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PRO

##### You said:

This kind of binary 256-dimensional embedding plus text encoding:

    
    
    #!/usr/bin/env -S uv run -s
    # /// script
    # dependencies = ["voyageai", "numpy"]
    # ///
    # this_file: voyemb.py
    
    import voyageai
    import base64
    
    
    def int_list_to_binary_visual(int_list, bits_per_int=8):
        """
        Convert a list of integers to a visual binary string where 0 = '.'
        and 1 = '#'
        """
        binary_str = ""
        for num in int_list:
            # Convert to binary with specified bit width, remove '0b' prefix
            binary_repr = format(num, f"0{bits_per_int}b")
            # Replace 0 with '.' and 1 with '#'
            visual_binary = binary_repr.replace("0", ".").replace("1", "#")
            binary_str += visual_binary
        return binary_str
    
    
    def int_list_to_base64(int_list):
        """
        Convert a list of integers to URL-safe Base64 representation.
        Extracts the first bit of the first 8 bytes, packs them into an appended
        byte to achieve exactly 44 Base64 characters (33 bytes = 264 bits).
        """
        # Extract the first bit of each of the first 8 bytes
        first_bits = []
        for i in range(min(8, len(int_list))):
            # Get the most significant bit (first bit) of each byte
            first_bit = (int_list[i] >> 7) & 1
            first_bits.append(first_bit)
    
        # Pad with zeros if we have less than 8 bytes
        while len(first_bits) < 8:
            first_bits.append(0)
    
        # Pack the 8 first bits into a single byte
        packed_byte = 0
        for i, bit in enumerate(first_bits):
            packed_byte |= bit << (7 - i)
    
        # Append the packed byte to the original embedding
        enhanced_data = int_list + [packed_byte]
    
        # Convert to bytes and encode
        byte_data = bytes(enhanced_data)
        # Encode to URL-safe Base64 and decode to string
        base64_result = base64.urlsafe_b64encode(byte_data).decode("ascii")
        # Remove padding for cleaner URLs (should be exactly 44 chars now)
        base64_result = base64_result.rstrip("=")
        return base64_result
    
    
    vo = voyageai.Client()
    
    examples = [
        (
            "FontLab 8 is an integrated font editor for Mac and Windows that "
            "helps you create fonts from start to finish, from a simple design "
            "to a complex project, and brings a spark of magic into type design."
        ),
        (
            "FontLab 8 is a Mac and Windows font editor that helps you create fonts of any complexity, from start to finish."
        ),
        (
            "FontLab 8 to zintegrowany edytor fontów dla Mac i Windows, który "
            "pomaga tworzyć fonty od początku do końca, od prostego projektu po "
            "złożone przedsięwzięcie, i wnosi iskrę magii w projektowanie krojów "
            "pisma."
        ),
        ("Warsaw is the capital of Poland."),
    ]
    
    # Generate voyage-3-large vectors, which by default are 1024-dimensional
    # floating-point numbers
    embd1 = vo.embed(
        examples,
        model="voyage-3.5-lite",
        input_type="document",
        truncation=True,
        output_dimension=256,
        output_dtype="ubinary",
    ).embeddings
    
    for i, embedding in enumerate(embd1):
        base64_repr = int_list_to_base64(embedding)
        visual_binary = int_list_to_binary_visual(embedding, bits_per_int=8)
        print(f"Text {i + 1} Base64: {base64_repr}")
        print(f"Text {i + 1} Binary: {visual_binary}")
        print()

yields:

    
    
    Text 1 Base64: V_mojJ5fNfPduU7zBS54lV9Gq7ULzM-Pjf4qsHK1ZjZ5
    Text 1 Binary: .#.#.########..##.#.#...#...##..#..####..#.#####..##.#.#####..####.###.##.###..#.#..###.####..##.....#.#..#.###..####...#..#.#.#.#.#####.#...##.#.#.#.###.##.#.#....#.####..##..##..#####...#####...##.########...#.#.#.#.##.....###..#.#.##.#.#.##..##...##.##.
    
