Code review analysis for BM25 paper recommendation implementation

[Copilot]

User requested code review via @copilot review on PR #2. Previous attempt created empty PR #3 without performing actual review.

Review Scope

Analyzed BM25 algorithm implementation in backend/app/api/v1/arxiv.py (98 additions, 15 deletions):

• Replaced token overlap scoring with BM25 relevance ranking
• Weighted scoring across title (1.2), summary (1.0), authors (0.6)
• Phrase matching bonus (0.1) for contiguous query matches
• Composite score: 65% BM25, 25% token coverage, 10% phrase bonus

Issues Identified

Non-standard IDF calculation (line 268):

idf = math.log(1 + (doc_count - df + 0.5) / (df + 0.5))

Standard BM25 omits the +1. Current formula ensures non-negative IDF but deviates from reference implementation.

Global average length (line 239):
Uses combined average across all fields. Standard BM25 normalizes each field independently against its own average length.

Basic tokenizer (line 207):

[t.lower() for t in re.findall(r"\w+", text)]

May split hyphenated terms, underscores in scientific notation (e.g., "BERT-base" → ["bert", "base"]).

Positive Aspects

• Core BM25 logic correctly implements term frequency and document length normalization
• Clear parameter exposure for tuning (k1, b, weights)
• Phrase matching provides useful signal for exact query matches

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