The understanding and modeling of complex physical phenomena through dynamical systems has historically driven scientific progress, as it provides the tools for predicting the behavior of different systems under diverse conditions through time. The discovery of dynamical systems has been indispensable in engineering, as it allows for the analysis and prediction of complex behaviors for computational modeling, diagnostics, prognostics, and control of engineered systems. Joining recent efforts that harness the power of symbolic regression in this domain, we propose a novel framework for the end-to-end discovery of ordinary differential equations (ODEs), termed Grammar-based ODE Discovery Engine (GODE). The proposed methodology combines formal grammars with dimensionality reduction and stochastic search for efficiently navigating high-dimensional combinatorial spaces. Grammars allow us to seed domain knowledge and structure for both constraining, as well as, exploring the space of candidate expressions. GODE proves to be more sample- and parameter-efficient than state-of-the-art transformer-based models and to discover more accurate and parsimonious ODE expressions than both genetic programming- and other grammar-based methods for more complex inference tasks, such as the discovery of structural dynamics. Thus, we introduce a tool that could play a catalytic role in dynamics discovery tasks, including modeling, system identification, and monitoring tasks.

Neural Information Processing Systems http://nips.cc/

Perception is often described as a predictive process based on an optimal inference with respect to a generative model. We study here the principled construction of a generative model specifically crafted to probe motion perception. In that context, we first provide an axiomatic, biologically-driven derivation of the model. This model synthesizes random dynamic textures which are defined by stationary Gaussian distributions obtained by the random aggregation of warped patterns. Importantly, we show that this model can equivalently be described as a stochastic partial differential equation. Using this characterization of motion in images, it allows us to recast motion-energy models into a principled Bayesian inference framework. Finally, we apply these textures in order to psychophysically probe speed perception in humans. In this framework, while the likelihood is derived from the generative model, the prior is estimated from the observed results and accounts for the perceptual bias in a principled fashion.

Results from these preliminary experiments were not reported in the paper but we report the results here in the supplementary materials. The standard bounding boxes were used as provided with the ImageNet dataset. If images had 0 bounding boxes, they were discarded for this dataset. See Section 2 in the main paper and consult Bashivan et al. (2019) for full details on the sampling procedure and chosen parameters. Code from Bashivan et al. (2019) was open-sourced at Biological measurements (Gattass et al. (1981, 1988)) have demonstrated that in primates, the As described in the paper, we employed two baseline models ('ResNet' and'coarse fixations') and two The'ResNet' baseline model directly feeds the full image through a standard ResNet architecture (32x32 for CIFAR10 or 320x320 for ImageNet).

In this work, we introduce a modification to traditional reinforcement learning which we call observational dropout, whereby we limit the agents ability to observe the real environment at each timestep.

Large language models (LLMs) are increasingly trained with reinforcement learning from verifiable rewards (RLVR), yet real-world deployment demands models that can self-improve without labels or external judges. Existing self-improvement approaches primarily rely on self-confirmation signals (e.g., confidence, entropy, or consistency) to generate rewards. This reliance drives models toward over-confident, majority-favored solutions, causing an entropy collapse that degrades pass@n and reasoning complexity. To address this, we propose EVOL-RL, a label-free framework that mirrors the evolutionary principle of balancing selection with variation. Concretely, EVOL-RL retains the majority-voted answer as an anchor for stability, but adds a novelty-aware reward that scores each sampled solution by how different its reasoning is from other concurrently generated responses. This majority-for-stability + novelty-for-exploration rule mirrors the variation-selection principle: selection prevents drift, while novelty prevents collapse. Evaluation results show that EVOL-RL consistently outperforms the majority-only baseline; e.g., training on label-free AIME24 lifts Qwen3-4B-Base AIME25 pass@1 from baseline's 4.6% to 16.4%, and pass@16 from 18.5% to 37.9%. EVOL-RL not only prevents in-domain diversity collapse but also improves out-of-domain generalization (from math reasoning to broader tasks, e.g., GPQA, MMLU-Pro, and BBEH). The code is available at: https://github.com/YujunZhou/EVOL-RL.

Adversarial Imitation Learning (AIL) methods, while effective in settings with limited expert demonstrations, are often considered unstable. These approaches typically decompose into two components: Density Ratio (DR) estimation $\frac{ρ_E}{ρ_π}$, where a discriminator estimates the relative occupancy of state-action pairs under the policy versus the expert; and Reward Assignment (RA), where this ratio is transformed into a reward signal used to train the policy. While significant research has focused on improving density estimation, the role of reward assignment in influencing training dynamics and final policy performance has been largely overlooked. RA functions in AIL are typically derived from divergence minimization objectives, relying heavily on human design and ingenuity. In this work, we take a different approach: we investigate the discovery of data-driven RA functions, i.e, based directly on the performance of the resulting imitation policy. To this end, we leverage an LLM-guided evolutionary framework that efficiently explores the space of RA functions, yielding \emph{Discovered Adversarial Imitation Learning} (DAIL), the first meta-learnt AIL algorithm. Remarkably, DAIL generalises across unseen environments and policy optimization algorithms, outperforming the current state-of-the-art of \emph{human-designed} baselines. Finally, we analyse why DAIL leads to more stable training, offering novel insights into the role of RA functions in the stability of AIL. Code is publicly available: https://github.com/shshnkreddy/DAIL.

Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many objectives, that arise in real-world logistic scenarios, better support for the decision maker can be achieved through better understanding of the often complex fitness landscape. This paper makes a contribution in this direction by presenting a technique that allows a visualisation and analysis of the local and global relationships between objectives in optimisation problems with many objectives. The proposed technique uses four steps: First, the global pairwise relationships are analysed using the Kendall correlation method; then, the ranges of the values found on the given Pareto front are estimated and assessed; next, these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade-offs between multiple objectives; and finally, local relationships are identified using scatter plots. Experiments are presented for three combinatorial optimisation problems: multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem, and multiobjective vehicle routing problem with time windows . Results show that the proposed technique helps in the gaining of insights into the problem difficulty arising from the relationships between objectives.

The diversity of patterns that emerge from complex systems motivates their use for scientific or artistic purposes. When exploring these systems, the challenges faced are the size of the parameter space and the strongly non-linear mapping between parameters and emerging patterns. In addition, artists and scientists who explore complex systems do so with an expectation of particular patterns. Taking these expectations into account adds a new set of challenges, which the exploration process must address. We provide design choices and their implementation to address these challenges; enabling the maximization of the diversity of patterns discovered in the user's region of interest -- which we call the constrained diversity -- in a sample-efficient manner. The region of interest is expressed in the form of explicit constraints. These constraints are formulated by the user in a system-agnostic way, and their addition enables interactive system exploration leading to constrained diversity, while maintaining global diversity.