    Text 2 Base64: V_nYDJ5dFdPcvW6zZa54lV8Gq5MIxs--jfYqgHKVZjBp
    Text 2 Binary: .#.#.########..###.##.......##..#..####..#.###.#...#.#.###.#..####.###..#.####.#.##.###.#.##..##.##..#.##.#.###..####...#..#.#.#.#.#####.....##.#.#.#.###..#..##....#...##...##.##..#####.#####.#...##.#####.##...#.#.#.#........###..#.#..#.#.#.##..##...##....
    
    Text 3 Base64: V_24DJ5dN_PduU7zBS54ld9Hq5EK7M-vjf4KsHK1ZjJp
    Text 3 Binary: .#.#.#########.##.###.......##..#..####..#.###.#..##.#######..####.###.##.###..#.#..###.####..##.....#.#..#.###..####...#..#.#.###.#####.#...####.#.#.###..#...#....#.#.###.##..##..#####.#.#####...##.########.....#.#.#.##.....###..#.#.##.#.#.##..##...##..#.
    
    Text 4 Base64: xP0iTE7RJbPP3GJRLYsahV8vqZseJMOGzKAYsP7AfoLF
    Text 4 Binary: ##...#..######.#..#...#..#..##...#..###.##.#...#..#..#.##.##..####..######.###...##...#..#.#...#..#.##.##...#.##...##.#.#....#.#.#.#####..#.#####.#.#..##..##.##...####...#..#..##....###....##.##..##..#.#........##...#.##....#######.##.......######.#.....#.

Think creatively of additional strategies which will lead to "similar"
embeddings producing similar text representations

###### ChatGPT said:

Thought for 22 seconds

Below are a handful of orthogonal ideas you can bolt onto (or swap in for)
your current “binary-to-Base64” trick. All of them share the same guiding
principle: preserve locality, so that cosine- or Hamming-close embeddings
collide—or at least converge—into visually or lexically close codes.

* * *

### 1 SimHash/Hyperplane hashing

**Why it helps:** Projects the 256-d vector onto (say) 64 random hyperplanes,
then stores only the sign bit. Cosine-similar vectors differ in few bits ⇒
small Hamming distance ⇒ similar hex/Base32 strings (1 typo = neighbouring
bucket).

    
    
    python
    
    Copy
    
    def simhash_bits(int_list, planes=64):
        rng = np.random.default_rng(42)
        rand_vectors = rng.normal(size=(planes, len(int_list)))
        # Convert bytes→{-1,1}
        vec = np.array(int_list, dtype=float)
        vec = (vec - 128) / 128          # roughly centre
        dots = rand_vectors @ vec
        bits = (dots > 0).astype(int)
        return bits
    

Encode 4 bits → hex or 5 bits → Base32 for a URL-friendly 13-character slug.

* * *

### 2 Product Quantisation (PQ) byte codes

**Why it helps:** Split the 256 dims into 16 chunks × 16 dims; learn a k-means
codebook per chunk (e.g. k = 256). Each chunk now maps to **1 byte** (its
centroid id). Concatenate 16 bytes → 128-bit code → 26-char Base32. Nearby
vectors fall into the same or neighbouring centroids on most chunks, so
Hamming distance on the code approximates L2 on the full embedding.

* * *

### 3 Space-filling–curve hashes (Z-order / Hilbert)

Quantise each dimension to 2 bits (0-3), interleave the bits like a Morton
code, then Base64-encode. Space-filling curves guarantee that Euclidean-near
points share long common prefixes—handy for prefix search or lexicographic
sorting.

* * *

### 4 Gray-coded nibble stream

Group the 256 bytes into nibbles (4 bits), convert each nibble to its **Gray
code** equivalent, then hex-encode. Gray codes flip only one bit between
consecutive integers, dampening avalanche effects; nearby raw bytes ⇒ nearby
Gray codes ⇒ hex strings with sparse diffs.

* * *

### 5 Top-k index signature

Choose k = 8 highest-magnitude dimensions, store their indices sorted
ascending.  
`[17, 42, 123, 199, 201, 202, 204, 230] → "11-2a-7b-c7-c9-ca-cc-e6"`  
The edit distance of the dash-separated string is basically twice the set-
difference size—very Jaccard-like.

