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Neural networks that can grow or both grow and shrink during learning, referred to as growing neural networks and elastic neural networks, respectively, have recently been explored in offline continual learning with a particular focus on catastrophic forgetting. Driven by the observations that 1) online continual learning closely resembles how animals learn; 2) loss of plasticity---the progressive decline in a learning network's ability to learn---is another crucial challenge facing continual learning; and 3) incremental introduction of randomly initialized hidden units was recently shown to help preserve plasticity, in this paper, we study the plasticity of several foundational growing and elastic networks in online continual learning. Our experiments in supervised learning settings show that adaptive growing networks, which incrementally incorporate new, randomly initialized units to the network while keeping all existing connections adaptive, can maintain high prediction accuracy without losing plasticity despite the continuous increase in the dead hidden unit proportion. Furthermore, we demonstrate that adaptive elastic networks, which in addition to progressively adding new hi

We consider growing open chemical reaction systems (CRSs), in which autocatalytic chemical reactions are encapsulated in a finite volume and its size can change in conjunction with the reactions. The thermodynamics of growing CRSs is indispensable for understanding biological cells and designing protocells by clarifying the physical conditions and costs for their growing states. In this work, we establish a thermodynamic theory of growing CRSs by extending the Hessian geometric structure of non-growing CRSs. The theory provides the environmental conditions to determine the fate of the growing CRSs; growth, shrinking or equilibration. We also identify thermodynamic constraints; one to restrict the possible states of the growing CRSs and the other to further limit the region where a nonequilibrium steady growing state can exist. Moreover, we evaluate the entropy production rate in the steady growing state. The growing nonequilibrium state has its origin in the extensivity of thermodynamics, which is different from the conventional nonequilibrium states with constant volume. These results are derived from general thermodynamic considerations without assuming any specific thermodynamic

Reinforcement learning for flow-matching text-to-speech is complicated by deterministic ODE sampling: trajectory-level policy-gradient methods typically convert the ODE into an SDE and track per-step likelihood ratios, introducing stochastic perturbations and substantial overhead. We propose GROW, a group-relative advantage-weighted on-policy RL method that acts directly on the standard flow-matching objective. For each prompt, GROW samples a group of on-policy utterances, separately standardizes intelligibility and speaker-similarity rewards within the group, and combines them to reweight flow-matching regression. A Wasserstein-2 velocity penalty anchors the updated model to a frozen pretrained reference. A group-mean reward baseline is introduced to convert reward weighting into advantage weighting. For strong pretrained TTS models with concentrated rewards, positive exponential weighting is dominated by reward-agnostic self-imitation, whereas a zero-mean signed advantage preserves effective within-group credit assignment. Instantiated on DiTAR and evaluated on LibriSpeech and Seed-TTS EN/ZH, GROW reduces average WER from 2.016 to 1.558 and raises speaker similarity from 0.676 to

Developmental Graph Cellular Automata (DGCA) are a novel model for morphogenesis, capable of growing directed graphs from single-node seeds. In this paper, we show that DGCAs can be trained to grow reservoirs. Reservoirs are grown with two types of targets: task-driven (using the NARMA family of tasks) and task-independent (using reservoir metrics). Results show that DGCAs are able to grow into a variety of specialized, life-like structures capable of effectively solving benchmark tasks, statistically outperforming `typical' reservoirs on the same task. Overall, these lay the foundation for the development of DGCA systems that produce plastic reservoirs and for modeling functional, adaptive morphogenesis.

This paper presents general strong duality results when testing hypotheses by betting against them. A bet is an e-variable for a composite null hypothesis $\Pcal$: a nonnegative random variable $X$ whose expected value is at most one under every $P \in \mathcal P$. Following Kelly, Breiman, Cover, Shafer, and Grunwald et al. (2024), we study a natural minimax \emph{log-optimality} criterion: given a composite alternative $\Qcal$, we characterize the ``GROW value'' $\sup_{X} \inf_{Q} \E_{Q}[\log X]$. This paper generalizes the results of Larsson et al. (2025) from (arbitrary $\mathcal P$ and) simple $\mathcal Q$ to arbitrary $\mathcal Q$. We prove that there always exists a minimizing information-projection pair between the weak-$*$ closures of the convex hulls of arbitrary $\mathcal P$ and $\mathcal Q$, and show that the GROW value for \emph{bounded} e-variables always equals their relative entropy. We also prove a similarly general strong duality for the REGROW criterion with bounded e-variables and arbitrary bounded offsets. Under various assumptions our results extend to unbounded e-variables, and examples show that without any assumptions such extensions fail. Our results are a

College students face well-being challenges driven by academic pressure, financial strain, and social expectations. While campus counseling and student-success programs offer support, access is often limited by stigma, waitlists, and scheduling constraints. Existing digital tools focus on emotional check-ins or chatbots and may overlook structured goal setting and aligning goals with personal values. We present GROW, a goal-centered well-being coaching system that puts values-aligned goals at the center of the student experience. GROW combines the SMART framework with principles from Acceptance and Commitment Therapy in a conversational AI coach that helps students clarify aspirations, break them into concrete steps, and reflect on progress. The system links action plans with Google Calendar, sends reminders, and provides a dashboard that shows progress and engagement. We evaluated GROW through interviews with clinical psychologists, student-success staff, and faculty, followed by a one-week deployment with 30 undergraduates. Findings offer design implications for interactive systems that support engagement, accountability, and sense of purpose in higher education.

