# Show HN: I implemented a neural network in SQL > Source: > Published: 2026-07-13 20:00:10+00:00 - [Notifications](/login?return_to=%2Fxqlsystems%2Fxarray-sql)You must be signed in to change notification settings - [Fork 16](/login?return_to=%2Fxqlsystems%2Fxarray-sql) ## Expand file tree / Copy path# nn.py More file actions 488 lines (446 loc) · 18.8 KB / Copy path# nn.py ## File metadata and controls 488 lines (446 loc) · 18.8 KB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 # /// script # requires-python = ">=3.12" # dependencies = [ # "xarray_sql", # "xarray", # "numpy", # "s3fs", # "zarr<3", # ] # # [tool.uv.sources] # xarray_sql = { path = "..", editable = true } # /// 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 # Drop zero-valued pixels from the (dominant) layer-0 contraction. A background # pixel contributes 0 * weight = 0, so skipping those rows shrinks the join # *exactly* — the result is identical, and the speedup scales with the fraction # of zeros (a dark background). On dense inputs it is a no-op. # # Measured ~1.8x on real Fashion-MNIST (~50% zero pixels): 2.56 -> 1.45 s/step. 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) # To float64, lazily (no full read). This zarr already stores images # as float in [0, 1]; only integer-encoded sources ([0, 255]) rescale. 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: # Offline fallback: a separable synthetic set (per-class template + # noise), so the same pipeline still learns without the network. A pool # larger than N_SAMPLES so the SQL subsample still has something to pick. 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), } ) # Integer index coords are the SQL join keys (sample, height, width). 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() # One Dataset splits into two tables: pixels (sample, height, width) and # labels (sample). The dim names are the join keys. ctx.from_dataset( "mnist", mnist, chunks=dict(sample=CHUNK), table_names={ ("sample", "height", "width"): "pixels", ("sample",): "labels", }, ) # Draw a random N_SAMPLES subset in SQL (ORDER BY random() LIMIT), carrying # each sample's label and a train/test tag. `data` is the working label # table: cache() pins the chosen subset so every downstream query sees the # same split without rescanning the source. `ORDER BY random()` shuffles the # whole label column, so the subset is order-independent even if the on-disk # samples are class-sorted. 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) # Materialise just the sampled images once: a single lazy scan of the full # dataset extracts the ~N_SAMPLES subset into `pixels`, which the per-step # forward joins instead of rescanning the source 60x. Only the subset lives # in memory; the full set stays lazy. 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) # The gradient averages over the actual train count (random, ~frac * N), # read once from the materialized split. 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, # Each layer table is one chunk: weights on (inp_i, out_i) and the bias # vector on (out_i,), so every dim needs a size here. 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) }, }, ) # Unify the per-layer weight tables into one working weight(layer, inp, out, # val) relation the loop rewrites in place, tagging each layer with its # index. 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()) # The biases live in their own bias(layer, out, val) relation, summed into # each layer's pre-activation as a separate term (z = W @ a + b). 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()) # The zero-pixel skip. fwd0 has no WHERE (it forwards all samples), so it # needs a fresh `WHERE`; g0 already filters to the train split, so it # appends an `AND`. Empty strings when the flag is off. 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): # # --- forward pass ----------------------------------------------------- # # Each layer contracts its activation with the weight table (JOIN on the # shared index + grouped SUM), then adds the layer's bias as a separate # term (JOIN the bias table on `out`), and keeps the pre-activation z # (tanh(z) for hidden, linear output). .cache() materialises each stage # so the per-step plan stays flat. # # The forward runs over ALL samples: train rows drive learning, test # rows ride along so we can score them from the same logits. Only delta2 # is restricted to train, so the gradients (and the trained weights) are # identical to a train-only forward — test is never backpropagated. 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) # Output layer is linear (softmax lives in the loss / output error), # but still gets its bias summed in. 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) # # --- backward pass ---------------------------------------------------- # # Output error delta2 = softmax(logits) - onehot(label). The one # hand-derived rule: softmax couples classes through a per-sample # normaliser. 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) # Weight gradient of layer 2: fwd1.T @ delta2 / N. 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) # Bias gradient of layer 2: the mean output error per unit. 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) # Propagate to layer 1: delta1 = (delta2 @ W2.T) * tanh'(z1). The local # derivative is grad(tanh(z), z) at fwd1's pre-activation. 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) # Propagate to layer 0: delta0 = (delta1 @ W1.T) * tanh'(z0). 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) # # --- SGD update: one query per relation ------------------------------- # # weight <- weight - lr * gradient and bias <- bias - lr * gradient, # joining every layer at once against the per-layer gradients tagged # with their layer index. 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: # Train cross-entropy (logits span all samples, so filter to train). 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] # Accuracy per split: argmax the shared logits, join the split label. # Both come from the one all-samples forward — no second pass. 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}" ) # The trained parameters come back out as xarray in the *same shape as the # input model*: one weight variable per layer with its own (inp_i, out_i) # dims, plus one bias variable per layer on (out_i,). Each is read from its # relation by the `layer` column, so the result is a ragged set of per-layer # matrices and vectors — no dense array padded with NaN. 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()