Infact, bysubstitutingp =1n into Equation (8), weobtain: Proposition 5.For q = ( c,..., c, 0) Rn withc = 2 Δ logn, theexpectederrorE [ E ( MPF, q)] ofpermute-and-flipisatleastΔ2 log ( n).

Multiperspective Fusion (MPF) is a novel posttraining alignment framework for large language models (LLMs) developed in response to the growing need for easy bias mitigation. Built on top of the SAGED pipeline, an automated system for constructing bias benchmarks and extracting interpretable baseline distributions, MPF leverages multiperspective generations to expose and align biases in LLM outputs with nuanced, humanlike baselines. By decomposing baseline, such as sentiment distributions from HR professionals, into interpretable perspective components, MPF guides generation through sampling and balancing of responses, weighted by the probabilities obtained in the decomposition. Empirically, we demonstrate its ability to align LLM sentiment distributions with both counterfactual baselines (absolute equality) and the HR baseline (biased for Top Univeristy), resulting in small KL divergence, reduction of calibration error and generalization to unseen questions. This shows that MPF offers a scalable and interpretable method for alignment and bias mitigation, compatible with deployed LLMs and requiring no extensive prompt engineering or finetuning.

Trajectory prediction modules are key enablers for safe and efficient planning of autonomous vehicles (AVs), particularly in highly interactive traffic scenarios. Recently, learning-based trajectory predictors have experienced considerable success in providing state-of-the-art performance due to their ability to learn multimodal behaviors of other agents from data. In this paper, we present an algorithm called multi-predictor fusion (MPF) that augments the performance of learning-based predictors by imbuing them with motion planners that are tasked with satisfying logic-based rules. MPF probabilistically combines learning- and rule-based predictors by mixing trajectories from both standalone predictors in accordance with a belief distribution that reflects the online performance of each predictor. In our results, we show that MPF outperforms the two standalone predictors on various metrics and delivers the most consistent performance.

Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function. We propose a new parameter fitting method, Minimum Probability Flow (MPF), which is applicable to any parametric model. We demonstrate parameter estimation using MPF in two cases: a continuous state space model, and an Ising spin glass. In the latter case it outperforms current techniques by at least an order of magnitude in convergence time with lower error in the recovered coupling parameters.

Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable normalization factor or sampling from the equilibrium distribution of the model. This is achieved by establishing dynamics that would transform the observed data distribution into the model distribution, and then setting as the objective the minimization of the KL divergence between the data distribution and the distribution produced by running the dynamics for an infinitesimal time. Score matching, minimum velocity learning, and certain forms of contrastive divergence are shown to be special cases of this learning technique. We demonstrate parameter estimation in Ising models, deep belief networks and an independent component analysis model of natural scenes. In the Ising model case, current state of the art techniques are outperformed by at least an order of magnitude in learning time, with lower error in recovered coupling parameters.