Manan Chopra

Sadanand Singh, Allam Reddy, Manan Chopra

Reinforcement learning with verifiable rewards can in principle train calibrated probabilistic forecasters, since a proper scoring rule such as the Brier score is computed from outcomes alone and is minimized in expectation by the true probability. In practice it degrades calibration, and existing remedies address epistemic uncertainty, where a model's confidence accompanies a verifiably correct or incorrect answer. We study aleatoric forecasting, where the forecast itself is the output and the label is one stochastic outcome, taking NFL in-game win probability as a testbed with the betting market as a reference. Rewarding the realized per-play outcome fails, because the single outcome is a noisy target and the policy gradient corrupts the chain of thought. We introduce a verifiable, label-free reward, a state-conditioned empirical win rate estimated from past outcomes, that removes the label noise, and we keep the gradient off the reasoning, by direct prediction or a gradient mask, so it cannot be corrupted. Trained with this reward alone, without human labels or supervised fine-tuning, a 7B model reaches the calibration of the betting market by direct prediction and is better calibrated than a zero-shot frontier model. That frontier model and a tabular estimator reach the same Brier score as this model, identifying the market's small remaining edge as live in-game information beyond their shared inputs. Masking the gradient, rather than dropping the chain of thought, preserves reasoning from which the forecast follows, which ordinary chain-of-thought training corrupts.

Sadanand Singh, Allam Reddy, Manan Chopra

We present a convolutional variational autoencoder for cryptocurrency implied-volatility surfaces, together with a deployable predictor that combines it with a quadratic smile re-fit through a deterministic per-tenor routing rule. Trained on 6,034 fully-filled hourly Binance Options surfaces of BTC and ETH spanning May-October 2023 and parameterised on a common $6 \times 7$ tenor-delta grid, the model attains a hidden-cell surface-completion RMSE in the 0.94-1.56 vol-point range across both markets and mask rates 10-50%. The hybrid predictor attains 0.83 vol points at 50% masking against 7.00 for the smile re-fit alone, an eightfold reduction obtained at no additional inference cost. Under structurally-correlated hole patterns that emulate the withdrawal of an entire tenor of strikes, the smile re-fit incurs 9.6-13.1 vol points of error while the learned model remains at 1.5-1.9, isolating a regime in which the generative model is the only viable predictor. Joint training on BTC and ETH improves the in-distribution model on both markets by 9-27% relative to the better-performing single-symbol counterpart, indicating a substantially shared vol-surface manifold across the two largest cryptocurrencies over the observation window. The hybrid is calendar- and butterfly-arbitrage-free at the listed strikes, a property that the parametric smile re-fit alone fails at high mask rates. The per-snapshot reconstruction error of the trained model flags the late-October ETF-anticipation rally and the August $17$, $2023$ flash crash as elevated-error periods without supervision. All training and evaluation infrastructure is released to support reproducible follow-on work.

Sadanand Singh, Allam Reddy, Manan Chopra

Retrieval-augmented generation (RAG) is routinely extended with methods meant to improve retrieval: query expansion, hierarchical and cross-document summarization, graph-based expansion, per-query routing, rank fusion, and corrective re-retrieval. The benefits reported for these methods come almost exclusively from homogeneous corpora, predominantly Wikipedia prose. Whether they hold on the mixed-format collections common in practice, where code, markdown, tables, scientific PDFs, and prose are interleaved within one corpus, has not been measured. To study this directly, we build \textbf{HetDocQA}, a heterogeneous benchmark with \emph{chunker-agnostic} span-overlap relevance labels and collection-disjoint splits, and pair it with MuSiQue and QASPER as homogeneous controls. We evaluate eight methods on a shared backbone, with bootstrap confidence intervals and multiple-comparison correction. A strong cross-encoder reranker accounts for most of the pipeline's quality; beyond it, only two methods yield reliable gains: query expansion and SSCC. SSCC, a per-source calibrated corrector introduced here, sets a separate acceptance threshold for each score source and helps only on heterogeneous data. The remaining reranking and pool-expansion methods in common use, among them hierarchical summarization, graph expansion, routing, and rank fusion, give no reliable gain once that reranker is present.