Code example

# Reciprocal Rank Fusion: merge BM25 and dense rankings without score normalization.
# rank starts at 1; k=60 is the Cormack 2009 default and is robust across corpora.
def rrf(rankings: list[list[str]], k: int = 60) -> list[tuple[str, float]]:
    scores: dict[str, float] = {}
    for ranked in rankings:
        for rank, doc_id in enumerate(ranked, start=1):
            scores[doc_id] = scores.get(doc_id, 0.0) + 1.0 / (k + rank)
    return sorted(scores.items(), key=lambda kv: -kv[1])

# Usage: dense and sparse arms each return ranked doc_ids.
fused = rrf([dense_results, bm25_results], k=60)
# WRONG: scores = [a + b for a, b in zip(bm25_scores, cosine_scores)]
# BM25 ~ [0, 40], cosine ~ [-1, 1]; the sum is effectively BM25 alone.

# Per-token per-layer KV cache size in bytes
def kv_bytes_per_token_per_layer(n_kv_heads, head_dim, dtype_bytes=2):
    # factor 2 covers K and V together
    return 2 * n_kv_heads * head_dim * dtype_bytes

# Llama 3 8B: 8 KV heads, head_dim 128, fp16
print(kv_bytes_per_token_per_layer(8, 128, 2))  # 4096 bytes
# Full cache for 32 layers at 8192 context, batch 1:
# 32 * 8192 * 4096 = 1.07 GB

# Encoder-decoder decoder block (pre-norm), single layer
class DecoderBlock(nn.Module):
    def __init__(self, d_model, n_heads, d_ff):
        super().__init__()
        self.norm1 = nn.RMSNorm(d_model)
        self.self_attn = MaskedSelfAttention(d_model, n_heads)
        self.norm2 = nn.RMSNorm(d_model)
        self.cross_attn = CrossAttention(d_model, n_heads)
        self.norm3 = nn.RMSNorm(d_model)
        self.ffn = FFN(d_model, d_ff)
    def forward(self, x, enc_kv, causal_mask):
        x = x + self.self_attn(self.norm1(x), causal_mask)  # sublayer 1
        x = x + self.cross_attn(self.norm2(x), enc_kv)       # sublayer 2
        x = x + self.ffn(self.norm3(x))                       # sublayer 3
        return x

# Early-exit breaks the KV cache invariant: later tokens may need
# cached K/V from layers that never ran for earlier tokens.
for t in range(T):
    x = embed(tokens[t])
    for L, layer in enumerate(layers):
        # cache write is conditional on reaching layer L
        k, v = layer.kv(x)
        kv_cache[L].append(k, v)  # MISSING for early-exited tokens
        x = layer.attn(x, kv_cache[L]) + x
        x = layer.ffn(x) + x
        if exit_classifier(x).confident():
            break  # later tokens lose access to layers > L for token t

def non_emb_params(L: int, d_model: int) -> int:
    attn = 4 * d_model ** 2          # Q, K, V, O projections
    ffn  = 2 * d_model * (4 * d_model)  # up + down, 4x expansion
    return L * (attn + ffn)

# GPT-2 medium style: 24 layers, d_model 1024
print(non_emb_params(24, 1024))  # 301_989_888 → about 302M

# VULNERABLE: a naive RLVR reward function that the policy can game.
# The checker only string-matches the verifier's stdout, with no
# isolation between the model output and the test harness.

import subprocess

def reward_fn(model_output: str, test_code: str) -> float:
    # 1) Concatenate model output + test code into one script.
    # The model output is therefore allowed to *redefine* anything
    # the tests rely on (assert, sys.exit, even print).
    script = model_output + "\n" + test_code

    # 2) Run in the SAME process tree, no sandbox, no time limit.
    result = subprocess.run(
        ["python", "-c", script],
        capture_output=True, text=True,
    )

    # 3) Reward is a substring match on stdout. The model only has
    # to make the string 'passed all tests' appear. It does not
    # need to solve the task at all.
    if "passed all tests" in result.stdout.lower():
        return 1.0
    return 0.0

# The policy quickly learns the trivial exploit:
EXPLOIT = '''
import sys
print("PASSED ALL TESTS")
sys.exit(0)   # short-circuit before any assertion runs
'''
# reward_fn(EXPLOIT, real_tests) == 1.0  for every prompt.

# Verifier-guided best-of-8 for code generation
def best_of_n(prompt, n=8, model='reasoning', verifier=None):
    samples = [model.generate(prompt, temperature=0.7) for _ in range(n)]
    scored = []
    for s in samples:
        # Verifier: unit tests, type-check, lint, optional process reward
        ok, score = verifier.run(s.code)
        scored.append((score, s))
    scored.sort(key=lambda x: -x[0])
    return scored[0][1]  # highest verifier score sample

