Spaces:
Sleeping
Sleeping
File size: 15,140 Bytes
2e818da | 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 | from __future__ import annotations
import math
import time
from typing import Iterable
from app.schemas.visual_lesson import (
AttentionLessonDraft,
CompiledBranch,
CompiledLesson,
EvidenceClaim,
EvidenceSource,
NumericAssertion,
PanelSpec,
TensorInput,
TensorOperation,
TimelineStep,
VisualLessonPayload,
VisualLessonSpec,
)
DEFAULT_TOKENS = ["Research", "Mate", "reads", "papers"]
EMBEDDINGS = [[1.0, 0.0, 1.0], [0.0, 1.0, 1.0], [1.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
WQ = [[1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]
WK = [[1.0, 0.0], [0.0, 1.0], [0.5, 0.5]]
WV = [[1.0, 0.0], [0.0, 1.0], [1.0, -1.0]]
DK = 2
TOLERANCE = 1e-6
class AttentionCompilerError(ValueError):
pass
def _shape(matrix: list[list[float]]) -> tuple[int, int]:
if not matrix or not matrix[0]:
raise AttentionCompilerError("Tensor matrices must not be empty")
width = len(matrix[0])
if any(len(row) != width for row in matrix):
raise AttentionCompilerError("Tensor matrices must be rectangular")
return len(matrix), width
def _matmul(left: list[list[float]], right: list[list[float]]) -> list[list[float]]:
left_rows, left_cols = _shape(left)
right_rows, right_cols = _shape(right)
if left_cols != right_rows:
raise AttentionCompilerError(f"Cannot multiply shapes {(left_rows, left_cols)} and {(right_rows, right_cols)}")
return [
[sum(left[i][k] * right[k][j] for k in range(left_cols)) for j in range(right_cols)]
for i in range(left_rows)
]
def _matmul_transpose_right(left: list[list[float]], right: list[list[float]]) -> list[list[float]]:
_, left_cols = _shape(left)
_, right_cols = _shape(right)
if left_cols != right_cols:
raise AttentionCompilerError("Query and key widths must match")
return [[sum(a * b for a, b in zip(left_row, right_row)) for right_row in right] for left_row in left]
def _softmax_rows(matrix: list[list[float]]) -> list[list[float]]:
result: list[list[float]] = []
for row in matrix:
finite_values = [value for value in row if math.isfinite(value)]
if not finite_values:
raise AttentionCompilerError("Softmax row has no finite values")
row_max = max(finite_values)
exponentials = [math.exp(value - row_max) if math.isfinite(value) else 0.0 for value in row]
denominator = sum(exponentials)
result.append([value / denominator for value in exponentials])
return result
def _apply_causal_mask(matrix: list[list[float]], enabled: bool) -> list[list[float]]:
if not enabled:
return [row[:] for row in matrix]
return [
[value if column <= row_index else -1e9 for column, value in enumerate(row)]
for row_index, row in enumerate(matrix)
]
def _round_matrix(matrix: list[list[float]]) -> list[list[float]]:
return [[round(value, 8) if math.isfinite(value) else value for value in row] for row in matrix]
class AttentionCompiler:
def operation_graph(self) -> list[TensorOperation]:
return [
TensorOperation(operation_id="q-projection", op="matmul", inputs=["embeddings", "Wq"], output="Q"),
TensorOperation(operation_id="k-projection", op="matmul", inputs=["embeddings", "Wk"], output="K"),
TensorOperation(operation_id="v-projection", op="matmul", inputs=["embeddings", "Wv"], output="V"),
TensorOperation(operation_id="attention-logits", op="matmul_transpose_right", inputs=["Q", "K"], output="logits"),
TensorOperation(operation_id="scale", op="divide_sqrt_dimension", inputs=["logits"], output="scaledLogits", dimension=DK),
TensorOperation(operation_id="mask", op="apply_causal_mask", inputs=["scaledLogits"], output="maskedLogits"),
TensorOperation(operation_id="normalize", op="softmax_rows", inputs=["maskedLogits"], output="attentionWeights"),
TensorOperation(operation_id="aggregate", op="matmul", inputs=["attentionWeights", "V"], output="output"),
]
def compile_operations(
self,
operations: list[TensorOperation],
*,
causal: bool,
input_tensors: dict[str, list[list[float]]] | None = None,
) -> dict[str, list[list[float]]]:
expected = [
("matmul", ("embeddings", "Wq"), "Q"),
("matmul", ("embeddings", "Wk"), "K"),
("matmul", ("embeddings", "Wv"), "V"),
("matmul_transpose_right", ("Q", "K"), "logits"),
("divide_sqrt_dimension", ("logits",), "scaledLogits"),
("apply_causal_mask", ("scaledLogits",), "maskedLogits"),
("softmax_rows", ("maskedLogits",), "attentionWeights"),
