Modern language models address complex questions through chain-of-thought (CoT) reasoning (Wei et al., 2023) and retrieval augmentation (Lewis et al., 2021), yet struggle with error propagation and knowledge integration. Tree-structured reasoning methods, particularly the Probabilistic Tree-of-Thought (ProbTree)(Cao et al., 2023) framework, mitigate these issues by decomposing questions into hierarchical structures and selecting answers through confidence-weighted aggregation of parametric and retrieved knowledge (Yao et al., 2023). However, ProbTree's static implementation introduces two key limitations: (1) the reasoning tree is fixed during the initial construction phase, preventing dynamic adaptation to intermediate results, and (2) each node requires exhaustive evaluation of all possible solution strategies, creating computational inefficiency. We present a dynamic reinforcement learning (Sutton and Barto, 2018) framework that transforms tree-based reasoning into an adaptive process. Our approach incrementally constructs the reasoning tree based on real-time confidence estimates, while learning optimal policies for action selection (decomposition, retrieval, or aggregation). This maintains ProbTree's probabilistic rigor while improving both solution quality and computational efficiency through selective expansion and focused resource allocation. The work establishes a new paradigm for treestructured reasoning that balances the reliability of probabilistic frameworks with the flexibility required for real-world question answering systems. Code available at: https://github.com/ahmedehabb/From-Roots-to-Rewards-Dynamic-Tree-Reasoning-with-RL

Particle filters are a frequent choice for inference tasks in nonlinear and non-Gaussian state-space models. They can either be used for state inference by approximating the filtering distribution or for parameter inference by approximating the marginal data (observation) likelihood. A good proposal distribution and a good resampling scheme are crucial to obtain low variance estimates. However, traditional methods like multinomial resampling introduce nondifferentiability in PF-based loss functions for parameter estimation, prohibiting gradient-based learning tasks. This work proposes a differentiable resampling scheme by deterministic sampling from an empirical cumulative distribution function. We evaluate our method on parameter inference tasks and proposal learning.

A resampling scheme provides a way to switch low-weight particles for sequential Monte Carlo with higher-weight particles representing the objective distribution. The less the variance of the weight distribution is, the more concentrated the effective particles are, and the quicker and more accurate it is to approximate the hidden Markov model, especially for the nonlinear case. We propose a repetitive deterministic domain with median ergodicity for resampling and have achieved the lowest variances compared to the other resampling methods. As the size of the deterministic domain $M\ll N$ (the size of population), given a feasible size of particles, our algorithm is faster than the state of the art, which is verified by theoretical deduction and experiments of a hidden Markov model in both the linear and non-linear cases.

Mixup is a highly successful technique to improve generalization of neural networks by augmenting the training data with combinations of random pairs. Selective mixup is a family of methods that apply mixup to specific pairs, e.g. only combining examples across classes or domains. These methods have claimed remarkable improvements on benchmarks with distribution shifts, but their mechanisms and limitations remain poorly understood. We examine an overlooked aspect of selective mixup that explains its success in a completely new light. We find that the non-random selection of pairs affects the training distribution and improve generalization by means completely unrelated to the mixing. For example in binary classification, mixup across classes implicitly resamples the data for a uniform class distribution - a classical solution to label shift. We show empirically that this implicit resampling explains much of the improvements in prior work. Theoretically, these results rely on a regression toward the mean, an accidental property that we identify in several datasets. We have found a new equivalence between two successful methods: selective mixup and resampling. We identify limits of the former, confirm the effectiveness of the latter, and find better combinations of their respective benefits.

Data augmentation is a prevalent technique for improving performance in various machine learning applications. We propose SeqAug, a modality-agnostic augmentation method that is tailored towards sequences of extracted features. The core idea of SeqAug is to augment the sequence by resampling from the underlying feature distribution. Resampling is performed by randomly selecting feature dimensions and permuting them along the temporal axis. Experiments on CMU-MOSEI verify that SeqAug is modality agnostic; it can be successfully applied to a single modality or multiple modalities. We further verify its compatibility with both recurrent and transformer architectures, Figure 1: The bag of all extracted features. We assume that and also demonstrate comparable to state-of-the-art results.

It has been widely documented that the sampling and resampling steps in particle filters cannot be differentiated. The {\itshape reparameterisation trick} was introduced to allow the sampling step to be reformulated into a differentiable function. We extend the {\itshape reparameterisation trick} to include the stochastic input to resampling therefore limiting the discontinuities in the gradient calculation after this step. Knowing the gradients of the prior and likelihood allows us to run particle Markov Chain Monte Carlo (p-MCMC) and use the No-U-Turn Sampler (NUTS) as the proposal when estimating parameters. We compare the Metropolis-adjusted Langevin algorithm (MALA), Hamiltonian Monte Carlo with different number of steps and NUTS. We consider two state-space models and show that NUTS improves the mixing of the Markov chain and can produce more accurate results in less computational time.

In Byzantine robust distributed optimization, a central server wants to train a machine learning model over data distributed across multiple workers. However, a fraction of these workers may deviate from the prescribed algorithm and send arbitrary messages to the server. While this problem has received significant attention recently, most current defenses assume that the workers have identical data. For realistic cases when the data across workers is heterogeneous (non-iid), we design new attacks which circumvent these defenses leading to significant loss of performance. We then propose a simple resampling scheme that adapts existing robust algorithms to heterogeneous datasets at a negligible computational cost. We theoretically and experimentally validate our approach, showing that combining resampling with existing robust algorithms is effective against challenging attacks.

Resampling is a key component of sample-based recursive state estimation in particle filters. Recent work explores differentiable particle filters for end-to-end learning. However, resampling remains a challenge in these works, as it is inherently non-differentiable. We address this challenge by replacing traditional resampling with a learned neural network resampler. We present a novel network architecture, the particle transformer, and train it for particle resampling using a likelihood-based loss function over sets of particles. Incorporated into a differentiable particle filter, our model can be end-to-end optimized jointly with the other particle filter components via gradient descent. Our results show that our learned resampler outperforms traditional resampling techniques on synthetic data and in a simulated robot localization task.

Generally, accurate prediction of the minor class is crucial but it's hard to achieve since there is not much information about the minor class. One approach to deal with this problem is to preliminarily resample the dataset, i.e., add new elements to the dataset or remove existing ones. Resampling can be done in various ways which raises the problem of choosing the most appropriate one. In this paper we experimentally investigate impact of resampling on classification accuracy, compare resampling methods and highlight key points and difficulties of resampling.