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✓✓ 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 Not peer-reviewed.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)
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권장 내용
# 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)
전체 llms.txt는 도메인 전체 분석이 필요합니다 (곧 출시)
이 파일을 도메인 루트의 https://synthcore.org/llms.txt에 업로드하세요. ChatGPT, Claude, Perplexity 등의 AI 에이전트가 이 파일을 확인하여 사이트 구조를 파악합니다.
이 사이트에는 이미 llms.txt 파일이 있습니다.
유효한 형식# 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
접근성
JavaScript 없이 콘텐츠 이용 가능
(100/100)
Content available without JavaScript
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Page size: 37KB
AI 발견 가능성
robots.txt가 AI 봇 허용
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✓ robots.txt
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JSON-LD found: Organization, SoftwareApplication, WebSite, WebPage, BreadcrumbList, DefinedTermSet, DefinedTermSet, DefinedTermSet, ScholarlyArticle, TechArticle
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lang="en"
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Content ratio: 24.1% (9051 content chars / 37518 HTML bytes)
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"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",
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"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\">"
}
]
}
]
}API를 사용하여 프로그래밍 방식으로 가져올 수 있습니다 (곧 출시)
이 JSON은 내부용입니다 — Markdown 및 llms.txt 파일과 달리 사이트에 업로드하기 위한 것이 아닙니다. 시간에 따른 점수 추적을 위한 기준값으로 저장하거나, 개발팀과 공유하거나, CI/CD 파이프라인에 통합하세요.
결과 공유
또는 AI에게 개선 방법을 물어보세요
다른 의견도 들어보시겠어요?
Cloudflare에도 무료 스캐너가 있는데, 던지는 질문이 다릅니다. 그쪽은 에이전트가 호출할 수 있도록 사이트가 게시한 것(MCP 서버 카드, Agent Skills, API 카탈로그, DNS 레코드)을 채점합니다. 저희는 에이전트가 콘텐츠에 도달해 읽고 이해할 수 있는지를 채점합니다. 한쪽은 좋고 다른 쪽은 나쁠 수 있으니 두 점수가 다른 것은 당연합니다. 서로 다른 질문에 대한 답이고, 둘 다 알아둘 가치가 있습니다.
Cloudflare로 synthcore.org 검사하기배지 삽입
이 배지를 사이트에 추가하세요. AI 준비도 점수가 변경되면 자동으로 업데이트됩니다.
Script 권장
<script src="https://agentready.md/badge.js" data-id="2429183e-b7da-4c55-9ff4-cc94fbd7f71b" data-domain="synthcore.org"></script>
Markdown
[](https://agentready.md/ko/r/synthcore.org)곧 출시: 전체 도메인 분석
전체 도메인을 크롤링하고, llms.txt를 생성하고, AI 준비도 점수를 시간에 따라 모니터링하세요. 대기자 명단에 등록하여 알림을 받으세요.
명단에 등록되었습니다! 서비스 출시 시 알려드리겠습니다.