# svd-lowrank: truncated-SVD compression of pol_mid.json plain tables

Source: github.com/gtmcknight/amm-sim @ 4812a6382311624e1506aca131ca35c378f930d9, research/solved (Taylor / gtmcknight). pol_mid.json sha256 efbb5ee102db4d312f64565d9bf7232b6becbe02b624164f744a402bbbf2983b.

**Bottom line:** the best setting tried that fits in 12 KB (ranks 4/6/6, 11,571 bytes) loses **0.464 se 0.014** on the report seeds. **It misses the < 0.2 target.** Low rank can't fit the jump in the tables well (see Problems).

## Gate (P)
On seeds 10000..12047, the full pol_mid.json with `plain:soft=1` scored **+2.828 vs HA**, from per-seed edges against `calib_out_2048.json` HA rows. The README states +2.828. So the plain/Gaussian version reproduces. gates.py itself was not run.

## Tables (step 1)
| name | shape | rows (axis, step) | columns (axis) | min | max |
|---|---|---|---|---|---|
| A0, B0 | 321x13 | w = (row-160)*5 bps, -800..+800 | rival R: -30..+30 bps in 5 bps steps (FB=6) | -24.262 | 800.0 |
| A1, B1 | 321x49 | same | rival at W2L x 5 bps (W2L non-uniform in 5-bps units: 0,±1..±12 step 1, ±14,17,20,25,30,40,50,60,80,100,130,160, i.e. -800..+800 bps) | -31.323 | 800.0 |
| A2, B2 | 321x49 | same | same W2L | -31.333 | 800.0 |

Values are ask (A) and bid (B) offsets in bps. **B is the exact point mirror of A**: B[i][j] = A[320-i][C-1-j], max difference 0.0. So only A0, A1 and A2 are stored. The tables have a discontinuity: along a row, the offset jumps from about -18 to about +33 where the policy switches to the "displaced" regime. Rows above the center equal w, which means a zero fee.

## Method
- Each of A0, A1 and A2 is fitted with a truncated SVD of rank k_t.
- The fit only targets what the fee depends on. A cell with fee 0 (A <= w) may decode to any value <= w. This is done with an alternating fill over 60 iterations: refit the SVD, then replace the free cells by min(reconstruction, w).
- Factors: U*sqrt(S) and V*sqrt(S). U's columns are equalised to the same range, then U and V are each quantised to int16 with one shared per-table scale.
- I also tried a row weighting toward |w| < 60 bps. It made the central error worse, so it is not used.
- Scoring uses real.py's own `RealPolicy`/`report()` with `plain:soft=1`. A wrapper (`pair.py`) imports real.py and calls `report()` on a chosen seed range, run with `python3 -I`. **This differs from the brief's command:** real.py hard-codes seeds 10000..10000+NSEED, so the choose set 60000.. can't be passed on its command line. The policy code and the replica are unmodified.
- Loss = mean over seeds of (full edge minus decoded edge), on the same seeds.

## Encoding (exact byte layout)
All little-endian. Blob = `b"SVD1"` (4 bytes), then three table records in the order A0 (C=13), A1 (C=49), A2 (C=49). Each record is:
- `uint8 k`
- `uint32 SCALE`
- `int16 U[321][k]`, row-major (row i at offset 2*k*i)
- `int16 V[C][k]`, row-major

Value in bps: `A[i][j] = (Σ_r U[i][r]*V[j][r]) * SCALE / 2^40`. The dot product fits in int64; in Solidity use int256, then `* SCALE >> 40` (signed: divide, or use sar).

B tables: `B[i][j] = A[320-i][C-1-j]`.

Size of the chosen blob: 4 + (5+2*4*334) + 2*(5+2*6*370) = **11,571 bytes**.

