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#
from __future__ import annotations
from typing import Callable
import numpy as np
import xarray as xr
import datetime
import xarray_sql as xql
SIDE = 28 # images are 28x28; flatten index is height * SIDE + width
WIDTHS = ( SIDE * SIDE,
196,
32,
10,
) # 784 pixels -> 196 -> 32 tanh -> 10 softmax
N_SAMPLES, TRAIN_FRAC = 700, 0.7 # total samples; fraction used for training
LR, STEPS, CHUNK = 0.5, 60, 250
#
SKIP_ZERO_PIXELS = True
def fashion_mnist(): """The whole training set, left lazy so SQL streams and samples it.
The real path returns a dask-backed (chunked) Dataset — nothing is pulled
into memory here; from_dataset reads it chunk by chunk on demand, and
the random subsample happens later in SQL. The offline fallback is a small
synthetic set built in memory.
"""
try:
ds = xr.open_dataset(
"s3://carbonplan-share/xbatcher/fashion-mnist-train.zarr",
engine="zarr",
chunks=None,
backend_kwargs={"storage_options": {"anon": True}},
)
if "channel" in ds.dims:
ds = ds.isel(channel=0, drop=True)
images = ds["images"].astype("float64")
if not np.issubdtype(ds["images"].dtype, np.floating):
images = images / 255.0
ds = ds.assign(images=images, labels=ds["labels"].astype("int64")) except Exception:
rng = np.random.default_rng(0) n = 3 * N_SAMPLES
templates = rng.standard_normal((10, SIDE, SIDE))
labels = rng.integers(0, 10, n).astype("int64")
images = templates[labels] + 0.6 * rng.standard_normal((n, SIDE, SIDE))
ds = xr.Dataset(
{
"images": (("sample", "height", "width"), images),
"labels": (("sample",), labels),
}
)
return ds[["images", "labels"]].assign_coords(
sample=np.arange(ds.sizes["sample"]),
height=np.arange(ds.sizes["height"]),
width=np.arange(ds.sizes["width"]),
)
def build_model_with_table_names(
init_weight: Callable[[int, int], np.ndarray],
init_bias: Callable[[int], np.ndarray],
widths=WIDTHS,
) -> tuple[xr.Dataset, dict[tuple[str, ...], str]]:
"""The network as one Dataset that splits into tables per layer.
Layer i is a weight matrix layer_i (inp_i, out_i) and a separate
bias vector bias_i (out_i,).
"""
weights = {
f"layer_{i}": ((f"inp_{i}", f"out_{i}"), init_weight(inp, out))
for i, (inp, out) in enumerate(zip(widths[:-1], widths[1:]))
}
biases = {
f"bias_{i}": ((f"out_{i}",), init_bias(out))
for i, out in enumerate(widths[1:])
}
coords = {}
coords.update(
{f"inp_{i}": np.arange(inp) for i, inp in enumerate(widths[:-1])}
)
coords.update(
{f"out_{i}": np.arange(out) for i, out in enumerate(widths[1:])}
)
ds = xr.Dataset({**weights, **biases}, coords=coords)
names: dict[tuple[str, ...], str] = {}
for i in range(len(weights)):
names[(f"inp_{i}", f"out_{i}")] = f"layer{i}"
names[(f"out_{i}",)] = f"bias{i}"
return ds, names
def main():
rng = np.random.default_rng(1)
mnist = fashion_mnist()
ctx = xql.XarrayContext()
ctx.from_dataset(
"mnist",
mnist,
chunks=dict(sample=CHUNK),
table_names={
("sample", "height", "width"): "pixels",
("sample",): "labels",
},
)
data = ctx.sql(f"""
SELECT sample, labels,
CASE WHEN random() < {TRAIN_FRAC} THEN 'train' ELSE 'test' END AS split
FROM mnist.labels
ORDER BY random()
LIMIT {N_SAMPLES}
""").cache()
ctx.register_table("data", data)
pixels = ctx.sql("""
SELECT p.sample, p.height, p.width, p.images
FROM mnist.pixels p JOIN data d ON p.sample = d.sample
""").cache()
ctx.register_table("pixels", pixels)
n_train = ctx.sql(
"SELECT COUNT(*) AS n FROM data WHERE split = 'train'"
).to_pandas()["n"][0]
def init_weight(inp: int, out: int):
"""Small random weights."""
return rng.standard_normal((inp, out)) * 0.1
def init_bias(out: int):
"""Biases start at zero."""
