tveasey commented on code in PR #12582:
URL: https://github.com/apache/lucene/pull/12582#discussion_r1372862574


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lucene/core/src/java/org/apache/lucene/util/ScalarQuantizer.java:
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@@ -0,0 +1,267 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.lucene.util;
+
+import static org.apache.lucene.search.DocIdSetIterator.NO_MORE_DOCS;
+
+import java.io.IOException;
+import java.util.Arrays;
+import java.util.Random;
+import java.util.stream.IntStream;
+import org.apache.lucene.index.FloatVectorValues;
+import org.apache.lucene.index.VectorSimilarityFunction;
+
+/** Will scalar quantize float vectors into `int8` byte values */
+public class ScalarQuantizer {
+
+  public static final int SCALAR_QUANTIZATION_SAMPLE_SIZE = 25_000;
+
+  private final float alpha;
+  private final float scale;
+  private final float minQuantile, maxQuantile, configuredQuantile;
+
+  /**
+   * @param minQuantile the lower quantile of the distribution
+   * @param maxQuantile the upper quantile of the distribution
+   * @param configuredQuantile The configured quantile/confidence interval 
used to calculate the
+   *     quantiles.
+   */
+  public ScalarQuantizer(float minQuantile, float maxQuantile, float 
configuredQuantile) {
+    assert maxQuantile >= maxQuantile;
+    this.minQuantile = minQuantile;
+    this.maxQuantile = maxQuantile;
+    this.scale = 127f / (maxQuantile - minQuantile);
+    this.alpha = (maxQuantile - minQuantile) / 127f;
+    this.configuredQuantile = configuredQuantile;
+  }
+
+  /**
+   * Quantize a float vector into a byte vector
+   *
+   * @param src the source vector
+   * @param dest the destination vector
+   * @param similarityFunction the similarity function used to calculate the 
quantile
+   * @return the corrective offset that needs to be applied to the score
+   */
+  public float quantize(float[] src, byte[] dest, VectorSimilarityFunction 
similarityFunction) {
+    assert src.length == dest.length;
+    float correctiveOffset = 0f;
+    for (int i = 0; i < src.length; i++) {
+      float v = src[i];
+      float dx = Math.max(minQuantile, Math.min(maxQuantile, src[i])) - 
minQuantile;
+      float dxs = scale * dx;
+      float dxq = Math.round(dxs) * alpha;
+      correctiveOffset += minQuantile * (v - minQuantile / 2.0F) + (dx - dxq) 
* dxq;
+      dest[i] = (byte) Math.round(dxs);
+    }
+    if (similarityFunction.equals(VectorSimilarityFunction.EUCLIDEAN)) {
+      return 0;
+    }
+    return correctiveOffset;
+  }

Review Comment:
   This comes from a linear analysis of the error terms in the dot product as a 
function of quantisation error `(x - lower) - (upper - lower) / n_bins * 
x_quantised`. Specifically, this accounts for linear terms in this error in an 
"average" sense (where we borrow an idea from ScaNN and make the correction 
accurate for retrieved vectors which are similar to the query vector). We plan 
to write up the idea behind this approach in full elsewhere. In fact, for 7 bit 
quantisation the effect on quality of retrieval is relatively small, but for 
fewer bits we found it significantly improved recall.



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