## Tradeoff (choose set, seeds 60000..61023, n=1024)
| setting (k for A0,A1,A2; fee-aware fit) | bytes | loss | se |
|---|---|---|---|
| 3,3,3 | 6,463 | 1.331 | 0.026 |
| 5,5,5 | 10,759 | 0.522 | 0.022 |
| **4,6,6** | **11,571** | **0.468** | **0.020** |

Not scored on seeds, cell error only (fee-space rms over the central rows 100..220):
- Plain SVD without the fee-aware fill is slightly worse than with it. At k=5, A1 rms 3.64 vs 3.56.
- Row weighting is worse.
- k=6 on all three tables needs 12,9xx bytes, which is over 12 KB.

On a 64-seed probe (60000..60063), plain rank 5 lost 0.739 se 0.097.

## Chosen
- **Setting:** ranks 4/6/6, fee-aware fit, 11,571 bytes.
- **Report set:** seeds 10000..12047, n=2048, loss **0.4641**, se **0.0143**.
- **Score vs HA:** full +2.828 vs HA, decoded about +2.36.
- **Per 512-seed segment:** 0.473, 0.484, 0.444, 0.456.
- **Worst 5 seeds (full minus decoded):** 11826: 3.349, 10132: 2.942, 10772: 2.900, 11610: 2.752, 11770: 2.340.

## Lookup cost
Bilinear interpolation of a rank-k table equals a dot product of interpolated factors: `u = (1-f)U[i] + fU[i+1]`, `v = (1-g)V[j] + gV[j+1]`, value = `Σ u_r v_r * SCALE >> 40`.

For one offset (ask, k=6):
- 4k = 24 int16 reads (2 U rows, 2 V rows). These are contiguous: 2k bytes per row, so a row is one 32-byte word read when k <= 16.
- About 4k lerp multiplies, plus k multiplies and k-1 adds for the dot, plus 1 scale multiply and shift. That is roughly 30 multiplies and 30 adds.

The bid uses the mirrored indices `(320-i-1.., C-1-j..)` with the same cost, so ask+bid costs 48 reads and about 60 multiplies. Phase 0 (k=4) costs 16 reads per offset. Any column search over W2L is extra and the same as for the full tables.

## Decoder (standalone, stdlib + numpy)
```python
import struct
import numpy as np


def decode(blob):
    """Decode an SVD1 blob into the six plain tables of pol_mid.json (lists of lists, bps).

    Layout, little-endian: b'SVD1' then, for A0 (C=13), A1 (C=49), A2 (C=49) in that order:
      uint8 k, uint32 SCALE, int16 U[321][k] row-major, int16 V[C][k] row-major.
    A[i][j] = (sum_r U[i][r] * V[j][r]) * SCALE / 2**40   (bps; i = row, j = column)
    B tables are the point mirror of A (exact in pol_mid.json): B[i][j] = A[320-i][C-1-j].
    """
    assert blob[:4] == b'SVD1'
    p = 4
    out = {}
    for name, C in (('0', 13), ('1', 49), ('2', 49)):
        k, sc = struct.unpack_from('<BI', blob, p); p += 5
        U = np.frombuffer(blob, '<i2', 321 * k, p).reshape(321, k).astype(np.int64); p += 2 * 321 * k
        V = np.frombuffer(blob, '<i2', C * k, p).reshape(C, k).astype(np.int64); p += 2 * C * k
        A = (U @ V.T).astype(float) * sc / 2.0 ** 40
        out['A' + name] = A.tolist()
        out['B' + name] = A[::-1, ::-1].tolist()
    assert p == len(blob)
    return out
```
To produce a real.py-loadable file: `d=json.load(open('pol_mid.json')); d.update(decode(blob)); json.dump(d, open('dec.json','w'))`, then `python3 -I real.py dec.json plain:soft=1`.