("matmul", ("attentionWeights", "V"), "output"),
]
actual = [(op.op, tuple(op.inputs), op.output) for op in operations]
if actual != expected:
raise AttentionCompilerError("Operation graph does not match the approved attention operation graph")
defaults: dict[str, list[list[float]]] = {
"embeddings": [row[:] for row in EMBEDDINGS],
"Wq": [row[:] for row in WQ],
"Wk": [row[:] for row in WK],
"Wv": [row[:] for row in WV],
}
source_inputs = input_tensors or defaults
required_shapes = {"embeddings": (4, 3), "Wq": (3, 2), "Wk": (3, 2), "Wv": (3, 2)}
if set(source_inputs) != set(required_shapes):
raise AttentionCompilerError("Attention inputs must contain only embeddings, Wq, Wk, and Wv")
for tensor_id, expected_shape in required_shapes.items():
if _shape(source_inputs[tensor_id]) != expected_shape:
raise AttentionCompilerError(f"{tensor_id} must have shape {expected_shape}")
if not all(math.isfinite(value) for row in source_inputs[tensor_id] for value in row):
raise AttentionCompilerError(f"{tensor_id} contains non-finite values")
tensors = {tensor_id: [row[:] for row in values] for tensor_id, values in source_inputs.items()}
for operation in operations:
if operation.op == "matmul":
tensors[operation.output] = _matmul(tensors[operation.inputs[0]], tensors[operation.inputs[1]])
elif operation.op == "matmul_transpose_right":
tensors[operation.output] = _matmul_transpose_right(tensors[operation.inputs[0]], tensors[operation.inputs[1]])
elif operation.op == "divide_sqrt_dimension":
divisor = math.sqrt(operation.dimension)
tensors[operation.output] = [[value / divisor for value in row] for row in tensors[operation.inputs[0]]]
elif operation.op == "apply_causal_mask":
tensors[operation.output] = _apply_causal_mask(tensors[operation.inputs[0]], causal)
elif operation.op == "softmax_rows":
tensors[operation.output] = _softmax_rows(tensors[operation.inputs[0]])
else:
raise AttentionCompilerError(f"Unsupported operation: {operation.op}")
return {key: _round_matrix(value) for key, value in tensors.items()}
def _assertions(self, tensors: dict[str, list[list[float]]], *, causal: bool) -> list[NumericAssertion]:
results: list[NumericAssertion] = []
expected_shapes = {"Q": (4, 2), "K": (4, 2), "V": (4, 2), "attentionWeights": (4, 4), "output": (4, 2)}
for tensor_id, expected in expected_shapes.items():
passed = _shape(tensors[tensor_id]) == expected
results.append(NumericAssertion(
assertion_id=f"shape-{tensor_id}", kind="shape", tensor_id=tensor_id,
passed=passed, detail=f"expected {expected}, got {_shape(tensors[tensor_id])}",
))
finite = all(math.isfinite(value) for matrix in tensors.values() for row in matrix for value in row)
results.append(NumericAssertion(assertion_id="finite", kind="finite", tensor_id="all", passed=finite))
row_sum_ok = all(abs(sum(row) - 1.0) <= TOLERANCE for row in tensors["attentionWeights"])
results.append(NumericAssertion(assertion_id="attention-row-sum", kind="row_sum", tensor_id="attentionWeights", passed=row_sum_ok))
masked_ok = True
if causal:
masked_ok = all(
abs(value) <= TOLERANCE
for row_index, row in enumerate(tensors["attentionWeights"])
for value in row[row_index + 1 :]
)
results.append(NumericAssertion(assertion_id="causal-mask", kind="masked_zero", tensor_id="attentionWeights", passed=masked_ok))
expected_output = _round_matrix(_matmul(tensors["attentionWeights"], tensors["V"]))
aggregate_ok = all(
abs(a - b) <= TOLERANCE
for actual_row, expected_row in zip(tensors["output"], expected_output)
for a, b in zip(actual_row, expected_row)
)
results.append(NumericAssertion(assertion_id="weighted-output", kind="matmul_close", tensor_id="output", passed=aggregate_ok))
if not all(result.passed for result in results):
failed = ", ".join(result.assertion_id for result in results if not result.passed)
raise AttentionCompilerError(f"Attention assertions failed: {failed}")
return results
@staticmethod
def _safe_tokens(tokens: Iterable[str]) -> list[str]:
candidate = [str(token).strip() for token in tokens]
if len(candidate) != 4 or any(not token or len(token) > 18 or any(ch in token for ch in "<>\n\r") for token in candidate):
return DEFAULT_TOKENS[:]
return candidate
@staticmethod
def _panels(claim_ids: list[str]) -> list[PanelSpec]:
definitions = [
("tokens", "token_strip", "Tokens", ["tokens"]),
