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--git a/main.tex b/main.tex index 2a2c99f..a3b6624 100644 --- a/main.tex +++ b/main.tex @@ -204,7 +204,7 @@ design is presented in Section~\ref{section:d-cliques}) along with an empirical illustration of its benefits. In Section~\ref{section:clique-averaging-momentum}, we show how to further reduce bias with Clique Averaging and how to use it to -implement momentum. We present the results or our extensive experimental +implement momentum. We present the results of our extensive experimental study in Section~\ref{section:non-clustered}. We review some related work in Section~\ref{section:related-work}, and conclude with promising directions for future work in Section~\ref{section:conclusion}. @@ -489,13 +489,13 @@ amount of messages traveling on the network, it also introduces its own bias. Figure~\ref{fig:connected-cliques-bias} illustrates the problem on the simple case of two cliques connected by one inter-clique edge (here, -between the green node of the left clique and the purple node of the right +between the green node of the left clique and the pink node of the right clique). Let us focus on node A. With weights computed as in \eqref{eq:metro}, node A's self-weight is $\frac{12} {110}$, the weight between A and the green node connected to B is $\frac{10}{110}$, and all other neighbors of A have a weight of $\frac{11}{110}$. Therefore, the -gradient at A is biased towards its own class (purple) and against the green +gradient at A is biased towards its own class (pink) and against the green class. A similar bias holds for all other nodes without inter-clique edges with respect to their respective classes. For node B, all its edge weights (including its self-weight) are equal to $\frac{1} @@ -648,14 +648,14 @@ significantly reduces the variance across nodes in this setup. \centering \begin{subfigure}[b]{0.48\textwidth} % To regenerate the figure, from directory results/mnist -% python ../../../learn-topology/tools/plot_convergence.py fully-connected-cliques/all/2021-03-10-10:19:44-CET no-init-no-clique-avg/fully-connected-cliques/all/2021-03-12-11:12:49-CET random-10/all/2021-03-17-20:28:12-CET random-10-diverse/all/2021-03-17-20:28:35-CET --labels 'd-clique (fcc)' 'd-clique (fcc) no clique avg.' '10 random edges' '10 random edges (all classes represented)' --add-min-max --legend 'lower right' --ymin 88 --ymax 92.5 --yaxis test-accuracy --save-figure ../../figures/d-cliques-mnist-linear-comparison-to-non-clustered-topologies.png --font-size 13 +% python ../../../../Software/non-iid-topology-simulator/tools/plot_convergence.py fully-connected-cliques/all/2021-03-10-10:19:44-CET no-init-no-clique-avg/fully-connected-cliques/all/2021-03-12-11:12:49-CET random-10/all/2021-07-23-11:59:56-CEST random-10-diverse/all/2021-03-17-20:28:35-CET --labels 'd-clique (fcc)' 'd-clique (fcc) no clique avg.' '10 random edges' '10 random edges (all classes represented)' --add-min-max --legend 'lower right' --ymin 80 --ymax 92.5 --yaxis test-accuracy --save-figure ../../figures/d-cliques-mnist-linear-comparison-to-non-clustered-topologies.png --font-size 13 \centering \includegraphics[width=\textwidth]{figures/d-cliques-mnist-linear-comparison-to-non-clustered-topologies} \caption{MNIST with Linear Model} \end{subfigure} \hfill % To regenerate the figure, from directory results/cifar10 -% python ../../../learn-topology/tools/plot_convergence.py no-init/fully-connected-cliques/all/2021-03-13-18:32:55-CET no-init-no-clique-avg/fully-connected-cliques/all/2021-03-13-18:34:35-CET random-10/all/2021-03-17-20:30:03-CET random-10-diverse/all/2021-03-17-20:30:41-CET random-10-diverse-unbiased-gradient/all/2021-03-17-20:31:14-CET --labels 'd-clique (fcc) clique avg.' 'd-clique (fcc) no clique avg.' '10 random edges' '10 random edges (all classes repr.)' '10 random (all classes repr.) with unbiased grad.' --add-min-max --legend 'upper left' --yaxis test-accuracy --save-figure ../../figures/d-cliques-cifar10-linear-comparison-to-non-clustered-topologies.png --ymax 119 --font-size 13 +% python ../../../../Software/non-iid-topology-simulator/tools/plot_convergence.py no-init/fully-connected-cliques/all/2021-03-13-18:32:55-CET no-init-no-clique-avg/fully-connected-cliques/all/2021-03-13-18:34:35-CET random-10/all/2021-07-23-14:33:48-CEST random-10-diverse/all/2021-03-17-20:30:41-CET random-10-diverse-unbiased-gradient/all/2021-03-17-20:31:14-CET --labels 'd-clique (fcc) clique avg.' 