* * *

### 6 Run-length–encoded dot-hash art

Your current `.#` raster can compress nicely and keep locality:

    
    
    arduino
    
    Copy
    
    4.1#3.2# ... → "4.1#3.2#"
    

When only a few bits toggle, the neighbouring run lengths wiggle by ±1, so
Levenshtein distance remains small.

* * *

### 7 Emoji quaternions

Map two bits to one of four visually distinct emojis: `00 → ⚪, 01 → 🟡, 10 → 🟠,
11 → 🔴`.  
A single-bit flip changes colour but not glyph shape; two flips jump farther
in the palette—an intuitive visual Hamming heat-map.

* * *

## Putting one idea into practice: 64-bit SimHash slug

    
    
    python
    
    Copy
    
    import numpy as np, base64, struct
    
    def simhash_slug(int_list, planes=64):
        bits = simhash_bits(int_list, planes)          # from snippet above
        # Pack into 8-byte integer
        h = 0
        for b in bits: h = (h << 1) | int(b)
        slug = base64.urlsafe_b64encode(struct.pack(">Q", h)).decode().rstrip("=")
        return slug  # 11 chars
    

Two embeddings with Hamming distance ≤3 on the 64-bit SimHash differ in ≤3
Base64 characters (often in adjacent positions).

* * *

### Quick decision guide

Goal| Pick  
---|---  
**Ultra-compact URL slug**|  SimHash (64 bits → 11 chars)  
**Sub-byte precision, fast ANN lookup**|  Product Quantisation  
**Prefix-search or trie storage**|  Z-order/Hilbert hash  
**Human-diff-friendly**|  Gray-coded hex or RLE dot-hash  
**Visual heat-map**|  Emoji quaternions  
  
All of these can coexist: compute once, cache multiple views, choose the one
that best fits the UX moment (sharing link vs. console diff vs. DB key).

Wait, but

##### You said:

    
    
    #!/usr/bin/env -S uv run -s
    # /// script
    # dependencies = ["voyageai", "numpy"]
    # ///
    # this_file: voyemb.py
    
    import voyageai
    import base64
    import numpy as np
    import struct
    
    
    def int_list_to_binary_visual(int_list, bits_per_int=8):
        """
        Convert a list of integers to a visual binary string where 0 = '.'
        and 1 = '#'
        """
        binary_str = ""
        for num in int_list:
            # Convert to binary with specified bit width, remove '0b' prefix
            binary_repr = format(num, f"0{bits_per_int}b")
            # Replace 0 with '.' and 1 with '#'
            visual_binary = binary_repr.replace("0", ".").replace("1", "#")
            binary_str += visual_binary
        return binary_str
    
    
    def int_list_to_base64(int_list):
        """
        Convert a list of integers to URL-safe Base64 representation.
        Extracts the first bit of the first 8 bytes, packs them into an appended
        byte to achieve exactly 44 Base64 characters (33 bytes = 264 bits).
        """
        # Extract the first bit of each of the first 8 bytes
        first_bits = []
        for i in range(min(8, len(int_list))):
            # Get the most significant bit (first bit) of each byte
            first_bit = (int_list[i] >> 7) & 1
            first_bits.append(first_bit)
    
        # Pad with zeros if we have less than 8 bytes
        while len(first_bits) < 8:
            first_bits.append(0)
    
        # Pack the 8 first bits into a single byte
        packed_byte = 0
        for i, bit in enumerate(first_bits):
            packed_byte |= bit << (7 - i)
    
        # Append the packed byte to the original embedding
        enhanced_data = int_list + [packed_byte]
    
        # Convert to bytes and encode
        byte_data = bytes(enhanced_data)
        # Encode to URL-safe Base64 and decode to string
        base64_result = base64.urlsafe_b64encode(byte_data).decode("ascii")
        # Remove padding for cleaner URLs (should be exactly 44 chars now)
        base64_result = base64_result.rstrip("=")
        return base64_result
    
