Prompting is one of the main ways to adapt a pretrained model to target tasks. Besides manually constructing prompts, many prompt optimization methods have been proposed in the literature. Method development is mainly empirically driven, with less emphasis on a conceptual understanding of prompting. In this paper we discuss how optimal prompting can be understood through a Bayesian view, which also implies some fundamental limitations of prompting that can only be overcome by tuning weights. The paper explains in detail how meta-trained neural networks behave as Bayesian predictors over the pretraining distribution, whose hallmark feature is rapid in-context adaptation. Optimal prompting can be studied formally as conditioning these Bayesian predictors, yielding criteria for target tasks where optimal prompting is and is not possible. We support the theory with educational experiments on LSTMs and Transformers, where we compare different versions of prefix-tuning and different weight-tuning methods. We also confirm that soft prefixes, which are sequences of real-valued vectors outside the token alphabet, can lead to very effective prompts for trained and even untrained networks by manipulating activations in ways that are not achievable by hard tokens. This adds an important mechanistic aspect beyond the conceptual Bayesian theory.

In-context learning, the ability of large language models to perform tasks using only examples provided in the prompt, has recently been adapted for time series forecasting. This paradigm enables zero-shot prediction, where past values serve as context for forecasting future values, making powerful forecasting tools accessible to non-experts and increasing the performance when training data are scarce. Most existing zero-shot forecasting approaches rely on transformer architectures, which, despite their success in language, often fall short of expectations in time series forecasting, where recurrent models like LSTMs frequently have the edge. Conversely, while LSTMs are well-suited for time series modeling due to their state-tracking capabilities, they lack strong in-context learning abilities. We introduce that closes this gap by leveraging xLSTM, an enhanced LSTM with competitive in-context learning skills. Unlike transformers, state-space models, or parallelizable RNNs such as RWKV, TiRex retains state tracking, a critical property for long-horizon forecasting. To further facilitate its state-tracking ability, we propose a training-time masking strategy called CPM. TiRex sets a new state of the art in zero-shot time series forecasting on the Hugging Face benchmarks and, outperforming significantly larger models including (Prior Labs), (Amazon), (Google), and (Salesforce) across both short-and long-term forecasts.

Traditional multi-population models, such as the Li-Lee framework, rely on the assumption of mean-reverting country-specific deviations. However, recent data from high-longevity clusters suggest a systemic break in this paradigm. We identify a stationarity paradox where mortality residuals in countries like Sweden and West Germany exhibit persistent unit roots, leading to a systematic mispricing of longevity risk in linear models. To address these non-linearities, we propose Hybrid-Lift, a neural-actuarial framework that combines Hierarchical LSTM networks with a Mean-Bias Correction (MBC) anchoring mechanism. Positioned as a governance-friendly model challenger rather than a replacement of classical approaches, the framework exhibits selective superiority on out-of-sample validation (2012-2020): it outperforms Li-Lee by 17.40% in Sweden and 12.57% in West Germany, while remaining comparable for near-linear regimes such as Switzerland and Japan. We complement the predictive model with an integrated governance suite comprising SHAP-based cross-country influence mapping, a dual uncertainty framework for regulatory capital calibration (Swiss ES 99.0% of +1.153 years), and a reverse stress test identifying the critical shock threshold for solvency buffer exhaustion. This research provides evidence that neural networks, when properly anchored by actuarial principles, can serve as effective model challengers for longevity risk management under the SST and Solvency II standards.

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A.1 Experimental Settings All language models in Table 1 have the same Transformer configuration: a 16-layer model with a hidden size of 128 with 8 heads, and a feed-forward dimension of 2048. We use a dropout [75, 76, 77] rate of 0.1. The batch size is 96 and we train for about 120 epochs with Adam optimiser [78] with an initial learning rate of 0.00025 and 2000 learning rate warm-up steps. All models are trained with a back-propagation span of 256 tokens. During training, these segments are treated independently, except for the + full context cases in Table 1 where the states (both recurrent states and fast weight states) from a segment are used as initialisation for the subsequent segment. The models in + full context cases are also evaluated in the same way by carrying over the context throughout the evaluation text with a batch size of one. For all other cases, the evaluation is done by going through the text with a sliding window of size 256 with a batch size of one. Transformer states are computed for all positions in each window, but only the last position is used to compute perplexity (except in the first segment where all positions are used for evaluation) [2].

This is the supplementary information pertaining to the main manuscript. In this supplementary material, we provide the comparative performance of Neurochaos Learning with Deep Neural Network, 1DConvolutional Neural Network (1D CNN), and Long Short term Memory (LSTM) for evaluation of cause-effect classification of timeseries data generated from coupled chaotic master-slave system and autoregressive (AR) processes. We also check whether each of these architectures are able to preserve cause-effect relationship between the corresponding features extracted from the original cause and effect time series. To evaluate the efficacy of Neurochaos Learning (NL: ChaosNet) and deep learning algorithms for the classification of cause-effect, we used simulated datasets from (a) coupled autoregressive (AR) processes, and (b) coupled 1D chaotic skew tent-maps in master-slave configuration. The governing equations for the coupled AR processes are the following: M(t)=a1M(t 1)+γr(t), (1) S(t)=a2S(t 1)+ηM(t 1)+γr(t), (2) where M(t) and S(t) are the independent and the dependent (or the cause and effect) time series respectively; a1 = 0.8, a2 = 0.9, the noise intensity γ = 0.03 and r(t) is independent and identically distributed additive Gaussian noise drawn from a standard normal distribution.

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