New blog

app/projects/graph-attention-topology/page.tsx

@@ -14,34 +14,34 @@ const paperLinks = [
 
 const highlights = [
   {
-    value: "No known graph",
-    label: "Learns topology without prior adjacency examples.",
+    value: "No graph labels",
+    label: "Learns from trajectories without seeing adjacency examples.",
   },
   {
     value: "Unknown dynamics",
-    label: "Uses observed states instead of hand-specified equations.",
+    label: "Works from observed state sequences, not hand-written dynamics.",
   },
   {
-    value: "Attention as edges",
-    label: "Interprets learned attention scores as the graph estimate.",
+    value: "Attention becomes edges",
+    label: "Uses attention scores as the topology estimate.",
   },
 ];
 
 const steps = [
-  "Embed every agent into a shared latent space.",
-  "Project embeddings into key/query vectors and compute pairwise attention.",
-  "Translate observed agent states into values.",
-  "Predict the next state and read the attention matrix as topology.",
+  "Put each agent in a shared latent space.",
+  "Build key/query pairs and compute attention between agents.",
+  "Use observed states as the values passed through attention.",
+  "Forecast the next state, then threshold attention to recover topology.",
 ];
 
 export const metadata: Metadata = {
   title: "Graph Attention Topology Inference",
   description:
-    "Project page for Graph Attention Inference of Network Topology in Multi-Agent Systems.",
+    "A project page for inferring hidden multi-agent network topology with graph attention.",
   openGraph: {
     title: "Graph Attention Inference of Network Topology in Multi-Agent Systems",
     description:
-      "A graph-attention approach for inferring hidden network topology from multi-agent trajectories.",
+      "Inferring hidden network topology from multi-agent trajectories with graph attention.",
     type: "article",
     publishedTime: "2024-10-26",
     images: [
@@ -117,7 +117,7 @@ export default function GraphAttentionProjectPage() {
                 Graph Attention Inference of Network Topology
               </h1>
               <p className="max-w-[43rem] text-[1.12rem] leading-8 text-graph-soft sm:text-[1.25rem]">
-                Inferring the hidden graph behind a multi-agent system by training attention to predict what each agent does next.
+                We use next-state prediction to expose the interaction graph behind a multi-agent system.
               </p>
             </div>
 
@@ -196,14 +196,14 @@ export default function GraphAttentionProjectPage() {
               <div className="space-y-5">
                 <p className="graph-kicker">Overview</p>
                 <h2 className="max-w-[42rem] text-balance text-4xl font-semibold leading-tight text-graph-ink sm:text-5xl">
-                  Predict the next state, then read the graph from what the model attended to.
+                  Train on motion. Read the graph from attention.
                 </h2>
                 <div className="space-y-5 text-[1.02rem] leading-8 text-graph-soft">
                   <p>
-                    The paper studies a practical problem in networked multi-agent systems: the agents move, synchronize, or converge, but the interaction graph behind that behavior is not given.
+                    In many multi-agent systems, you can watch agents move, synchronize, or settle, but you are not given who influences whom.
                   </p>
                   <p>
-                    The model is trained on state trajectories from consensus dynamics and Kuramoto oscillators. During prediction, attention scores between agent embeddings become an interpretable approximation of the adjacency matrix.
+                    This project tests whether a predictor trained on trajectories can recover that missing adjacency matrix. On consensus dynamics and Kuramoto oscillators, the learned attention scores become a usable proxy for edges.
                   </p>
                 </div>
               </div>
@@ -211,7 +211,7 @@ export default function GraphAttentionProjectPage() {
               <Figure
                 src={simulationImage}
                 alt="Consensus and Kuramoto simulation examples with adjacency matrices"
-                caption="Simulation examples: consensus dynamics and Kuramoto oscillators paired with their hidden adjacency matrices."
+                caption="Consensus and Kuramoto trajectories, each paired with the hidden adjacency matrix used for simulation."
                 className="rounded-md"
               />
             </section>
@@ -221,10 +221,10 @@ export default function GraphAttentionProjectPage() {
                 <div className="space-y-5">
                   <p className="graph-kicker">Method</p>
                   <h2 className="text-balance text-4xl font-semibold leading-tight text-graph-ink sm:text-5xl">
-                    A topology estimate falls out of the attention layer.
+                    The graph is never supervised directly.
                   </h2>
                   <p className="text-[1.02rem] leading-8 text-graph-soft">
-                    Instead of supervising the graph directly, the model learns to forecast the system. The attention matrix is then thresholded and compared with the true graph.
+                    The model learns the dynamics first. After training, we threshold the attention matrix and compare the inferred edges with the true graph.
                   </p>
                 </div>
 
@@ -243,7 +243,7 @@ export default function GraphAttentionProjectPage() {
               <Figure
                 src={architectureImage}
                 alt="Architecture diagram showing agent embeddings, key-query attention, values, predictions, and loss"
-                caption="Architecture: embeddings produce key/query vectors; observed states produce values; the attention matrix approximates adjacency."
+                caption="Model layout: embeddings create key/query vectors, states provide values, and attention is later read as adjacency."
                 className="rounded-md"
               />
             </section>
@@ -252,31 +252,31 @@ export default function GraphAttentionProjectPage() {
               <div className="max-w-[46rem] space-y-5">
                 <p className="graph-kicker">Results</p>
                 <h2 className="text-balance text-4xl font-semibold leading-tight text-graph-ink sm:text-5xl">
-                  Strongest graph recovery appears with smaller systems, and more simulations help larger systems.
+                  Smaller systems recover cleanly; larger ones improve with more simulations.
                 </h2>
                 <p className="text-[1.02rem] leading-8 text-graph-soft">
-                  F1 link-prediction scores are above a random baseline for both tested dynamics. Consensus dynamics are easier than Kuramoto oscillators, while additional simulation data improves larger-agent inference.
+                  F1 scores beat a random baseline for both dynamics. Consensus is the easier case; Kuramoto needs more data as the number of agents grows.
                 </p>
               </div>
 
               <Figure
                 src={resultsImage}
                 alt="F1 score results for consensus dynamics and Kuramoto oscillators"
-                caption="F1 results across system size and number of simulations for consensus dynamics and Kuramoto oscillators."
+                caption="F1 link-prediction results across system size and simulation count."
                 className="rounded-md"
               />
 
               <div className="grid gap-6 md:grid-cols-[minmax(0,0.78fr)_minmax(0,1fr)] md:items-start">
                 <div className="rounded-md border border-graph-line bg-graph-panel p-5">
-                  <p className="font-mono text-[0.72rem] uppercase text-graph-muted">training behavior</p>
+                  <p className="font-mono text-[0.72rem] uppercase text-graph-muted">training trace</p>
                   <p className="mt-3 text-[1.02rem] leading-8 text-graph-soft">
-                    Attention first learns the obvious self-dependencies, then gradually recovers inter-agent structure as training progresses.
+                    Early training mostly finds self-dependencies. Later epochs start assigning weight to the agent-to-agent links.
                   </p>
                 </div>
                 <Figure
                   src={attentionImage}
                   alt="Attention matrices over training epochs and predicted graphs"
-                  caption="Attention values through training stages, from true graph to predicted graph."
+                  caption="Attention during training, from the true graph reference to the final predicted graph."
                   className="rounded-md"
                 />
               </div>