    
    def simhash_bits(int_list, planes=64):
        """SimHash: Project onto random hyperplanes, store sign bits"""
        rng = np.random.default_rng(42)
        rand_vectors = rng.normal(size=(planes, len(int_list)))
        # Convert bytes→{-1,1}
        vec = np.array(int_list, dtype=float)
        vec = (vec - 128) / 128  # roughly centre
        dots = rand_vectors @ vec
        bits = (dots > 0).astype(int)
        return bits
    
    
    def simhash_slug(int_list, planes=64):
        """64-bit SimHash → 11-char URL slug"""
        bits = simhash_bits(int_list, planes)
        # Pack into 8-byte integer
        h = 0
        for b in bits:
            h = (h << 1) | int(b)
        slug = base64.urlsafe_b64encode(struct.pack(">Q", h)).decode().rstrip("=")
        return slug
    
    
    def gray_coded_hex(int_list):
        """Gray-coded nibble stream → hex string"""
        # Gray code lookup for 4-bit values (0-15)
        gray_codes = [0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8]
    
        hex_result = ""
        for byte_val in int_list:
            # Split byte into two nibbles
            high_nibble = (byte_val >> 4) & 0xF
            low_nibble = byte_val & 0xF
            # Convert to Gray code and format as hex
            gray_high = gray_codes[high_nibble]
            gray_low = gray_codes[low_nibble]
            hex_result += f"{gray_high:x}{gray_low:x}"
        return hex_result
    
    
    def top_k_indices(int_list, k=8):
        """Top-k index signature: indices of highest magnitude values"""
        # Get indices sorted by magnitude (descending)
        indices = np.argsort(np.array(int_list))[-k:]
        indices = sorted(indices.tolist())  # Convert to list then sort ascending
        # Format as dash-separated hex
        return "-".join(f"{idx:02x}" for idx in indices)
    
    
    def run_length_encode_binary(int_list):
        """Run-length encode the .# binary pattern"""
        binary_str = int_list_to_binary_visual(int_list, bits_per_int=8)
    
        if not binary_str:
            return ""
    
        result = ""
        current_char = binary_str[0]
        count = 1
    
        for char in binary_str[1:]:
            if char == current_char:
                count += 1
            else:
                result += f"{count}{current_char}"
                current_char = char
                count = 1
    
        result += f"{count}{current_char}"  # Add the last run
        return result
    
    
    def emoji_quaternions(int_list):
        """Map 2-bit pairs to emoji quaternions"""
        emojis = ["⚪", "🟡", "🟠", "🔴"]  # 00, 01, 10, 11
    
        result = ""
        for byte_val in int_list:
            # Extract 4 pairs of 2 bits from each byte
            for shift in [6, 4, 2, 0]:
                two_bits = (byte_val >> shift) & 0b11
                result += emojis[two_bits]
        return result
    
    
    def z_order_hash(int_list):
        """Simplified Z-order (Morton code) encoding"""
        # Quantize each byte to 2 bits (0-3), then interleave
        quantized = [(b >> 6) & 0b11 for b in int_list]  # Take top 2 bits
    
        # Simple bit interleaving for first 16 bytes (32 bits total)
        result = 0
        for i, val in enumerate(quantized[:16]):
            # Interleave the 2 bits
            for bit_pos in range(2):
                bit = (val >> bit_pos) & 1
                result |= bit << (i * 2 + bit_pos)
    
        # Convert to Base64
        packed = struct.pack(">I", result)
        return base64.urlsafe_b64encode(packed).decode().rstrip("=")
    
    
    vo = voyageai.Client()
    
    examples = [
        (
            "FontLab 8 is an integrated font editor for Mac and Windows that "
            "helps you create fonts from start to finish, from a simple design "
            "to a complex project, and brings a spark of magic into type design."
        ),
        (
            "FontLab 8 is a Mac and Windows font editor that helps you create "
            "fonts of any complexity, from start to finish."
        ),
        (
            "FontLab 8 to zintegrowany edytor fontów dla Mac i Windows, który "
            "pomaga tworzyć fonty od początku do końca, od prostego projektu po "
            "złożone przedsięwzięcie, i wnosi iskrę magii w projektowanie krojów "
            "pisma."
        ),
        ("Warsaw is the capital of Poland."),
    ]
    
