arXiv subjects

Madhulatha Mandarapu

Publications and source records attributed to Madhulatha Mandarapu.

2 recordsLinked to original sources

arXiv2026

Bounded, Indeterminate, or a Bug: A Condition-Aware Oracle for Differential Testing of SQL Aggregates

Differential database testing compares results across engines and calls a discrepancy a bug. For floating-point aggregates this is unsound: engines legitimately disagree because floating-point arithmetic is not associative. Practice patches this with an epsilon; the leading oracles avoid floating point entirely. We give the oracle this practice lacks, and show its decisive quantity is not the query but the engine's algorithm. Ground truth is the exact rational value of the stored doubles -- arithmetic, not another engine -- and each discrepancy is classified exact, bounded, or indeterminate. The relative error of an aggregate f under an algorithm A obeys rel_err <= C_A(n,u) * kappa_f^p, so the testability boundary, beyond which no oracle can separate a bug from rounding, is kappa*_{f,A} = (1/C_A)^{1/p}. SUM and AVG are the linear case p=1; variance is p=2 for the one-pass algorithm and p=1 for Welford. Across eight engines in four classes the measured exponent recovers each algorithm, and ClickHouse is the lone one-pass engine (p=2.05); engine-wide, it returns zero standard deviation, NaN correlation and wrong-sign regression, while every other engine stays exact and the vendor ships the Welford fix. Its variance is untestable at a condition number 10^6 below SUM's, which ordinary storage conventions (epoch-nanosecond timestamps, tight sensors) cross -- there ClickHouse errs by 2100%. A randomised hunt of 360 tests finds zero anomalies, evidence the oracle is sound. Code and data are public.

cs.DB↗

arXiv2026

Removable and Irreducible: A Token-Cost Ledger for the Multilingual Tokenization Tax

Large language models pay a well-documented tax on non-English text: the same content costs several times more tokens, and because attention is quadratic in sequence length, far more compute. We ask how much of this tax is removable. Framing the token layer as source coding -- transformer compute is monotone in sequence length, whose per-atom floor is the Shannon rate $H/\log_2 V$, an object already applied to tokenizers in prior work -- we assemble a token-cost ledger that splits each language's cost, at fixed parallel content, into a removable coding redundancy, a residual coding slack, an intrinsic-content term, and an orthogonal, irreducible grapheme-to-phoneme term that governs the multimodal rather than the text cost. On FLORES-200 across eight languages, a production tokenizer costs up to $8.9\times$ more tokens for Indic scripts than for English; a script-matched code trained on $1,012$ sentences removes a median $64\%$ of that excess (bootstrap 95\% CI $[0.638, 0.647]$), and a script-fair information floor shows the intrinsic content differs by under $6\%$ -- the tax is representational, not informational. A constructed code removes $98\%$ of a controlled source's redundancy, and the token tax implies up to $79\times$ attention cost. We are explicit about scope and failure: this is compute-and-memory accounting, not a model-quality claim; we neither measure nor claim the cross-lingual direction of the orthographic term; and our matched code is a conservative small-data demonstration. We contribute the unifying ledger, the removable-versus-intrinsic attribution, and an open one-command harness.

cs.CL↗