return np.zeros(out) model, table_names = build_model_with_table_names(init_weight, init_bias)
ctx.from_dataset(
"model",
model,
table_names=table_names,
chunks={
**{
f"inp_{i}": model.sizes[f"inp_{i}"]
for i in range(len(WIDTHS) - 1)
},
**{
f"out_{i}": model.sizes[f"out_{i}"]
for i in range(len(WIDTHS) - 1)
},
},
)
seed = " UNION ALL ".join(
f"SELECT {i} AS layer, inp_{i} AS inp, out_{i} AS out, layer_{i} AS val "
f"FROM model.layer{i}"
for i in range(len(WIDTHS) - 1)
)
ctx.register_table("weight", ctx.sql(seed).cache())
bias_seed = " UNION ALL ".join(
f"SELECT {i} AS layer, out_{i} AS out, bias_{i} AS val FROM model.bias{i}"
for i in range(len(WIDTHS) - 1)
)
ctx.register_table("bias", ctx.sql(bias_seed).cache())
zero_where = "WHERE images <> 0" if SKIP_ZERO_PIXELS else ""
zero_and = "AND images <> 0" if SKIP_ZERO_PIXELS else ""
for step in range(STEPS):
#
#
#
fwd0 = ctx.sql(f""" WITH c AS (
-- z = x @ W: matmul of the input and first weight matrix
SELECT a.sample, w.out AS out, SUM(a.val * w.val) AS z
FROM (
SELECT sample, height * {SIDE} + width AS inp, images AS val
FROM pixels
{zero_where}
) a
JOIN weight w ON a.inp = w.inp AND w.layer = 0
GROUP BY a.sample, w.out
)
-- activation(z + b): Add in the bias term, then perform activation
SELECT c.sample, c.out AS out, c.z + b.val AS z,
tanh(c.z + b.val) AS val
FROM c JOIN bias b ON c.out = b.out AND b.layer = 0
""").cache()
ctx.deregister_table("fwd0")
ctx.register_table("fwd0", fwd0)
fwd1 = ctx.sql(f"""
WITH c AS (
SELECT a.sample, w.out AS out, SUM(a.val * w.val) AS z
FROM (SELECT sample, out AS inp, val FROM fwd0) a
JOIN weight w ON a.inp = w.inp AND w.layer = 1
GROUP BY a.sample, w.out
)
SELECT c.sample, c.out AS out, c.z + b.val AS z,
tanh(c.z + b.val) AS val
FROM c JOIN bias b ON c.out = b.out AND b.layer = 1
""").cache()
ctx.deregister_table("fwd1")
ctx.register_table("fwd1", fwd1)
logits = ctx.sql(f"""
WITH c AS (
SELECT a.sample, w.out AS out, SUM(a.val * w.val) AS z
FROM (SELECT sample, out AS inp, val FROM fwd1) a
JOIN weight w ON a.inp = w.inp AND w.layer = 2
GROUP BY a.sample, w.out
)
SELECT c.sample, c.out AS out, c.z + b.val AS z
FROM c JOIN bias b ON c.out = b.out AND b.layer = 2
""").cache()
ctx.deregister_table("logits")
ctx.register_table("logits", logits)
#
#
delta2 = ctx.sql(f"""
WITH m AS (SELECT sample, MAX(z) AS m FROM logits GROUP BY sample),
e AS (SELECT logits.sample, logits.out, exp(logits.z - m.m) AS e
FROM logits JOIN m ON logits.sample = m.sample),
s AS (SELECT sample, SUM(e) AS s FROM e GROUP BY sample)
SELECT e.sample, e.out,
e.e / s.s - CASE WHEN e.out = y.labels THEN 1.0 ELSE 0.0 END AS val
FROM e JOIN s ON e.sample = s.sample JOIN data y ON y.sample = e.sample
-- restrict the error to train, so every downstream gradient is train-only
WHERE e.sample IN (SELECT sample FROM data WHERE split = 'train')
""").cache()
ctx.deregister_table("delta2")
ctx.register_table("delta2", delta2)
g2 = ctx.sql(f"""
SELECT a.inp AS inp, d.out AS out, SUM(a.val * d.val) / {n_train} AS val
FROM (SELECT sample, out AS inp, val FROM fwd1) a
JOIN delta2 d ON a.sample = d.sample
GROUP BY a.inp, d.out
""").cache()
ctx.deregister_table("g2")
ctx.register_table("g2", g2)
gb2 = ctx.sql(f"""
SELECT out, SUM(val) / {n_train} AS val FROM delta2 GROUP BY out
""").cache()
ctx.deregister_table("gb2")
ctx.register_table("gb2", gb2)
delta1 = ctx.sql(f"""
WITH dc AS (
SELECT d.sample, w.inp AS out, SUM(d.val * w.val) AS val
FROM delta2 d JOIN weight w ON d.out = w.out AND w.layer = 2
GROUP BY d.sample, w.inp
)
SELECT dc.sample, dc.out,
dc.val * grad(tanh(fwd1.z), fwd1.z) AS val
FROM dc JOIN fwd1 ON dc.sample = fwd1.sample AND dc.out = fwd1.out
""").cache()
ctx.deregister_table("delta1")
ctx.register_table("delta1", delta1)