'd-clique (fcc) no clique avg.' '10 random edges' '10 random edges (all classes repr.)' '10 random (all classes repr.) with unbiased grad.' --add-min-max --legend 'upper left' --yaxis test-accuracy --save-figure ../../figures/d-cliques-cifar10-linear-comparison-to-non-clustered-topologies.png --ymax 119 --font-size 13 \begin{subfigure}[b]{0.48\textwidth} \centering \includegraphics[width=\textwidth]{figures/d-cliques-cifar10-linear-comparison-to-non-clustered-topologies} @@ -695,7 +695,7 @@ proposed with D-Cliques. \begin{subfigure}[htbp]{0.48\textwidth} \centering % To regenerate the figure, from directory results/mnist -% python ../../../learn-topology/tools/plot_convergence.py no-init/fully-connected-cliques/all/2021-03-12-11:12:01-CET rm-1-edge/all/2021-03-18-17:28:27-CET rm-5-edges/all/2021-03-18-17:29:10-CET rm-1-edge-unbiased-grad/all/2021-03-18-17:28:47-CET rm-5-edges-unbiased-grad/all/2021-03-18-17:29:36-CET --add-min-max --ymin 85 --ymax 92.5 --legend 'lower right' --yaxis test-accuracy --labels 'fcc with clique grad.' 'fcc -1 edge/clique, no clique avg.' 'fcc -5 edges/clique, no clique avg.' 'fcc -1 edge/clique, clique avg.' 'fcc -5 edges/clique, clique avg.' --save-figure ../../figures/d-cliques-mnist-clique-clustering-fcc.png --font-size 13 +% python ../../../learn-topology/tools/plot_convergence.py no-init/fully-connected-cliques/all/2021-03-12-11:12:01-CET rm-1-edge/all/2021-03-18-17:28:27-CET rm-5-edges/all/2021-03-18-17:29:10-CET rm-1-edge-unbiased-grad/all/2021-03-18-17:28:47-CET rm-5-edges-unbiased-grad/all/2021-03-18-17:29:36-CET --add-min-max --ymin 85 --ymax 92.5 --legend 'lower right' --yaxis test-accuracy --labels 'fcc with clique grad.' 'fcc -1 edge/clique, no clique grad.' 'fcc -5 edges/clique, no clique grad.' 'fcc -1 edge/clique, clique grad.' 'fcc -5 edges/clique, clique grad.' --save-figure ../../figures/d-cliques-mnist-clique-clustering-fcc.png --font-size 13 \includegraphics[width=\textwidth]{figures/d-cliques-mnist-clique-clustering-fcc} \caption{\label{fig:d-cliques-mnist-clique-clustering} MNIST} \end{subfigure} @@ -717,9 +717,9 @@ proposed with D-Cliques. So far, we have used a fully-connected inter-clique topology for D-Cliques, which has the advantage of bounding the -average shortest path to $2$ between any pair of nodes. This choice requires $ +average shortest path to $3$ between any pair of nodes. This choice requires $ \frac{n}{c}(\frac{n}{c} - 1)$ inter-clique edges, which scales quadratically -in the number of nodes $n$ for a given clique size $c$. This can become significant at larger scales when $n$ is +in the number of nodes $n$ for a given clique size $c$\footnote{We consider \textit{directed} edges in the analysis: the number of undirected edges is half and does not affect asymptotic behavior.}. This can become significant at larger scales when $n$ is large compared to $c$. In this last series of experiments, we evaluate the effect of choosing sparser @@ -730,7 +730,7 @@ to create cliques as a starting point. The inter-clique topology with (almost) fewest possible edges is a \textit{ring}, which -uses $\frac{n}{c} - 1$ inter-clique edges and therefore scales linearly in +uses $\frac{2n}{c}$ inter-clique edges and therefore scales linearly in $n$. We also consider another topology that scales linearly and achieves a logarithmic @@ -741,18 +741,23 @@ assembled in larger groups of $c$ cliques that are connected internally with one edge per pair of cliques, but with only one edge between pairs of larger groups. The topology is built recursively such that $c$ groups will themselves form a -larger group at the next level up. This results in at most $nc$ edges per node if edges are evenly distributed, and therefore also scales linearly in the number of nodes. +larger group at the next level up. This results in at most $c$ edges per node +if edges are evenly distributed: i.e., each group within the same level adds +at most $c-1$ edges to other groups, leaving one node per group with $c-1$ +edges that can receive an additional edge to connect with other groups at the next level. +Since