## Encoder used (for regeneration)
`python3 enc.py 4,6,6 1 0 out.bin out.json`. It needs dec.py alongside and pol_mid.json at the path in POL.
```python
"""encode pol_mid.json plain tables as int16 truncated SVD.
usage: enc.py k mode rowsd out.bin out.json
mode 0: plain SVD of A.  mode 1: SVD fitted only to what the fee depends on: cells with fee 0 (A <= w)
may decode to anything <= w (alternating fill, 60 iterations). rowsd > 0: row weights 1 + 20 exp(-(w/rowsd)^2)."""
import sys, glob, json, struct
sys.path.insert(0, glob.glob('venv/lib/python*/site-packages')[0])
import numpy as np
from dec import decode

POL = 'amm-sim/research/solved/pol_mid.json'
W = (np.arange(321) - 160) * 5.0


def fit(T, k, mode, rowsd):
    wt = np.ones(321) if rowsd <= 0 else 1.0 + 20.0 * np.exp(-(W / rowsd) ** 2)
    sw = np.sqrt(wt)[:, None]
    free = T <= W[:, None] + 1e-9          # fee 0 cells: any value <= w gives the same fee
    X = T.copy()
    for it in range(60 if mode == 1 else 1):
        U, S, Vt = np.linalg.svd(X * sw, full_matrices=False)
        Uk = U[:, :k] * np.sqrt(S[:k]) / sw; Vk = Vt[:k].T * np.sqrt(S[:k])
        R = Uk @ Vk.T
        if mode == 1:
            X = np.where(free, np.minimum(R, W[:, None]), T)
    return Uk, Vk


def encode(k, mode, rowsd):
    d = json.load(open(POL))
    out = bytearray(b'SVD1')
    for name, kk in zip(('A0', 'A1', 'A2'), k if len(k) == 3 else k * 3):
        T = np.array(d[name], dtype=float)
        Uk, Vk = fit(T, kk, mode, rowsd)
        su = np.abs(Uk).max(axis=0)
        Uk = Uk / su * su.max(); Vk = Vk * su / su.max()     # equalise column ranges of U
        su1 = np.abs(Uk).max() / 32767; sv1 = np.abs(Vk).max() / 32767
        qU = np.round(Uk / su1).astype(np.int64)
        # given quantised U, refit V by least squares on the same target, then quantise
        qV = np.round(Vk / sv1).astype(np.int64)
        sc = int(round(su1 * sv1 * 2 ** 40))
        assert 0 < sc < 2 ** 32, sc
        out += struct.pack('<BI', kk, sc)
        out += qU.astype('<i2').tobytes() + qV.astype('<i2').tobytes()
    return bytes(out)


def feeerr(A, T):
    fa = np.maximum(A - W[:, None], 0); ft = np.maximum(T - W[:, None], 0)
    return np.abs(fa - ft)


if __name__ == '__main__':
    k, mode, rowsd = [int(x) for x in sys.argv[1].split(',')], int(sys.argv[2]), float(sys.argv[3])
    blob = encode(k, mode, rowsd)
    open(sys.argv[4], 'wb').write(blob)
    d = json.load(open(POL))
    tabs = decode(blob)
    s = []
    for nm in ('A0', 'A1', 'A2'):
        e = feeerr(np.array(tabs[nm]), np.array(d[nm]))
        c = e[100:221]
        s.append(f'{nm} fee-err max {e.max():.2f} rms {np.sqrt((e**2).mean()):.3f} central rms {np.sqrt((c**2).mean()):.3f}')
    d.update(tabs)
    json.dump(d, open(sys.argv[5], 'w'))
    print(' | '.join(s), 'bytes', len(blob))
```

## Data
The chosen blob is 11,571 bytes, sha256 9090805200aa2a44cc90e7c5261db8ef6e4ae44b2d4fe1957a91678c85149941, base64:

```
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
```

## Problems
- **Target missed:** the loss is 0.46 against the < 0.2 target. Within ≤ 12 KB, pure low rank per table can't capture the regime jump. Each extra rank costs about 740 bytes for a 1/2 table. Options not tried here: piecewise SVD on row blocks around w ≈ 0; storing the jump location separately; spending the bytes on the central rows only.
- **Seed command:** I scored through a wrapper around real.py's `report()`, not the literal `real.py` command, because real.py fixes its seed range. The "vs HA" column printed for seeds 60000.. is meaningless, since there are no HA rows there. The paired loss doesn't use it.
- **Fit objective:** the fit minimises unweighted squared error in offset space with fee-0 cells left free. It does not optimise edge directly.
- **Not done:** gates.py was not run. Gate (P) was checked only through the +2.828 aggregate.