("projections", "tensor_matrix", "Queries, keys, and values", ["Q", "K", "V"]),
("scores", "tensor_matrix", "Scaled query-key scores", ["logits", "scaledLogits"]),
("heatmap", "attention_heatmap", "Attention weights", ["attentionWeights"]),
("connections", "weighted_attention", "Weighted connections", ["attentionWeights"]),
("aggregation", "vector_aggregation", "Weighted value aggregation", ["V", "output"]),
("equation", "equation", "Scaled dot-product attention", ["Q", "K", "V", "attentionWeights", "output"]),
("evidence", "evidence", "Evidence and assumptions", []),
]
return [
PanelSpec(panel_id=panel_id, panel_type=panel_type, title=title, bindings=bindings, claim_ids=claim_ids, order=index)
for index, (panel_id, panel_type, title, bindings) in enumerate(definitions)
]
@staticmethod
def _timeline(draft: AttentionLessonDraft, claim_ids: list[str]) -> list[TimelineStep]:
defaults = [
"Start with four tokens and small illustrative embeddings.",
"Project each embedding into query, key, and value vectors.",
"Compare every query with every key using dot products.",
"Scale logits by the square root of the key dimension.",
"Apply the optional causal mask before normalization.",
"Normalize each score row into attention weights.",
"Use the weights to combine value vectors into outputs.",
]
explanations = draft.teaching_steps if len(draft.teaching_steps) == 7 else defaults
definitions = [
("inputs", "Inputs", [], ["tokens"]),
("project", "Project Q, K, and V", ["q-projection", "k-projection", "v-projection"], ["tokens", "projections"]),
("compare", "Compare queries and keys", ["attention-logits"], ["scores", "connections"]),
("scale", "Scale the logits", ["scale"], ["scores", "equation"]),
("mask", "Apply a causal mask", ["mask"], ["scores", "heatmap"]),
("softmax", "Normalize with softmax", ["normalize"], ["heatmap", "connections", "equation"]),
("aggregate", "Aggregate the values", ["aggregate"], ["aggregation", "equation"]),
]
return [
TimelineStep(
step_id=step_id, label=label, explanation=explanations[index], operation_ids=operation_ids,
active_panel_ids=active_panels, claim_ids=claim_ids,
)
for index, (step_id, label, operation_ids, active_panels) in enumerate(definitions)
]
def compile_spec(self, spec: VisualLessonSpec) -> CompiledLesson:
input_tensors = {item.tensor_id: item.values for item in spec.inputs}
branches: list[CompiledBranch] = []
for branch_id, causal in (("unmasked", False), ("causal", True)):
tensors = self.compile_operations(spec.operations, causal=causal, input_tensors=input_tensors)
assertions = self._assertions(tensors, causal=causal)
branches.append(CompiledBranch(branch_id=branch_id, tensors=tensors, assertions=assertions))
return CompiledLesson(branches=branches, assertions_passed=True)
def build_payload(
self,
*,
project_id: str,
prompt: str,
draft: AttentionLessonDraft,
evidence_sources: list[EvidenceSource],
evidence_claims: list[EvidenceClaim],
warnings: list[str],
) -> VisualLessonPayload:
claim_ids = [claim.claim_id for claim in evidence_claims]
tokens = self._safe_tokens(draft.tokens)
operations = self.operation_graph()
spec = VisualLessonSpec(
project_id=project_id,
prompt=prompt,
title=draft.title or "Inside scaled dot-product attention",
interpretation=draft.interpretation,
requested_variant=draft.requested_variant,
lesson_variant=draft.lesson_variant,
variant_notice=draft.variant_notice,
tokens=tokens,
assumptions=draft.assumptions,
evidence_sources=evidence_sources,
evidence_claims=evidence_claims,
inputs=[
TensorInput(tensor_id="embeddings", label="Illustrative embeddings", values=EMBEDDINGS),
TensorInput(tensor_id="Wq", label="Illustrative query projection", values=WQ),
TensorInput(tensor_id="Wk", label="Illustrative key projection", values=WK),
TensorInput(tensor_id="Wv", label="Illustrative value projection", values=WV),
],
operations=operations,
assertions=[
NumericAssertion(assertion_id="attention-row-sum", kind="row_sum", tensor_id="attentionWeights"),
NumericAssertion(assertion_id="causal-mask", kind="masked_zero", tensor_id="attentionWeights"),
NumericAssertion(assertion_id="weighted-output", kind="matmul_close", tensor_id="output"),
],
panels=self._panels(claim_ids),
timeline=self._timeline(draft, claim_ids),
created_at=time.time(),
)
return VisualLessonPayload(spec=spec, compiled=self.compile_spec(spec), warnings=warnings)
|