With the widespread adoption of Large Language Models (LLMs), the prevalence of iterative interactions among these models is anticipated to increase. Notably, recent advancements in multi-round self-improving methods allow LLMs to generate new examples for training subsequent models. At the same time, multi-agent LLM systems, involving automated interactions among agents, are also increasing in prominence. Thus, in both short and long terms, LLMs may actively engage in an evolutionary process. We draw parallels between the behavior of LLMs and the evolution of human culture, as the latter has been extensively studied by cognitive scientists for decades. Our approach involves leveraging Iterated Learning (IL), a Bayesian framework that elucidates how subtle biases are magnified during human cultural evolution, to explain some behaviors of LLMs. This paper outlines key characteristics of agents' behavior in the Bayesian-IL framework, including predictions that are supported by experimental verification with various LLMs. This theoretical framework could help to more effectively predict and guide the evolution of LLMs in desired directions.

Efficiently tackling multiple tasks within complex environment, such as those found in robot manipulation, remains an ongoing challenge in robotics and an opportunity for data-driven solutions, such as reinforcement learning (RL). Model-based RL, by building a dynamic model of the robot, enables data reuse and transfer learning between tasks with the same robot and similar environment. Furthermore, data gathering in robotics is expensive and we must rely on data efficient approaches such as model-based RL, where policy learning is mostly conducted on cheaper simulations based on the learned model. Therefore, the quality of the model is fundamental for the performance of the posterior tasks. In this work, we focus on improving the quality of the model and maintaining the data efficiency by performing active learning of the dynamic model during a preliminary exploration phase based on maximize information gathering. We employ Bayesian neural network models to represent, in a probabilistic way, both the belief and information encoded in the dynamic model during exploration. With our presented strategies we manage to actively estimate the novelty of each transition, using this as the exploration reward. In this work, we compare several Bayesian inference methods for neural networks, some of which have never been used in a robotics context, and evaluate them in a realistic robot manipulation setup. Our experiments show the advantages of our Bayesian model-based RL approach, with similar quality in the results than relevant alternatives with much lower requirements regarding robot execution steps. Unlike related previous studies that focused the validation solely on toy problems, our research takes a step towards more realistic setups, tackling robotic arm end-tasks.

Collaborative machine learning involves training models on data from multiple parties but must incentivize their participation. Existing data valuation methods fairly value and reward each party based on shared data or model parameters but neglect the privacy risks involved. To address this, we introduce differential privacy (DP) as an incentive. Each party can select its required DP guarantee and perturb its sufficient statistic (SS) accordingly. The mediator values the perturbed SS by the Bayesian surprise it elicits about the model parameters. As our valuation function enforces a privacy-valuation trade-off, parties are deterred from selecting excessive DP guarantees that reduce the utility of the grand coalition's model. Finally, the mediator rewards each party with different posterior samples of the model parameters. Such rewards still satisfy existing incentives like fairness but additionally preserve DP and a high similarity to the grand coalition's posterior. We empirically demonstrate the effectiveness and practicality of our approach on synthetic and real-world datasets.

We consider convex optimization with non-smooth objective function and log-concave sampling with non-smooth potential (negative log density). In particular, we study two specific settings where the convex objective/potential function is either semi-smooth or in composite form as the finite sum of semi-smooth components. To overcome the challenges caused by non-smoothness, our algorithms employ two powerful proximal frameworks in optimization and sampling: the proximal point framework for optimization and the alternating sampling framework (ASF) that uses Gibbs sampling on an augmented distribution. A key component of both optimization and sampling algorithms is the efficient implementation of the proximal map by the regularized cutting-plane method. We establish the iteration-complexity of the proximal map in both semi-smooth and composite settings. We further propose an adaptive proximal bundle method for non-smooth optimization. The proposed method is universal since it does not need any problem parameters as input. Additionally, we develop a proximal sampling oracle that resembles the proximal map in optimization and establish its complexity using a novel technique (a modified Gaussian integral). Finally, we combine this proximal sampling oracle and ASF to obtain a Markov chain Monte Carlo method with non-asymptotic complexity bounds for sampling in semi-smooth and composite settings.

The effectiveness of Voting Advice Applications (VAA) is often compromised by the length of their questionnaires. To address user fatigue and incomplete responses, some applications (such as the Swiss Smartvote) offer a condensed version of their questionnaire. However, these condensed versions can not ensure the accuracy of recommended parties or candidates, which we show to remain below 40%. To tackle these limitations, this work introduces an adaptive questionnaire approach that selects subsequent questions based on users' previous answers, aiming to enhance recommendation accuracy while reducing the number of questions posed to the voters. Our method uses an encoder and decoder module to predict missing values at any completion stage, leveraging a two-dimensional latent space reflective of political science's traditional methods for visualizing political orientations. Additionally, a selector module is proposed to determine the most informative subsequent question based on the voter's current position in the latent space and the remaining unanswered questions. We validated our approach using the Smartvote dataset from the Swiss Federal elections in 2019, testing various spatial models and selection methods to optimize the system's predictive accuracy. Our findings indicate that employing the IDEAL model both as encoder and decoder, combined with a PosteriorRMSE method for question selection, significantly improves the accuracy of recommendations, achieving 74% accuracy after asking the same number of questions as in the condensed version.

