911.md)\n\n## Main\n- [Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization](https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression): Compress only the difference between the current client gradient and a persistent control variate, rather than compress…\n- [About](https://synthcore.org/about)\n- [SynthCore](https://synthcore.org/)\n- [Ideas](https://synthcore.org/ideas)\n- [Categories](https://synthcore.org/categories)\n- [Tags](https://synthcore.org/tags)\n- [Papers](https://synthcore.org/papers)\n- [API](https://synthcore.org/api)\n- [Memory](https://synthcore.org/category/memory)\n- [Memory](https://synthcore.org/tag/solves/memory)\n\n",
"llmsTxtExisting": "# SynthCore\n> Autonomous pipeline that extracts ML ideas from arXiv mathematics papers and empirically tests them (mechanism check, then benchmark vs tuned baseline over 8 paired seeds; verdicts computed by deterministic test code).\n\n- Ideas: https://synthcore.org/ideas\n- Verified ideas (beat a tuned baseline): https://synthcore.org/ideas?status=beats_baseline\n- Mechanism-confirmed ideas: https://synthcore.org/ideas?status=mechanism_works\n- About: https://synthcore.org/about\n- Analyzed papers: https://synthcore.org/papers\n- Categories: https://synthcore.org/categories\n- Tags: https://synthcore.org/tags\n- Structured data: /api/idea/{id}.json and JSON-LD on every idea page\n- JSON API (filter and page the whole corpus programmatically, no rate limit): https://synthcore.org/api\n\nCorpus: 8700 analyzed papers, 1845 ideas, 96 benchmark-verified.\n\nEvery idea is an AI-generated hypothesis, automatically tested. Not peer-reviewed.\n\n## Benchmark-verified ideas (selection)\n- [Derivative-conditioned fine-scale corrector](https://synthcore.org/idea/1850/derivative-conditioned-fine-scale-corrector) — usefulness 8/10, category architecture\n- [Power-Balanced Modular Neural Block](https://synthcore.org/idea/1829/power-balanced-modular-neural-block) — usefulness 8/10, category architecture\n- [Commutant-gated spectral loss](https://synthcore.org/idea/1815/commutant-gated-spectral-loss) — usefulness 8/10, category regularization\n- [Active-Set Reduced Differentiable QP Layer](https://synthcore.org/idea/1778/active-set-reduced-differentiable-qp-layer) — usefulness 8/10, category optimization\n- [Caustic-Aware Hamiltonian Feedback Layer](https://synthcore.org/idea/1777/caustic-aware-hamiltonian-feedback-layer) — usefulness 8/10, category dynamics\n- [Jacobian Tube Training](https://synthcore.org/idea/1711/jacobian-tube-training) — usefulness 8/10, category dynamics\n- [Zonotope-Bounded Latent State Space](https://synthcore.org/idea/1704/zonotope-bounded-latent-state-space) — usefulness 8/10, category dynamics\n- [Stable Rotating-Memory State Space](https://synthcore.org/idea/1631/stable-rotating-memory-state-space) — usefulness 8/10, category architecture\n- [Jacobian-Free Short-Trace Backpropagation](https://synthcore.org/idea/1624/jacobian-free-short-trace-backpropagation) — usefulness 8/10, category training\n- [Directional Conformal Residual Sets for Neural Dynamics](https://synthcore.org/idea/1593/directional-conformal-residual-sets-for-neural-dynamics) — usefulness 8/10, category regularization\n- [Heterogeneity-Calibrated Hopf RNN](https://synthcore.org/idea/1527/heterogeneity-calibrated-hopf-rnn) — usefulness 8/10, category dynamics\n- [Trajectory-Certified Contractive RNN](https://synthcore.org/idea/1436/trajectory-certified-contractive-rnn) — usefulness 8/10, category dynamics\n- [Defect-and-Jacobian Residual Dynamics](https://synthcore.org/idea/1358/defect-and-jacobian-residual-dynamics) — usefulness 8/10, category dynamics\n- [Conditional-Transport Discrete Reverse Diffusion](https://synthcore.org/idea/1342/conditional-transport-discrete-reverse-diffusion) — usefulness 8/10, category sampling\n- [Trajectory-Learned Actuator-Aware Funnel Network](https://synthcore.org/idea/1339/trajectory-learned-actuator-aware-funnel-network) — usefulness 8/10, category dynamics\n- [Lattice Error-Feedback Residual Blocks](https://synthcore.org/idea/1318/lattice-error-feedback-residual-blocks) — usefulness 8/10, category