Dense retrieval can return different evidence when a query is paraphrased, even when the meaning stays the same. This means that linguistic variation can create uncertainty in the evidence given to a retrieval-augmented generation (RAG) system. We study this problem across HotpotQA, FEVER, and SQuAD 2.0 using five dense encoders spanning 22M to 8B parameters and multiple model families. Paraphrase Jaccard distance remains 32 to 50 percent, showing that retrieval instability persists with stronger and alternative encoders. We then ask how much this problem can be reduced at inference time. Multi-source consensus over paraphrased queries and different retrievers improves retrieval coverage. Fixed source-type weights can help in harder settings. However, adapting those weights to each query using retrieval stability changes Coverage@20 by at most ±0.3 percentage points per setting. Retrieval stability is more useful as a label-free routing signal: on HotpotQA/MiniLM, routing only unstable queries through the stability-conditioned consensus configuration reduces retrieval calls by 47 percent for a 0.6 percentage-point Coverage@20 cost compared with always using that configuration. Overall, paraphrase-induced retrieval instability is a persistent source of uncertainty in retrieved evidence, and the query-adaptive stability component provides only a small marginal refinement.

Quantization reduces the deployment cost of large language models (LLMs). However, post-training quantization (PTQ) cannot fine-tune model parameters and often degrades accuracy in low-bit settings, while quantization-aware training (QAT) requires backpropagation and incurs high memory overhead. We propose ZeroQAT, a zeroth-order QAT framework supporting both weight and activation quantization. By using forward-only gradient estimation, ZeroQAT removes backpropagation and substantially reduces memory and computation while retaining end-to-end optimization benefits. We further introduce a lightweight variant of ZeroQAT for quantized fine-tuning, which freezes and pre-quantizes most parameters to further cut memory usage. Experiments show that ZeroQAT consistently outperforms representative PTQ and QAT baselines while requiring significantly less memory. For example, ZeroQAT enables fine-tuning of a 13B model at extremely low bit-widths (e.g., 2-4 bits) on a single 8GB GPU, and even allows fine-tuning a 6.7B model on a OnePlus 12 smartphone, demonstrating its practicality for end-to-end QAT on resource-limited edge devices.

Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning using outcome-level supervision, but this supervision is temporally coarse: it indicates whether a trajectory ends with a correct answer, without revealing when the reasoning becomes reliable or silently fails. Existing verbalized-confidence methods typically calibrate a single confidence score after the final answer, leaving intermediate uncertainty unobserved. We propose SCOPE (Stepwise Calibration with Outcome-grounded Prefix Evidence), which trains reasoning models to emit confidence after each reasoning step. SCOPE interprets step confidence as the model’s prefix-conditioned belief in the gold answer: how likely the gold answer is under the reasoning prefix generated so far. During training, SCOPE constructs a soft target by scoring the gold answer conditioned on each reasoning prefix under the current policy. It then distills this signal with a two-stage masked RL objective: the first stage stabilizes the output format and final-answer accuracy, while the second stage performs calibration-only masked updates by applying stepwise and final-confidence rewards only to the numerical tokens inside the emitted confidence spans. Experiments on mathematical reasoning benchmarks show that SCOPE improves stepwise and final-confidence calibration while preserving final-answer reasoning performance. We further show that the resulting confidence signals support downstream inference-time control, enabling more reliable Learn-Then-Test risk control and stronger confidence-weighted aggregation.

Fine-tuning large language models (LLMs) faces significant memory challenges due to the high cost of back-propagation. MeZO addresses this using zeroth-order (ZO) optimization, matching memory usage to inference but suffering from slow convergence due to varying curvatures across model parameters. To overcome this limitation, We propose HELENE, a scalable and memory-efficient optimizer that integrates annealed A-GNB gradients with diagonal Hessian estimation and layer-wise clipping as a second-order pre-conditioner. HELENE provably accelerates and stabilizes convergence by reducing dependence on total parameter space and scaling with the largest layer dimension. Experiments on RoBERTa-large and OPT-1.3B show up to a 20× speedup over MeZO with an average accuracy improvement of 1.5%. HELENE supports full and parameter-efficient fine-tuning, outperforming several state-of-the-art optimizers.