Deep research on the concept, formalization, algorithms, and variants of a "k-min token hedge" decoding/hedging strategy for language models. The researcher should assume the reader is technically sophisticated (machine learning researcher or engineer) and produce a comprehensive report that includes: 1) precise problem statement and mathematical formalization of what a "k-min token hedge" could mean in the context of autoregressive decoding and risk-averse/bounded-risk decoding strategies; 2) connections to existing literature (ensemble decoding, risk minimization, hedging in online learning, top-k selection, multiple-choice hedging, minimum Bayes risk decoding, beam search variations, MBR, token-level adversarial defense), including relevant citations and brief summaries; 3) algorithmic descriptions and pseudocode for plausible implementations (both greedy and sampling-based variants), including how to compute hedged token probabilities and selection rules, how to maintain and update k-min sets, and how to integrate model uncertainty and calibration; 4) theoretical analysis where possible: correctness, guarantees, expected-case behavior, worst-case risk bounds, and tradeoffs between k, latency, and calibration; 5) computational complexity and memory considerations for real-time decoding; 6) practical hyperparameters and tuning suggestions (how to choose k, interactions with temperature, top-p, beam width, number of models, and prompt engineering); 7) potential failure modes, adversarial examples, and mitigation strategies; 8) implementation notes for common frameworks (PyTorch and JAX), including vectorized approaches and how to leverage GPU/TPU efficiently; 9) suggested evaluation protocols, metrics, and datasets to test hedging performance for both accuracy/quality and safety/robustness (including human evaluation designs); and 10) a prioritized list of open research questions and promising directions for follow-up study. Effort level: deep research. Provide explicit references, links where possible, and clear, concise explanations suitable for feeding into a synthesis agent later. Do not synthesize other research results; treat this call as a standalone comprehensive report on k-min token hedge.

Deep research on techniques to combine multiple language models at decoding time and model-selection time, focusing on approaches that can be integrated with a token-level hedging strategy such as "k-min token hedge." The researcher should assume a technically sophisticated audience and produce a comprehensive report that includes: 1) a taxonomy and detailed description of ensemble and model-combination strategies: logit averaging, probability interpolation, rank aggregation, majority voting, mixture of experts (routing-based and non-routing), model selection via confidence/calibration, reranking with auxiliary discriminators, consensus decoding, committee-based approaches, and meta-model stacking for output selection; 2) precise mathematical formulations for each method and how they operate at token-level and sequence-level decoding; 3) practical algorithms and pseudocode showing how to integrate each method with token-level hedging (for example: using k-min token hedge per model then aggregating, or aggregating first then hedging), including computational considerations and variants for sampling-based and beam-based decoders; 4) evaluation criteria and metrics (perplexity, exact match, n-gram overlap, BLEU/ROUGE, BERTScore, MBR loss, human preference, calibration metrics, ensemble diversity measures), and experimental designs including ablation studies to compare strategies; 5) cost-latency-quality tradeoffs and recommended deployment patterns for low-latency vs. high-quality scenarios; 6) recommended approaches to combine model confidence and calibration with hedging (temperature scaling, isotonic regression, Platt scaling, ensemble calibration); 7) how to perform hyperparameter search (grid, Bayesian, population-based) over k, weights for averaging, temperature, beam width, and other knobs; 8) practical implementation patterns in PyTorch and JAX, including efficient batched inference across multiple models, memory and compute optimizations, and fallback strategies when some models fail or are slow; 9) safety, robustness, and adversarial considerations when combining models and using hedging, plus mitigation strategies and monitoring suggestions; and 10) a prioritized list of experiments and research questions that would most quickly identify the best combination strategies when integrating multiple models with k-min token hedge. Effort level: deep research. Provide explicit references and links where possible. Do not synthesize other research results; treat this call as a standalone comprehensive report on model combination techniques relevant to token-level hedging.