architecture\n- [Dephasing-Controlled Transport Layer](https://synthcore.org/idea/1272/dephasing-controlled-transport-layer) — usefulness 8/10, category dynamics\n- [Backward-Equivalent Quotient GNN](https://synthcore.org/idea/1121/backward-equivalent-quotient-gnn) — usefulness 8/10, category architecture\n- [Conservative Chapman–Enskog Neural Layer](https://synthcore.org/idea/1067/conservative-chapman-enskog-neural-layer) — usefulness 8/10, category architecture\n- [Kesten–Stigum Attenuated Message Passing](https://synthcore.org/idea/1020/kesten-stigum-attenuated-message-passing) — usefulness 8/10, category architecture",
"emergingProtocols": {
"oauthProtectedResource": {
"exists": false,
"url": "https://synthcore.org/.well-known/oauth-protected-resource"
},
"oauthDiscovery": {
"exists": false,
"url": "https://synthcore.org/.well-known/oauth-authorization-server"
},
"mcpServerCard": {
"exists": false,
"url": "https://synthcore.org/.well-known/mcp/server-card.json",
"draft": true
},
"a2aAgentCard": {
"exists": false,
"url": "https://synthcore.org/.well-known/agent-card.json"
},
"apiCatalog": {
"exists": false,
"url": "https://synthcore.org/.well-known/api-catalog"
},
"agentSkills": {
"exists": false,
"url": "https://synthcore.org/.well-known/agent-skills/index.json",
"draft": true
},
"count": 0,
"total": 6
},
"botAccess": {
"probed": true,
"bot": "OAI-SearchBot",
"controlStatus": 200,
"botStatus": 200,
"discriminates": false,
"refusedAsBot": false,
"edge": "Cloudflare",
"verifiable": false,
"detail": "This origin answers OAI-SearchBot exactly as it answers any other client (200). No edge-level filtering of AI crawlers observed."
},
"snippets": [
{
"id": "add_open_graph",
"title": "Add missing Open Graph tags",
"description": "Open Graph tags control how your page looks when shared on social media and how AI platforms preview your URL in answers.",
"language": "html",
"code": "<meta property=\"og:image\" content=\"https://yoursite.com/og-image.jpg\">\n<meta property=\"og:url\" content=\"https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression\">\n<meta property=\"og:type\" content=\"website\">",
"filename": "<head>",
"stacks": [
{
"id": "html",
"label": "HTML <head>",
"language": "html",
"filename": "<head>",
"code": "<meta property=\"og:image\" content=\"https://yoursite.com/og-image.jpg\">\n<meta property=\"og:url\" content=\"https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression\">\n<meta property=\"og:type\" content=\"website\">"
},
{
"id": "wordpress",
"label": "WordPress",
"language": "php",
"filename": "functions.php",
"code": "<?php\n// Quick Open Graph tags without a plugin (skip if Yoast / Rank Math is active)\nadd_action('wp_head', function () {\n if (!is_singular()) return;\n $post = get_queried_object();\n $title = get_the_title($post);\n $desc = get_the_excerpt($post) ?: wp_trim_words(strip_tags($post->post_content), 30);\n $image = get_the_post_thumbnail_url($post, 'large') ?: 'https://yoursite.com/og-image.jpg';\n $url = get_permalink($post);\n printf('<meta property=\"og:title\" content=\"%s\">' . \"\\n\", esc_attr($title));\n printf('<meta property=\"og:description\" content=\"%s\">' . \"\\n\", esc_attr($desc));\n printf('<meta property=\"og:image\" content=\"%s\">' . \"\\n\", esc_url($image));\n printf('<meta property=\"og:url\" content=\"%s\">' . \"\\n\", esc_url($url));\n echo '<meta property=\"og:type\" content=\"article\">' . \"\\n\";\n}, 5);"
},
{
"id": "nextjs",
"label": "Next.js",
"language": "typescript",
"filename": "app/page.tsx",
"code": "// Next.js App Router — Metadata API\nimport type { Metadata } from 'next';\n\nexport const metadata: Metadata = {\n title: \"Residual-only unbiased gradient compression — SynthCore\",\n description: \"Compress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control…\",\n openGraph: {\n title: \"Residual-only unbiased gradient compression — SynthCore\",\n description: \"Compress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control…\",\n url: \"https://synthcore.org/idea/1899/residual-only-unbiased-gradient-compression\",\n images: [\"https://yoursite.com/og-image.jpg\"],\n type: 'website',\n },\n};"
