Memory-constrained forecasting
Measured
19% lower tail-forecast error at equal memory
Same bytes. At the best size, 2 learned summaries beat 14× more raw history (28 past values).
Same memory, two ways to spend it
Slide the memory size. Both forecasters always get exactly the same bytes.
Raw history
28 past values
Learned summaries
2 slots of 14 numbers
Tail-forecast error, lower is better
19% lower, p < 0.001
75.8 KB: 2 learned slots against 28 raw values. Tail loss 0.01174 against 0.00949, 19% lower, p < 0.001.
Does it hold at every size?
11 of 12 comparisons are significant on their own, and the learned side is ahead in all 12. The exception is recency at the largest size (p = 0.205). Tap a size to move the slider.
| Recency | 13% lower, significant, p < 0.001 | 19% lower, significant, p < 0.001 | 18% lower, significant, p < 0.001 | 14% lower, significant, p < 0.001 | 9% lower, significant, p = 0.011 | 5% lower, not significant, p = 0.205 |
|---|---|---|---|---|---|---|
| Tail oracle | 40% lower, significant, p = 0.001 | 45% lower, significant, p < 0.001 | 46% lower, significant, p < 0.001 | 45% lower, significant, p < 0.001 | 43% lower, significant, p < 0.001 | 34% lower, significant, p = 0.002 |
Cells show the cut in q99 pinball loss. Compare the two sides within a cell, not across rows: the tail oracle’s losses are inflated by a readout mismatch. One market, one year of real electricity prices (499 nodes, 35,035 intervals, 3,504 held-out queries); other markets are not tested.
Exact numbers for all six sizes
| Learned / raw slots | Bytes | Recency raw | Recency learned | Recency p | Tail raw | Tail learned | Tail p |
|---|---|---|---|---|---|---|---|
| 1 / 14 | 61,876 | 0.01161 | 0.01009 | 0.0000283 | 0.07552 | 0.04501 | 0.00142 |
| 2 / 28 | 75,848 | 0.01174 | 0.009486 | 7.66e-10 | 0.07763 | 0.04269 | 0.000364 |
| 3 / 42 | 89,820 | 0.01173 | 0.009649 | 3.57e-8 | 0.0776 | 0.04215 | 0.000289 |
| 4 / 56 | 103,792 | 0.01175 | 0.0101 | 0.0000365 | 0.07623 | 0.04161 | 0.000326 |
| 5 / 70 | 117,764 | 0.01176 | 0.01068 | 0.0112 | 0.07267 | 0.04111 | 0.000535 |
| 6 / 84 | 131,736 | 0.01157 | 0.01101 | 0.205 | 0.06187 | 0.04059 | 0.00153 |
