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Use Hugging Face inline math syntax in the model card

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  1. README.md +7 -7
README.md CHANGED
@@ -33,7 +33,7 @@ CPU.
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  ## Model
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- Each row is one location and day, with up to two targets $y_1, y_2$ (log values, standardised).
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  $$
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  \begin{aligned}
@@ -45,16 +45,16 @@ $$
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  - **Location**: an 8-dim area embedding plus a station offset that starts near zero and is penalised, so a
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  station with little data falls back to its area.
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- - **Time**: fixed Gaussian bumps $b_k(t) = \exp\{-\tfrac12((t - c_k)/w)^2\}$ with centres every $w$ days, so the
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  level is a smooth function of time.
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  - **Shared trunk, two heads**: two layers of 64 with SiLU, then one linear head per target. A day where only one
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  target was observed still trains everything the other depends on.
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- **Loss.** An observed value is a mean of $n$ readings, so its variance around the level is $\sigma_j^2 / n + \tau_j^2$,
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- with $\sigma_j$, $\tau_j$ learned per target. The Gaussian negative log-likelihood is averaged over observed cells
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  only: a missing target is **masked**, not dropped. Added to it:
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- - a **curvature penalty** $\lambda \cdot \overline{(\mu_{t+1} - 2\mu_t + \mu_{t-1})^2}$ over every location's
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  predicted series on the **whole** day grid, observed or not, which keeps the level smooth through gaps;
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  - a small L2 penalty on the station offsets.
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@@ -65,8 +65,8 @@ cross-validation in the post:
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  | Setting | Value |
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  |---|---|
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- | curvature penalty $\lambda$ (`rough`) | 1e5 |
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- | bump spacing $w$ (`spacing`) | 30 days |
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  | hidden width | 64 |
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  | learning rate | 5e-3 |
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  | weight decay | 1e-4 |
 
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  ## Model
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+ Each row is one location and day, with up to two targets \\( y_1, y_2 \\) (log values, standardised).
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  $$
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  \begin{aligned}
 
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  - **Location**: an 8-dim area embedding plus a station offset that starts near zero and is penalised, so a
47
  station with little data falls back to its area.
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+ - **Time**: fixed Gaussian bumps \\( b_k(t) = \exp\big(-\tfrac12((t - c_k)/w)^2\big) \\) with centres every \\( w \\) days, so the
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  level is a smooth function of time.
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  - **Shared trunk, two heads**: two layers of 64 with SiLU, then one linear head per target. A day where only one
51
  target was observed still trains everything the other depends on.
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+ **Loss.** An observed value is a mean of \\( n \\) readings, so its variance around the level is \\( \sigma_j^2 / n + \tau_j^2 \\),
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+ with \\( \sigma_j \\), \\( \tau_j \\) learned per target. The Gaussian negative log-likelihood is averaged over observed cells
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  only: a missing target is **masked**, not dropped. Added to it:
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+ - a **curvature penalty** \\( \lambda \cdot \overline{(\mu_{t+1} - 2\mu_t + \mu_{t-1})^2} \\) over every location's
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  predicted series on the **whole** day grid, observed or not, which keeps the level smooth through gaps;
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  - a small L2 penalty on the station offsets.
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  | Setting | Value |
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  |---|---|
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+ | curvature penalty \\( \lambda \\) (`rough`) | 1e5 |
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+ | bump spacing \\( w \\) (`spacing`) | 30 days |
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  | hidden width | 64 |
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  | learning rate | 5e-3 |
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  | weight decay | 1e-4 |