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LLM-guided evolutionary search uses AI agents to improve programs for mathematical and computational problems by iteratively refining solutions and combining high-scoring methods. However, the process is often slow because the LLM generates a long textual chain of thought for each round and must repeat this generation many times to maintain population diversity. We present SwarmEvolve, a framework in which hundreds of low-cost agents per round work in swarms, reason in latent space without decoding to text, and share information by passing KV caches. Each swarm studies the problem from a different angle. A novelty filter keeps the most distinct agent ideas by directly measuring the distances between the agents' hidden state vectors. Crossover of ideas happens naturally in latent space, as a summarizer agent receives the combined KV caches of all swarm members. On 21 problems in mathematical discovery and scientific computing, SwarmEvolve gets the highest average score and needs a median of only 3 to 8 minutes to reach the best scores that other state-of-the-art frameworks reach in 60 minutes. On several problems, SwarmEvolve with Qwen3 8B improves on the solutions that AlphaEvolve first found with frontier LLMs. Our work shows that agent swarms that communicate in latent space offer a fast, low-cost approach to program search for scientific problems.

The Forward-Forward (FF) algorithm trains networks layer-by-layer using a local "goodness function," yet the choice of activity statistic remains an important design question. We systematically study how selectivity and activity shape affect FF learning, introducing selective goodness functions based on top-$k$ and entmax-weighted energy alongside shape-sensitive objectives based on normalized higher-order moments. In particular, we propose burstiness goodness, a parameter-free, scale-invariant excess-kurtosis objective that rewards heavy-tailed activity patterns. Our study examines goodness functions together with activation and label-injection choices across six small-image datasets, and uses controlled experiments to isolate their effects. In validation-tuned, five-seed Fashion-MNIST experiments with matched ReLU activation, standard label injection, and per-layer scoring, burstiness improves accuracy from $73.2\pm0.9\%$ to $88.6\pm0.4\%$ over sum-of-squares. On CIFAR-10, burstiness improves block-local ResNet-18 accuracy from $28.9\pm0.5\%$ to $46.8\pm2.5\%$ under the same separate per-block label pathway. These results show that activity-shape statistics can provide effective local learning signals across the tested settings. Code is available at https://github.com/suayptalha/ff-selectivity-shape.

The phenomenon of implicit bias has attracted interest in recent years as a fundamental aspect of the remarkable generalizing ability of neural networks. In a nutshell, it entails that gradient descent dynamics in many neural nets, even without any explicit regularizer in the loss function, converges to the solution of a regularized learning problem. In this work, we show that this phenomenon extends to non-linear spectral parameterizations in matrix sensing. More precisely, we propose a matrix network architecture called Spectral Neural Networks (abbrv. SNN) where each neuron applies nonlinear activation to the singular values of the input matrix. Conceptually, this entails coordinatizing the space of matrices by their singular values and singular vectors, as opposed to by their entries, a potentially fruitful perspective for matrix learning. We prove the exponentially fast decay of squared loss during the training dynamics of an SNN parameterized matrix sensing model under gradient flow (which is a continuous approximation of the discrete gradient descent), and also that the training implicitly selects an approximate solution that minimizes nuclear norm. We also demonstrate the effectiveness of the SNN architecture in the context of matrix sensing by empirical investigations. We believe that the SNN architecture has the potential to be of wide applicability in a broad class of matrix learning scenarios.

Language models must now generalize out of the box to novel environments and work inside inference-scaling search procedures, such as AlphaEvolve, that select rollouts with a variety of task-specific reward functions. Unfortunately, the standard paradigm of LLM post-training optimizes a pre-specified scalar reward, often leading current LLMs to produce low-entropy response distributions and thus to struggle at displaying the diversity that inference-time search will require. We propose Vector Policy Optimization (VPO), an RL algorithm that explicitly trains policies to anticipate diverse downstream reward functions and to produce diverse solutions. VPO exploits that rewards are often vector-valued in practice, like per-test-case correctness in code generation or, say, multiple different user personas or reward models. VPO combines multi-answer prompting with a set-level reward to train the LLM to produce sets of solutions that specialize to different trade-offs in the vector reward space. Across four tasks, VPO matches or beats the strongest scalar RL baselines on test-time search (e.g. pass@k and best@k), with the gap widening as the search budget grows. For evolutionary search, VPO models unlock problems that GRPO models cannot solve at all. As test-time search becomes standard, diversity may need to become the default post-training objective.

Dynamic flexible assembly flow shop scheduling with multi-product delivery, often with kitting supply and machine-level flexibility, can be found in many applications. It is difficult to design rules manually for it. Genetic programming (GP) has been used to automatically generate dispatching rules, enabling responsive scheduling while meeting high responsiveness demands. However, GP methods are dependent on fixed terminal sets and have poor interpretability. In this work, we develop an evolving dispatching rules framework (EvoDR) that leverages the semantic understanding and generation capabilities of large language models to achieve cross-domain integration of rule design and scheduling knowledge. In our proposed framework, multi-stage assembly supply decisions are modeled as priority sorting of directed edges based on heterogeneous graphs. A dual-expert co-evolution mechanism is proposed, which allows LLM-A to generate code and LLM-S conduct scheduling analysis and reflection. Guided by improvements in hybrid evaluation, adaptive rules that fit dynamic features are continuously evolved. Experimental results show that EvoDR can achieve lower average tardiness than other automatically designed state-of-the-art approaches. It also outperforms expert-designed competitors across 480 instances over 24 distinct scenarios with varying resource configurations and disturbance levels, and EvoDR demonstrates robust adaptability across diverse operating conditions.

Neural circuits must maintain functionality to drive effective behavior while their size, topology, geometry, and intrinsic dynamics change across development. To model developing visuomotor circuits and behavior, we investigated whether a single compact generative encoding could produce functional recurrent controllers across such changes. Building on the HyperNEAT algorithm, we represented this program as a compositional pattern-producing network that received developmental time as an input to generate age-specific connectivity. The developmental substrate prescribed neuronal birth, position, sensory organization, and intrinsic time constants. We tested this approach using two geometrically distinct developmental substrates and two visuomotor tasks: optomotor responses and phototaxis. Controllers optimized at only the initial or mature substrate generally failed when evaluated at other ages. In contrast, controllers optimized across multiple developmental snapshots maintained substantially higher and more consistent performance across trained and unseen ages. Optimization at only three developmental snapshots was often sufficient to produce effective behavior across the tested developmental interval. The resulting connectomes changed substantially with age and did not converge on a single trajectory of sparsity or connection-weight statistics. Controllers also differed in whether they relied on neurons born later in development. These results demonstrate that a shared spatiotemporal time-varying connectivity program can produce recurrent neural networks that preserve behavior across substantial developmental changes. Together, these results provide a framework for studying how functional stability can emerge without requiring structural or dynamical stability.