g1 = ctx.sql(f"""
SELECT a.inp AS inp, d.out AS out, SUM(a.val * d.val) / {n_train} AS val
FROM (SELECT sample, out AS inp, val FROM fwd0) a
JOIN delta1 d ON a.sample = d.sample
GROUP BY a.inp, d.out
""").cache()
ctx.deregister_table("g1")
ctx.register_table("g1", g1)
gb1 = ctx.sql(f"""
SELECT out, SUM(val) / {n_train} AS val FROM delta1 GROUP BY out
""").cache()
ctx.deregister_table("gb1")
ctx.register_table("gb1", gb1)
delta0 = ctx.sql(f"""
WITH dc AS (
SELECT d.sample, w.inp AS out, SUM(d.val * w.val) AS val
FROM delta1 d JOIN weight w ON d.out = w.out AND w.layer = 1
GROUP BY d.sample, w.inp
)
SELECT dc.sample, dc.out,
dc.val * grad(tanh(fwd0.z), fwd0.z) AS val
FROM dc JOIN fwd0 ON dc.sample = fwd0.sample AND dc.out = fwd0.out
""").cache()
ctx.deregister_table("delta0")
ctx.register_table("delta0", delta0)
g0 = ctx.sql(f"""
WITH a AS (
SELECT sample, height * {SIDE} + width AS inp, images AS val
FROM pixels
WHERE sample IN (SELECT sample FROM data WHERE split = 'train')
{zero_and}
)
SELECT a.inp AS inp, d.out AS out, SUM(a.val * d.val) / {n_train} AS val
FROM a JOIN delta0 d ON a.sample = d.sample
GROUP BY a.inp, d.out
""").cache()
ctx.deregister_table("g0")
ctx.register_table("g0", g0)
gb0 = ctx.sql(f"""
SELECT out, SUM(val) / {n_train} AS val FROM delta0 GROUP BY out
""").cache()
ctx.deregister_table("gb0")
ctx.register_table("gb0", gb0)
#
#
w = ctx.sql(f""" WITH grad AS (
SELECT 0 AS layer, inp, out, val FROM g0
UNION ALL SELECT 1 AS layer, inp, out, val FROM g1
UNION ALL SELECT 2 AS layer, inp, out, val FROM g2
)
SELECT w.layer, w.inp, w.out,
w.val - {LR} * COALESCE(g.val, 0) AS val
FROM weight w LEFT JOIN grad g
ON w.layer = g.layer AND w.inp = g.inp AND w.out = g.out
""").cache()
ctx.deregister_table("weight")
ctx.register_table("weight", w)
b = ctx.sql(f"""
WITH gb AS (
SELECT 0 AS layer, out, val FROM gb0
UNION ALL SELECT 1 AS layer, out, val FROM gb1
UNION ALL SELECT 2 AS layer, out, val FROM gb2
)
SELECT b.layer, b.out,
b.val - {LR} * COALESCE(g.val, 0) AS val
FROM bias b LEFT JOIN gb g
ON b.layer = g.layer AND b.out = g.out
""").cache()
ctx.deregister_table("bias")
ctx.register_table("bias", b)
if step % 5 == 0 or step == STEPS - 1:
loss = ctx.sql(f"""
WITH m AS (SELECT sample, MAX(z) AS m FROM logits GROUP BY sample),
e AS (SELECT logits.sample, logits.out, exp(logits.z - m.m) AS e
FROM logits JOIN m ON logits.sample = m.sample),
s AS (SELECT sample, SUM(e) AS s FROM e GROUP BY sample)
SELECT -AVG(ln(e.e / s.s)) AS loss
FROM e JOIN s ON e.sample = s.sample
JOIN data y ON y.sample = e.sample
WHERE e.out = y.labels
AND e.sample IN (SELECT sample FROM data WHERE split = 'train')
""").to_pandas()["loss"][0]
acc = (
ctx.sql(f"""
WITH pred AS (
SELECT sample, out,
ROW_NUMBER() OVER (PARTITION BY sample ORDER BY z DESC) AS rk
FROM logits)
SELECT d.split,
AVG(CASE WHEN p.out = d.labels THEN 1.0 ELSE 0.0 END) AS acc
FROM pred p JOIN data d ON d.sample = p.sample WHERE p.rk = 1
GROUP BY d.split
""")
.to_pandas()
.set_index("split")["acc"]
)
print(
f"step {step:2d}: loss {loss:.3f} "
f"train_acc {acc['train']:.3f} test_acc {acc['test']:.3f}"
)
trained = xr.Dataset(
{
**{
f"layer_{i}": ctx.sql(
f"SELECT inp AS inp_{i}, out AS out_{i}, val AS layer_{i} "
f"FROM weight WHERE layer = {i}"
).to_dataset(dims=[f"inp_{i}", f"out_{i}"])[f"layer_{i}"]
for i in range(len(WIDTHS) - 1)
},
**{
f"bias_{i}": ctx.sql(
f"SELECT out AS out_{i}, val AS bias_{i} "
f"FROM bias WHERE layer = {i}"
).to_dataset(dims=[f"out_{i}"])[f"bias_{i}"]
for i in range(len(WIDTHS) - 1)
},
}
)
print(f"trained {WIDTHS} MLP; weights -> xarray {dict(trained.sizes)}.")
print(trained)
trained.to_zarr(
f"fashion_mnist_mlp_"
f"{datetime.datetime.now().isoformat(timespec='seconds')}.zarr"
)
if __name__ == "__main__":
main()