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A negative slope means learning\n * is happening. The magnitude tells you how fast. A slope near zero\n * means the model has saturated at this data/capacity combination.\n *\n * Research context:\n * - The loss curve of an online learner is a compression curve.\n * Cumulative BPB is literally the code length per symbol.\n * - Shannon's source coding theorem gives the floor: entropy of the\n * source. The gap between model BPB and source entropy = model's\n * remaining ignorance.\n * - The slope at any point is the instantaneous \"compression gain.\"\n * Steep negative = rapid learning. Flat = saturated or stuck.\n * Positive = forgetting (distribution shift, or instability).\n *\n * What windowed slope tells you:\n * - Sustained negative slope → model is still learning useful patterns\n * - Slope flattening → approaching capacity limit (for this data/model)\n * - Sharp positive spike → distribution shift (phase transition)\n * - Slope recovery after spike → adaptation to new distribution\n * - Slope getting less negative each epoch → diminishing returns\n *\n * The \"angle\" metaphor: if you drew a tangent line at any point on\n * the loss curve, the angle below horizontal = learning speed.\n * Horizontal = no learning. Tilting up = forgetting.\n */\n\nexport interface SlopeWindow {\n startStep: number;\n endStep: number;\n slope: number; // bits/byte per step (negative = improving)\n meanLoss: number; // average loss in window\n phase: number; // dominant phase in window\n}\n\n/**\n * Compute windowed slopes from history.\n * Returns one SlopeWindow per window of `windowSize` entries,\n * stepping by `stride` entries.\n *\n * Slope is computed by linear regression over the window.\n */\nexport function computeSlopes(\n history: { loss: number; phase: number }[],\n windowSize: number = 50,\n stride: number = 25,\n): SlopeWindow[] {\n const results: SlopeWindow[] = [];\n if (history.length < windowSize) return results;\n\n for (let start = 0; start + windowSize <= history.length; start += stride) {\n const window = history.slice(start, start + windowSize);\n const n = window.length;\n\n // Linear regression: slope of loss vs position\n let sumX = 0, sumY = 0, sumXY = 0, sumXX = 0;\n for (let i = 0; i < n; i++) {\n sumX += i;\n sumY += window[i].loss;\n sumXY += i * window[i].loss;\n sumXX += i * i;\n }\n const slope = (n * sumXY - sumX * sumY) / (n * sumXX - sumX * sumX);\n const meanLoss = sumY / n;\n\n // Dominant phase: mode\n const phaseCounts: Record = {};\n for (const h of window) phaseCounts[h.phase] = (phaseCounts[h.phase] || 0) + 1;\n let maxCount = 0, dominantPhase = 0;\n for (const [p, c] of Object.entries(phaseCounts)) {\n if (c > maxCount) { maxCount = c; dominantPhase = parseInt(p); }\n }\n\n results.push({\n startStep: start,\n endStep: start + windowSize - 1,\n slope,\n meanLoss,\n phase: dominantPhase,\n });\n }\n\n return results;\n}\n\n/**\n * Detect distribution shifts: points where slope changes sign\n * from negative to positive (learning → forgetting).\n */\nexport function detectShifts(slopes: SlopeWindow[]): number[] {\n const shifts: number[] = [];\n for (let i = 1; i < slopes.length; i++) {\n if (slopes[i - 1].slope < -0.001 && slopes[i].slope > 0.001) {\n shifts.push(slopes[i].startStep);\n }\n }\n return shifts;\n}\n\n/**\n * Interpret slope for UI display.\n */\nexport function interpretSlope(slope: number): {\n label: string;\n color: string;\n description: string;\n} {\n if (slope < -0.01) return {\n label: \"learning fast\",\n color: \"#4ade80\",\n description: \"Model is rapidly improving its compression of this data.\",\n };\n if (slope < -0.002) return {\n label: \"learning\",\n color: \"#86efac\",\n description: \"Model is steadily improving. Patterns are being captured.\",\n };\n if (slope < 0.002) return {\n label: \"plateau\",\n color: \"#fcd34d\",\n description: \"Model has roughly saturated on current data/capacity.\",\n };\n if (slope < 0.01) return {\n label: \"drifting\",\n color: \"#fca5a5\",\n description: \"Loss is increasing slightly. Possible distribution shift.\",\n };\n return {\n label: \"forgetting\",\n color: \"#ef4444\",\n description: \"Loss rising sharply. Distribution shift or instability.\",\n };\n}\n","deleted","label",[178,160],"engine","permalink","https://www.val.town/x/c15r/microgpt/code/engine/analytics.ts","extension","actionData","errors"]