The code is available here.

Semantic-level watermarking (SWM) for large language models (LLMs) enhances watermarking robustness against text modifications and paraphrasing attacks by treating the sentence as the fundamental unit. However, existing methods still lack strong theoretical guarantees of robustness, and reject-sampling-based generation often introduces significant distribution distortions compared with unwatermarked outputs. In this work, we introduce a new theoretical framework on SWM through the concept of proxy functions (PFs) $\unicode{x2013}$ functions that map sentences to scalar values. Building on this framework, we propose PMark, a simple yet powerful SWM method that estimates the PF median for the next sentence dynamically through sampling while enforcing multiple PF constraints (which we call channels) to strengthen watermark evidence. Equipped with solid theoretical guarantees, PMark achieves the desired distortion-free property and improves the robustness against paraphrasing-style attacks. We also provide an empirically optimized version that further removes the requirement for dynamical median estimation for better sampling efficiency. Experimental results show that PMark consistently outperforms existing SWM baselines in both text quality and robustness, offering a more effective paradigm for detecting machine-generated text. Our code will be released at [this URL](https://github.com/PMark-repo/PMark).

We study the problem of non-disclosively collecting a sample of data that is balanced with respect to sensitive groups when group membership is unavailable or prohibited from use at collection time. Specifically, our collection mechanism does not reveal significantly more about group membership of any individual sample than can be ascertained from base rates alone. To do this, we adopt a fairness pipeline perspective, in which a learner can use a small set of labeled data to train a proxy function that can later be used for this filtering task. We then associate the range of the proxy function with sampling probabilities; given a new candidate, we classify it using our proxy function, and then select it for our sample with probability proportional to the sampling probability corresponding to its proxy classification. Importantly, we require that the proxy classification itself not reveal significant information about the sensitive group membership of any individual sample (i.e., it should be sufficiently non-disclosive). We show that under modest algorithmic assumptions, we find such a proxy in a sample- and oracle-efficient manner. Finally, we experimentally evaluate our algorithm and analyze generalization properties.

We study the problem of optimizing biological sequences, e.g., proteins, DNA, and RNA, to maximize a black-box score function that is only evaluated in an offline dataset. We propose a novel solution, bootstrapped training of score-conditioned generator (BootGen) algorithm. Our algorithm repeats a two-stage process. In the first stage, our algorithm trains the biological sequence generator with rank-based weights to enhance the accuracy of sequence generation based on high scores. The subsequent stage involves bootstrapping, which augments the training dataset with self-generated data labeled by a proxy score function. Our key idea is to align the score-based generation with a proxy score function, which distills the knowledge of the proxy score function to the generator. After training, we aggregate samples from multiple bootstrapped generators and proxies to produce a diverse design. Extensive experiments show that our method outperforms competitive baselines on biological sequential design tasks. We provide reproducible source code: \href{https://github.com/kaist-silab/bootgen}{https://github.com/kaist-silab/bootgen}.

In order to obtain reasonably accurate full loss distributions via a nested simulations approach as described in Bauer et al. (2012), their cash-flow-projection (CFP) models would need to be simulated several hundred thousand times. But the insurers are currently far from being endowed with sufficient computational capacities to perform such expensive simulation tasks. By applying suitable approximation techniques like the least-squares Monte Carlo (LSMC) approach of Bauer & Ha (2015), the insurers are able to overcome these computational hurdles though. For example, they can implement the LSMC framework formalized by Krah et al. (2018) and applied by e.g. Bettels et al. (2014) to derive their full loss distributions. The central idea of this framework is to carry out a comparably small number of wisely chosen Monte Carlo simulations and to feed the simulation results into a supervised machine learning algorithm that translates the results into a proxy function of the insurer's loss (output) with respect to the underlying risk factors (input). To guarantee a certain approximation quality, the proxy function has to pass an additional validation procedure before it can finally be used for the full loss distribution forecast. Machine Learning Calibration Algorithm Apart from the calibration and validation steps, we adopt the LSMC framework from Krah et al. (2018) without any changes.

For this purpose, we propose a stochastic procedure, the mirror descent, which performs gradient descent in the dual space. The generated estimates are additionally averaged in a recursive fashion with specific weights. Mirror descent algorithms have been developed in different contexts and they are known to be particularly efficient in high dimensional problems. Moreover their implementation is adapted to the online setting. The main result of the paper is the upper bound on the convergence rate for the generalization error.

For this purpose, we propose a stochastic procedure, the mirror descent, which performs gradient descent in the dual space. The generated estimates are additionally averaged in a recursive fashion with specific weights. Mirror descent algorithms have been developed in different contexts and they are known to be particularly efficient in high dimensional problems. Moreover their implementation is adapted to the online setting. The main result of the paper is the upper bound on the convergence rate for the generalization error.