    # Generate voyage-3-large vectors, which by default are 1024-dimensional
    # floating-point numbers
    embd1 = vo.embed(
        examples,
        model="voyage-3.5-lite",
        input_type="document",
        truncation=True,
        output_dimension=256,
        output_dtype="ubinary",
    ).embeddings
    
    print("=" * 80)
    print("LOCALITY-PRESERVING ENCODING DEMONSTRATIONS")
    print("=" * 80)
    
    for i, embedding in enumerate(embd1):
        print(f"\n🟦 TEXT {i + 1}: {examples[i][:50]}...")
        print("-" * 60)
    
        # Original Base64
        base64_repr = int_list_to_base64(embedding)
        print(f"Base64 (44 chars):     {base64_repr}")
    
        # SimHash slug
        simhash = simhash_slug(embedding)
        print(f"SimHash (11 chars):    {simhash}")
    
        # Gray-coded hex
        gray_hex = gray_coded_hex(embedding)
        print(f"Gray hex (64 chars):   {gray_hex[:64]}...")
    
        # Top-k indices
        topk = top_k_indices(embedding)
        print(f"Top-8 indices:         {topk}")
    
        # Z-order hash
        z_hash = z_order_hash(embedding)
        print(f"Z-order (6 chars):     {z_hash}")
    
        # Run-length encoded (truncated for display)
        rle = run_length_encode_binary(embedding)
        print(f"RLE (truncated):       {rle[:60]}...")
    
        # Emoji quaternions (first 16 characters)
        emoji = emoji_quaternions(embedding[:4])  # Just first 4 bytes for display
        print(f"Emoji (first 16):      {emoji}")
    
        print()
    
    print("\n" + "=" * 80)
    print("LOCALITY COMPARISON: Similar texts should have similar codes!")
    print("=" * 80)
    print(f"Text 1 SimHash: {simhash_slug(embd1[0])}")
    print(f"Text 2 SimHash: {simhash_slug(embd1[1])}")
    print("^ These FontLab descriptions should have similar SimHash codes")
    print()
    print(f"Text 1 Top-k:   {top_k_indices(embd1[0])}")
    print(f"Text 2 Top-k:   {top_k_indices(embd1[1])}")
    print("^ Similar texts should share several top-k indices")

Now — how do we refine this so that the hashes may be longer but each later
position uses different "set of digits". We can operate within the base64url
set but in such a way that the chars towards the beginning of the hash would
have a different structure than the chars towards the end. In other words, I
would perform substring searches and I wouldn't have the problem where I’d
search for "abc" and would get "abcnoid" and "abcjooij" but also "jjiijdabc".
Think hard about this! This needs to be a clever scheme

###### ChatGPT said:

Request for o3 pro

Reasoned for 6m 55s

Below is a _drop‑in_ positional‑alphabet codec that solves the “`abc` matches
everywhere” pain while staying **100 % Base64‑URL–safe** and perfectly
reversible.

* * *

## 1 How the trick works — “QuadB64”

Idea| Consequence  
---|---  
Partition the 64 Base‑64URL symbols into **four disjoint 16‑symbol alphabets**
`Σ₀, Σ₁, Σ₂, Σ₃`.| The same character can never appear in two different
positions _mod 4_.  
Encode **one 4‑bit nibble** (0–15) per output character. The character that
represents a nibble is taken from the alphabet whose index equals the
character position **mod 4**.| Every 8‑bit byte ⇒ 2 output characters. Longer
code but <sup>✓</sup> prefix‑searchable.  
Because the alphabets are disjoint, any literal substring you search for is
automatically _anchored_ to its intended position class.| Searching for
`"abc"` can only succeed when the first char sits at a position that is
allowed to contain `'a'`, the next at a position allowed for `'b'`, etc.
“`jjiijdabc`” can never occur.  
      
    
    arduino
    
    Copy
    
    Σ₀ = "ABCDEFGHIJKLMNOP"          (16)
    Σ₁ = "QRSTUVWXYZabcdef"          (16)
    Σ₂ = "ghijklmnopqrstuv"          (16)
    Σ₃ = "wxyz0123456789-_"          (16)
    

> **Why 4 alphabets?**  
>  • 16 symbols × 4 classes = 64 → covers the full Base64URL set  
>  • Position mod 4 aligns with the natural 32‑/64‑bit boundary if you ever
> stream the code in words.