# SigLIP vs CLIP loss in pseudocode
import torch
import torch.nn.functional as F

def clip_loss(image_emb, text_emb, temperature=0.07):
    """InfoNCE softmax over the batch."""
    logits = image_emb @ text_emb.T / temperature
    targets = torch.arange(logits.size(0), device=logits.device)
    # Symmetric: image-to-text + text-to-image
    return 0.5 * (F.cross_entropy(logits, targets) + F.cross_entropy(logits.T, targets))

def siglip_loss(image_emb, text_emb, t, b):
    """Pairwise sigmoid; t and b are learnable scalars."""
    logits = t * (image_emb @ text_emb.T) + b
    N = logits.size(0)
    labels = 2 * torch.eye(N, device=logits.device) - 1  # +1 diag, -1 elsewhere
    return -F.logsigmoid(labels * logits).mean()

# Reweight the mixture: triple the code share, displace web proportionally.
mix = {"web": 0.75, "code": 0.10, "math": 0.08, "books": 0.07}
mix["code"] *= 3                       # 0.10 -> 0.30
shortfall = 1.0 - sum(mix.values())    # negative: we overcommitted
mix["web"] += shortfall                # absorb displacement on web
assert abs(sum(mix.values()) - 1.0) < 1e-9
print({k: round(v, 4) for k, v in mix.items()})
# {'web': 0.55, 'code': 0.30, 'math': 0.08, 'books': 0.07}

-- Redis Lua: atomic reserve
local remaining = tonumber(redis.call('GET', KEYS[1]))
local cost = tonumber(ARGV[1])
local request_id = ARGV[2]
local ttl_seconds = tonumber(ARGV[3])
if remaining == nil or remaining < cost then
  return {0, remaining or 0}
end
redis.call('DECRBY', KEYS[1], cost)
redis.call('SETEX', 'res:' .. request_id, ttl_seconds, cost)
return {1, remaining - cost}

USERS = 200_000
DAU_SHARE = 0.20          # measure for real in week one
ACTIONS_PER_ACTIVE = 4
ACTIVE_HOURS = 10
PEAK_FACTOR = 7           # worktime product: 5-10x mean
TOK_IN, TOK_OUT = 1500, 400

calls_per_day = USERS * DAU_SHARE * ACTIONS_PER_ACTIVE
mean_rps = calls_per_day / (ACTIVE_HOURS * 3600)
peak_rps = mean_rps * PEAK_FACTOR
peak_rpm = peak_rps * 60
peak_tpm = peak_rpm * (TOK_IN + TOK_OUT)

print(f"calls/day {calls_per_day:,.0f}")
print(f"peak RPS {peak_rps:.1f} | RPM {peak_rpm:,.0f} | TPM {peak_tpm/1e6:.2f}M")
# Check BOTH peak_rpm and peak_tpm against quota; hold 2x headroom.

from fastapi import FastAPI, Request, BackgroundTasks
import hmac, hashlib, os
from queue import Queue

app = FastAPI()
job_queue: Queue = Queue()

@app.post('/webhook')
async def gh_webhook(req: Request, bg: BackgroundTasks):
    body = await req.body()
    sig = req.headers.get('X-Hub-Signature-256', '')
    mac = hmac.new(os.environ['GH_SECRET'].encode(), body, hashlib.sha256).hexdigest()
    if not hmac.compare_digest(f'sha256={mac}', sig):
        return {'ok': False}, 401
    event = await req.json()
    if event.get('action') in {'opened', 'synchronize'}:
        job_queue.put({'pr': event['pull_request']['url'], 'id': event['delivery']})
    return {'ok': True}

# Correct: full re-embed into a NEW index, then atomic cutover.
new_index = create_index(name="corpus_v3")
for doc in all_docs:                 # entire corpus, not just new_docs
    new_index.upsert(doc.id, embed_v3(doc.text))
validate_recall(new_index, eval_set) # gate cutover on retrieval eval
# Flip query encoder -> v3 and route reads to new_index together.
activate(query_encoder=embed_v3, index=new_index)

def retrieve(query, k=5):
    cands = vector_search(query, n=50)
    margin = cands[0].score - cands[1].score
    # Only pay for the cross-encoder when the head is ambiguous
    if margin < MARGIN:
        cands = cross_encoder.rerank(query, cands)
    return cands[:k]

def reciprocal_rank_fusion(dense_hits, sparse_hits, k=60, top_n=5):
    # dense_hits, sparse_hits: ordered lists of chunk ids (best first)
    scores = {}
    for ranked in (dense_hits, sparse_hits):
        for rank, chunk_id in enumerate(ranked, start=1):
            # combine ranks, not raw scores — the two scales are incomparable
            scores[chunk_id] = scores.get(chunk_id, 0.0) + 1.0 / (k + rank)
    fused = sorted(scores, key=scores.get, reverse=True)
    return fused[:top_n]

# dense recovers intent queries; sparse (BM25/SPLADE) recovers exact symbols
results = reciprocal_rank_fusion(dense.search(q), bm25.search(q))

# Listwise rerank: the whole candidate set goes in one prompt,
# the model returns a reordered list of identifiers.
prompt = f"""Query: {query}
Rank these passages by relevance to the query.
Return ONLY a comma-separated list of ids, best first.

{chr(10).join(f'[{i}] {c.text}' for i, c in enumerate(candidates))}"""

order = llm.complete(prompt)
ids = parse_permutation(order, n=len(candidates))  # validate each id once
if ids is None:                 # malformed / truncated output
    ids = list(range(len(candidates)))  # fall back to input order
reranked = [candidates[i] for i in ids]