Zero-shot In-context learning is the phenomenon where models can perform the task simply given the instructions. However, pre-trained large language models are known to be poorly calibrated for this task. One of the most effective approaches to handling this bias is to adopt a contrastive decoding objective, which accounts for the prior probability of generating the next token by conditioning on some context. This work introduces an Anti-Language Model objective with a decay factor designed to address the weaknesses of In-context Machine Translation. We conduct our experiments across 3 model types and sizes, 3 language directions, and for both greedy decoding and beam search ($B=5$). The proposed method outperforms other state-of-art decoding objectives, with up to $20$ BLEU point improvement from the default objective observed in some settings.

Many statistical analyses, in both observational data and randomized control trials, ask: how does the outcome of interest vary with combinations of observable covariates? How do various drug combinations affect health outcomes, or how does technology adoption depend on incentives and demographics? Our goal is to partition this factorial space into ``pools'' of covariate combinations where the outcome differs across the pools (but not within a pool). Existing approaches (i) search for a single ``optimal'' partition under assumptions about the association between covariates or (ii) sample from the entire set of possible partitions. Both these approaches ignore the reality that, especially with correlation structure in covariates, many ways to partition the covariate space may be statistically indistinguishable, despite very different implications for policy or science. We develop an alternative perspective, called Rashomon Partition Sets (RPSs). Each item in the RPS partitions the space of covariates using a tree-like geometry. RPSs incorporate all partitions that have posterior values near the maximum a posteriori partition, even if they offer substantively different explanations, and do so using a prior that makes no assumptions about associations between covariates. This prior is the $\ell_0$ prior, which we show is minimax optimal. Given the RPS we calculate the posterior of any measurable function of the feature effects vector on outcomes, conditional on being in the RPS. We also characterize approximation error relative to the entire posterior and provide bounds on the size of the RPS. Simulations demonstrate this framework allows for robust conclusions relative to conventional regularization techniques. We apply our method to three empirical settings: price effects on charitable giving, chromosomal structure (telomere length), and the introduction of microfinance.

Gaussian process latent variable models (GPLVMs) are a versatile family of unsupervised learning models, commonly used for dimensionality reduction. However, common challenges in modeling data with GPLVMs include inadequate kernel flexibility and improper selection of the projection noise, which leads to a type of model collapse characterized primarily by vague latent representations that do not reflect the underlying structure of the data. This paper addresses these issues by, first, theoretically examining the impact of the projection variance on model collapse through the lens of a linear GPLVM. Second, we address the problem of model collapse due to inadequate kernel flexibility by integrating the spectral mixture (SM) kernel and a differentiable random Fourier feature (RFF) kernel approximation, which ensures computational scalability and efficiency through off-the-shelf automatic differentiation tools for learning the kernel hyperparameters, projection variance, and latent representations within the variational inference framework. The proposed GPLVM, named advisedRFLVM, is evaluated across diverse datasets and consistently outperforms various salient competing models, including state-of-the-art variational autoencoders (VAEs) and GPLVM variants, in terms of informative latent representations and missing data imputation.

Sparse Bayesian learning has promoted many effective frameworks for brain activity decoding, especially for the reconstruction of muscle activity. However, existing sparse Bayesian learning mainly employs Gaussian distribution as error assumption in the reconstruction task, which is not necessarily the truth in the real-world application. On the other hand, brain recording is known to be highly noisy and contains many non-Gaussian noises, which could lead to significant performance degradation for sparse Bayesian learning method. The goal of this paper is to propose a new robust implementation for sparse Bayesian learning, so that robustness and sparseness can be realized simultaneously. Motivated by the great robustness of maximum correntropy criterion (MCC), we proposed an integration of MCC into the sparse Bayesian learning regime. To be specific, we derived the explicit error assumption inherent in the MCC and then leveraged it for the likelihood function. Meanwhile, we used the automatic relevance determination (ARD) technique for the sparse prior distribution. To fully evaluate the proposed method, a synthetic dataset and a real-world muscle activity reconstruction task with two different brain modalities were employed. Experimental results showed that our proposed sparse Bayesian correntropy learning framework improves significantly the robustness in a noisy regression task. The proposed method can realize higher correlation coefficient and lower root mean squared error in the real-world muscle activity reconstruction tasks. Sparse Bayesian correntropy learning provides a powerful tool for neural decoding which can promote the development of brain-computer interfaces.

In recent years, Neural Radiance Fields (NeRF) have emerged as a powerful tool for 3D reconstruction and novel view synthesis. However, the computational cost of NeRF rendering and degradation in quality due to the presence of artifacts pose significant challenges for its application in real-time and robust robotic tasks, especially on embedded systems. This paper introduces a novel framework that integrates NeRF-derived localization information with Visual-Inertial Odometry(VIO) to provide a robust solution for robotic navigation in a real-time. By training an absolute pose regression network with augmented image data rendered from a NeRF and quantifying its uncertainty, our approach effectively counters positional drift and enhances system reliability. We also establish a mathematically sound foundation for combining visual inertial navigation with camera localization neural networks, considering uncertainty under a Bayesian framework. Experimental validation in the photorealistic simulation environment demonstrates significant improvements in accuracy compared to a conventional VIO approach.