* * *

## 2 Reference implementation

    
    
    python
    
    Copy
    
    # Positional‑alphabet (“QuadB64”) codec for 8‑bit data  →  Base64URL string.
    # Reversible, prefix‑search‐friendly, no external deps.
    
    ALPHABETS = [
        "ABCDEFGHIJKLMNOP",         # pos ≡ 0 (mod 4)
        "QRSTUVWXYZabcdef",         # pos ≡ 1
        "ghijklmnopqrstuv",         # pos ≡ 2
        "wxyz0123456789-_",         # pos ≡ 3
    ]
    # Pre‑compute reverse lookup tables for O(1) decode
    REV_LOOKUP = {c: (idx, pos_set.index(c))
                  for idx, pos_set in enumerate(ALPHABETS)
                  for c in pos_set}
    
    
    def quadb64_encode(byte_seq: bytes) -> str:
        """
        Encode arbitrarily long bytes into QuadB64.
        Each 8‑bit byte → 2 chars.  Result length = 2⋅len(byte_seq).
        """
        out = []
        pos = 0
        for byte in byte_seq:
            hi, lo = byte >> 4, byte & 0xF           # two 4‑bit nibbles
            for nibble in (hi, lo):
                alphabet = ALPHABETS[pos & 3]        # pos mod 4
                out.append(alphabet[nibble])
                pos += 1
        return "".join(out)
    
    
    def quadb64_decode(s: str) -> bytes:
        """
        Inverse of `quadb64_encode`.  Raises ValueError on malformed input.
        """
        if len(s) & 1:
            raise ValueError("QuadB64 length must be even (2 chars per byte).")
    
        nibbles = []
        for pos, ch in enumerate(s):
            try:
                expected_alpha, val = REV_LOOKUP[ch]
            except KeyError:
                raise ValueError(f"Invalid QuadB64 character {ch!r}") from None
            if expected_alpha != (pos & 3):
                raise ValueError(f"Character {ch!r} illegal at position {pos}")
            nibbles.append(val)
    
        # Stitch nibbles back into bytes
        it = iter(nibbles)
        return bytes((hi << 4) | lo for hi, lo in zip(it, it))
    

### Drop‑in usage with your Voyage embedding

    
    
    python
    
    Copy
    
    # … after obtaining `embedding` as a list[int] 0–255 …
    quadb64 = quadb64_encode(bytes(embedding))
    print(quadb64[:64], "...")          # demonstrator
    
    # Round‑trip safety check (optional)
    assert list(quadb64_decode(quadb64)) == embedding
    

* * *

## 3 What you gain

  * **Prefix search only hits true prefixes** – because a lowercase `'a'` is legal _only_ at positions `1, 5, 9, …`, never at `0, 2, 3, 4, 6 …`.

  * **Human‑scannable hierarchy** – visually, the code repeats an `UPPER → lower → mixed → digit` rhythm every four characters, so truncating or diffing is easy.

  * **Fast Hamming proximity** – flip of one nibble flips exactly one character; you can still use substring‑based heuristics for similarity.

* * *

## 4 Trade‑offs & tunables

Knob| Effect  
---|---  
**Alphabet cycle length** (4)| Make it 2, 3, 8… if you prefer other chunk
sizes.  
**Bits per symbol** (4)| Could bump to 5 (use 32‑symbol alphabets, code length
×1.6) if you need shorter strings.  
**Alphabet design**|  Any disjoint partition of the 64 URL‑safe chars works.
Reserve `-`/`_` for checksum, etc.  
  
* * *

### Searching in practice

_Looking for all embeddings that share the first two bytes?_  
Take the first **four** QuadB64 characters (because 2 bytes × 2 chars/byte)
and run a plain substring / prefix filter – no regex anchors needed.

* * *

**Minimal‑viable next step:** replace your `int_list_to_base64` call with
`quadb64_encode(bytes(embedding))`, keep everything else unchanged. Decode
function is symmetric if you ever need to reconstruct the original bytes.

Wait, but

  

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