}
]
},
{
"id": "add_markdown_negotiation",
"title": "Support Markdown for Agents",
"description": "Let AI agents request a clean Markdown version of any page via content negotiation, .md alternate URLs, link tags or Link headers.",
"language": "html",
"code": "<!-- Mechanism 3: link tag advertising the .md alternate -->\n<link rel=\"alternate\" type=\"text/markdown\" href=\"/page.md\">",
"filename": "<head>",
"stacks": [
{
"id": "html",
"label": "HTML <head>",
"language": "html",
"filename": "<head>",
"code": "<!-- Mechanism 3: link tag advertising the .md alternate -->\n<link rel=\"alternate\" type=\"text/markdown\" href=\"/page.md\">"
},
{
"id": "express",
"label": "Express",
"language": "javascript",
"filename": "server.js",
"code": "// Mechanisms 1 + 4: content negotiation + Link header\napp.get('/page', (req, res) => {\n res.setHeader('Vary', 'Accept');\n res.setHeader('Link', '</page.md>; rel=\"alternate\"; type=\"text/markdown\"');\n if ((req.headers.accept || '').includes('text/markdown')) {\n res.type('text/markdown; charset=utf-8');\n return res.send(renderMarkdown('page'));\n }\n res.render('page');\n});"
},
{
"id": "fastify",
"label": "Fastify",
"language": "javascript",
"filename": "server.js",
"code": "// Mechanisms 1 + 4: content negotiation + Link header\nfastify.get('/page', async (req, reply) => {\n reply.header('Vary', 'Accept');\n reply.header('Link', '</page.md>; rel=\"alternate\"; type=\"text/markdown\"');\n if ((req.headers.accept || '').includes('text/markdown')) {\n return reply.type('text/markdown; charset=utf-8').send(renderMarkdown('page'));\n }\n return reply.view('/page.ejs');\n});"
},
{
"id": "nextjs",
"label": "Next.js",
"language": "typescript",
"filename": "app/page/route.ts",
"code": "// Next.js App Router — Route Handler returning Markdown\nimport { NextRequest } from 'next/server';\nimport { renderMarkdown } from '@/lib/md';\nexport async function GET(req: NextRequest) {\n const accept = req.headers.get('accept') || '';\n if (accept.includes('text/markdown')) {\n return new Response(await renderMarkdown('page'), {\n headers: {\n 'Content-Type': 'text/markdown; charset=utf-8',\n 'Vary': 'Accept',\n },\n });\n }\n // Fall through to the page component\n return new Response(null, { status: 404 });\n}"
},
{
"id": "wordpress",
"label": "WordPress",
"language": "php",
"filename": "functions.php",
"code": "<?php\n// Mechanism 1: respond to Accept: text/markdown on the same URL\nadd_action('template_redirect', function () {\n if (!is_singular()) return;\n $accept = $_SERVER['HTTP_ACCEPT'] ?? '';\n if (strpos($accept, 'text/markdown') === false) return;\n header('Content-Type: text/markdown; charset=utf-8');\n header('Vary: Accept');\n $post = get_queried_object();\n echo \"# \" . get_the_title($post) . \"\\n\\n\";\n echo wp_strip_all_tags(apply_filters('the_content', $post->post_content));\n exit;\n});"
},
{
"id": "static",
"label": "Hugo / Jekyll / Astro",
"language": "txt",
"filename": "static/page.md",
"code": "# Mechanism 2: serve .md alongside .html\n# Hugo: place page.md in /static/ — built unchanged\n# Jekyll: drop page.md in /assets/ — copied as-is\n# Astro: src/pages/page.md.ts that exports a GET returning markdown\n\n# Then advertise with mechanism 3 in <head>:\n# <link rel=\"alternate\" type=\"text/markdown\" href=\"/page.md\">"
}
]
}
]
}APIを使用してプログラムで取得できます（近日公開）
このJSONは内部使用向けです — MarkdownやllMs.txtファイルとは異なり、サイトにアップロードするものではありません。スコアの経時変化を追跡するための基準値として保存するか、開発チームと共有するか、CI/CDパイプラインに統合してください。
結果を共有
または AI に改善方法を聞く
セカンドオピニオンもどうぞ
Cloudflare も無料のスキャナーを公開していますが、問いが違います。あちらは、エージェントが呼び出すためにサイトが公開しているもの（MCP server card、Agent Skills、API カタログ、DNS レコード）を採点します。当社は、エージェントがコンテンツに到達し、読み、理解できるかを採点します。片方が高く、もう片方が低いサイトもあります。数字が食い違うのは当然です。別々の問いへの答えであり、どちらも知る価値があります。
Cloudflare で synthcore.org をスキャンバッジを埋め込む
このバッジをサイトに追加してください。AI対応スコアが変わると自動的に更新されます。
Script 推奨
<script src="https://agentready.md/badge.js" data-id="2429183e-b7da-4c55-9ff4-cc94fbd7f71b" data-domain="synthcore.org"></script>
Markdown
[](https://agentready.md/ja/r/synthcore.org)近日公開: ドメイン全体分析
ドメイン全体をクロールし、llms.txtを生成し、AI対応スコアを経時的にモニタリング。ウェイトリストに登録して通知を受け取りましょう。
リストに登録されました！サービス開始時にお知らせします。