Rejection sampling is a technique for sampling from difficult distributions. However, its use is limited due to a high rejection rate. Common adaptive rejection sampling methods either work only for very specific distributions or without performance guarantees. In this paper, we present pliable rejection sampling (PRS), a new approach to rejection sampling, where we learn the sampling proposal using a kernel estimator. Since our method builds on rejection sampling, the samples obtained are with high probability i.i.d. and distributed according to f. Moreover, PRS comes with a guarantee on the number of accepted samples.

Speculative sampling (SpS) has been successful in accelerating the decoding throughput of auto-regressive large language models by leveraging smaller draft models. SpS strictly enforces the generated distribution to match that of the verifier LLM. This is unnecessarily restrictive as slight variations of the verifier's distribution, such as sampling with top-$k$ or temperature, would also be acceptable. Typical acceptance sampling (TAS) alleviates this issue by accepting more tokens using entropy-based heuristics. However, this approach distorts the verifier distribution, potentially degrading output quality when the verifier encodes critical information. In this work, we formalize the speculative sampling algorithm through the lens of constrained optimization. Based on this formulation, we propose Cactus (constrained acceptance speculative sampling), a method that guarantees controlled divergence from the verifier distribution and increasing acceptance rates. Empirical results across a wide range of benchmarks confirm the effectiveness of our approach.

Inference acceleration of large language models (LLMs) has been put forward in many application scenarios and speculative decoding has shown its advantage in addressing inference acceleration. Speculative decoding usually introduces a draft model to assist the base LLM where the draft model produces drafts and the base LLM verifies the draft for acceptance or rejection. In this framework, the final inference speed is decided by the decoding speed of the draft model and the acceptance rate of the draft provided by the draft model. Currently the widely used draft models usually generate draft tokens for the next several positions in a non-autoregressive way without considering the correlations between draft tokens. Therefore, it has a high decoding speed but an unsatisfactory acceptance rate. In this paper, we focus on how to improve the performance of the draft model and aim to accelerate inference via a high acceptance rate. To this end, we propose a CTC-based draft model which strengthens the correlations between draft tokens during the draft phase, thereby generating higher-quality draft candidate sequences. Experiment results show that compared to strong baselines, the proposed method can achieve a higher acceptance rate and hence a faster inference speed.

When the activation function of a network is analytic (e.g., sigmoid

Therefore, it has a high decoding speed but an unsatisfactory acceptance rate.

We introduce the novel EAI framework for integrating emotion modeling into LLMs to examine the emotional impact on ethics and LLM-based decision-making in various strategic games, including bargaining and repeated games. Our experimental study with various LLMs demonstrated that emotions can significantly alter the ethical decision-making landscape of LLMs, highlighting the need for robust mechanisms to ensure consistent ethical standards. Our game-theoretic analysis revealed that LLMs are susceptible to emotional biases influenced by model size, alignment strategies, and primary pretraining language. Notably, these biases often diverge from typical human emotional responses, occasionally leading to unexpected drops in cooperation rates, even under positive emotional influence.

Additionally, to avoid gradients with infinite means even if DL is not contractive, we consider a spectral normalisation, so that instead of computing recursively η0 = ε and ηk = DLηk 1 for k {1,...,N},weset η0 =εand The motivation was to have a quadratic increase for the penalty term if the largest absolute eigenvalue approaches 1, and then smoothly switch to a linear function for values larger than δ2. The suggested approach can perform poorly for non-convex potentials or even convex potentials such as arsing in a logistic regression model for some data sets. The idea now is to run HMC with unit mass matrix for the transformed variables z = f 1(q) where q π. Hessian-vector products can similarly be computed using vector-Jacobian products: With g(z) = grad( U,z), we then compute 2 U(z)w = vjp(g,z,w)> for z = f 1(stop grad(f(zbL/2c)). We also stop all U gradients, i.e.