nodes have at most $c$ edges, $n$ nodes have at most $nc$ edges, therefore +this fractal scheme also scales linearly in the number of nodes. Finally, we propose to connect cliques according to a small-world-like topology~\cite{watts2000small} applied on top of a ring~\cite{stoica2003chord}. In this scheme, cliques are first arranged in a ring. Then each clique adds symmetric edges, both clockwise and -counter-clockwise on the ring, with the $ns$ closest cliques in sets of +counter-clockwise on the ring, with the $m$ closest cliques in sets of cliques that are exponentially bigger the further they are on the ring (see Algorithm~\ref{Algorithm:Smallworld} in the appendix for details on the construction). This ensures a good connectivity with other cliques that are close on the ring, while still keeping the average shortest -path small. This scheme uses $\frac{n}{c}*2(ns)\log(\frac{n}{c})$ inter-clique edges and +path small. This scheme uses $\frac{n}{c}*2(m)\log(\frac{n}{c})$ inter-clique edges and therefore grows in the order of $O(n\log(n))$ with the number of nodes. Figure~\ref{fig:d-cliques-cifar10-convolutional} shows the convergence diff --git a/results/cifar10/random-10/experiments.sh b/results/cifar10/random-10/experiments.sh index dc2eeb9..fa3888d 100755 --- a/results/cifar10/random-10/experiments.sh +++ b/results/cifar10/random-10/experiments.sh @@ -1,5 +1,5 @@ #!/usr/bin/env bash -TOOLS=../../../../learn-topology/tools; CWD="$(pwd)"; cd $TOOLS +TOOLS=../../$(cat ../../toolspath); CWD="$(pwd)"; cd $TOOLS BSZS=' 20 ' @@ -8,7 +8,7 @@ LRS=' ' for BSZ in $BSZS; do for LR in $LRS; - do python sgp-mnist.py --nb-nodes 100 --nb-epochs 100 --local-classes 1 --seed 1 --nodes-per-class 10 10 10 10 10 10 10 10 10 10 --global-train-ratios 1 1 1 1 1 1 1 1 1 1 --dist-optimization d-psgd --topology random-10 --metric dissimilarity --learning-momentum 0.9 --sync-per-mini-batch 1 --results-directory $CWD/all --learning-rate $LR --batch-size $BSZ "$@" --single-process --nb-logging-processes 10 --dataset cifar10 --model gn-lenet --accuracy-logging-interval 10 --validation-set-ratio 0.5 + do python simulate.py --nb-nodes 100 --nb-epochs 100 --local-classes 1 --seed 1 --nodes-per-class 10 10 10 10 10 10 10 10 10 10 --global-train-ratios 1 1 1 1 1 1 1 1 1 1 --dist-optimization d-psgd --topology random-10 --metric dissimilarity --learning-momentum 0.9 --sync-per-mini-batch 1 --results-directory $CWD/all --learning-rate $LR --batch-size $BSZ "$@" --single-process --nb-logging-processes 10 --dataset cifar10 --model gn-lenet --accuracy-logging-interval 10 --validation-set-ratio 0.5 done; done; diff --git a/results/mnist/random-10/experiments.sh b/results/mnist/random-10/experiments.sh index ba5dc2a..3423777 100755 --- a/results/mnist/random-10/experiments.sh +++ b/results/mnist/random-10/experiments.sh @@ -1,5 +1,5 @@ #!/usr/bin/env bash -TOOLS=../../../../learn-topology/tools; CWD="$(pwd)"; cd $TOOLS +TOOLS=../../$(cat ../../toolspath); CWD="$(pwd)"; cd $TOOLS BSZS=' 128 ' @@ -8,7 +8,7 @@ LRS=' ' for BSZ in $BSZS; do for LR in $LRS; - do python sgp-mnist.py --nb-nodes 100 --nb-epochs 100 --local-classes 1 --seed 1 --nodes-per-class 10 10 10 10 10 10 10 10 10 10 --global-train-ratios 0.802568 0.802568 0.802568 0.802568 0.802568 0.802568 0.802568 0.802568 0.802568 0.802568 --dist-optimization d-psgd --topology random-10 --metric dissimilarity --learning-momentum 0. --sync-per-mini-batch 1 --results-directory $CWD/all --learning-rate $LR --batch-size $BSZ "$@" --parallel-training --nb-workers 10 --dataset mnist --model linear + do python simulate.py --nb-nodes 100 --nb-epochs 100 --local-classes 1 --seed 1 --nodes-per-class 10 10 10 10 10 10 10 10 10 10 --global-train-ratios 0.802568 0.802568 0.802568 0.802568 0.802568 0.802568 0.802568 0.802568 0.802568 0.802568 --dist-optimization d-psgd --topology random-10 --metric dissimilarity --learning-momentum 0. --sync-per-mini-batch 1 --results-directory $CWD/all --learning-rate $LR --batch-size $BSZ "$@" --parallel-training --nb-workers 10 --dataset mnist --model linear done; done; diff --git a/results/toolspath b/results/toolspath new file mode 100644 index 0000000..188c1f8 --- /dev/null +++ b/results/toolspath @@ -0,0 +1 @@ +../../../Software/non-iid-topology-simulator/tools/ -- GitLab