In 2007, Erika Bohm-Vitense published a provocative figure suggesting that the solar rotation period and activity cycle made the Sun an outlier compared to the trends observed for stars in the Mount Wilson HK survey. A decade later, after the discovery of weakened magnetic braking (WMB), an evolutionary scenario was proposed that could account for the properties of the Sun if activity cycles grow longer and weaker in the WMB regime. Recent observations of the gradual onset of WMB suggest that the efficiency of the global stellar dynamo declines by at least two orders of magnitude as the stellar Rossby number approaches a critical point slightly above the solar value. A new sample of activity cycle data from the California Legacy Survey suggests that the Sun is not an outlier, and unambiguously confirms that activity cycles grow longer and weaker on stellar evolutionary timescales.

This study aims to extend the framework for assessing artificial intelligence, called GROW-AI (Growth and Realization of Autonomous Wisdom), designed to answer the question "Can machines grow up?" -- a natural successor to the Turing Test. The methodology applied is based on a system of six primary criteria (C1-C6), each assessed through a specific "game", divided into four arenas that explore both the human dimension and its transposition into AI. All decisions and actions of the entity are recorded in a standardized AI Journal, the primary source for calculating composite scores. The assessment uses the prior expert method to establish initial weights, and the global score -- Grow Up Index -- is calculated as the arithmetic mean of the six scores, with interpretation on maturity thresholds. The results show that the methodology allows for a coherent and comparable assessment of the level of "growth" of AI entities, regardless of their type (robots, software agents, LLMs). The multi-game structure highlights strengths and vulnerable areas, and the use of a unified journal guarantees traceability and replicability in the evaluation. The originality of the work lies in the conceptua

While the physics of disordered packing in non-growing systems is well understood, unexplored phenomena can emerge when packing takes place in growing domains. We study the arrangements of pigment cells (chromatophores) on squid skin as a biological example of a packed system on an expanding surface. We find that relative density fluctuations in cell numbers grow with spatial scale. We term this behavior ``hyperdisordered'', in contrast with hyperuniform behavior in which relative fluctuations tend to zero at large scale. We find that hyperdisordered scaling, akin to that of a critical system, is quantitatively reproduced by a model in which hard disks are randomly inserted in a homogeneously growing surface. In addition, we find that chromatophores increase in size during animal development, but maintain a stationary size distribution. The physical mechanisms described in our work may apply to a broad class of growing dense systems.

A complex system with many interacting individuals can be represented by a network consisting of nodes and links representing individuals and pairwise interactions, respectively. However, real-world systems grow with time and include many higher-order interactions. Such systems with higher-order interactions can be well described by a simplicial complex (SC), which is a type of hypergraph, consisting of simplexes representing sets of multiple interacting nodes. Here, capturing the properties of growing real-world systems, we propose a growing random SC (GRSC) model where a node is added and a higher dimensional simplex is established among nodes at each time step. We then rigorously derive various percolation properties in the GRSC. Finally, we confirm that the system exhibits an infinite-order phase transition as higher-order interactions accelerate the growth of the system and result in the advanced emergence of a giant cluster. This work can pave the way for interpreting growing complex systems with higher-order interactions such as social, biological, brain, and technological systems.

The ubiquitous deployment of deep learning systems on resource-constrained Edge devices is hindered by their high computational complexity coupled with their fragility to out-of-distribution (OOD) data, especially to naturally occurring common corruptions. Current solutions rely on the Cloud to train and compress models before deploying to the Edge. This incurs high energy and latency costs in transmitting locally acquired field data to the Cloud while also raising privacy concerns. We propose GEARnn (Growing Efficient, Accurate, and Robust neural networks) to grow and train robust networks in-situ, i.e., completely on the Edge device. Starting with a low-complexity initial backbone network, GEARnn employs One-Shot Growth (OSG) to grow a network satisfying the memory constraints of the Edge device using clean data, and robustifies the network using Efficient Robust Augmentation (ERA) to obtain the final network. We demonstrate results on a NVIDIA Jetson Xavier NX, and analyze the trade-offs between accuracy, robustness, model size, energy consumption, and training time. Our results demonstrate the construction of efficient, accurate, and robust networks entirely on an Edge device.

Real-world networks grow over time; statistical models based on node exchangeability are not appropriate. Instead of constraining the structure of the \textit{distribution} of edges, we propose that the relevant symmetries refer to the \textit{causal structure} between them. We first enumerate the 96 causal directed acyclic graph (DAG) models over pairs of nodes (dyad variables) in a growing network with finite ancestral sets that are invariant to node deletion. We then partition them into 21 classes with ancestral sets that are closed under node marginalization. Several of these classes are remarkably amenable to distributed and asynchronous evaluation. As an example, we highlight a simple model that exhibits flexible power-law degree distributions and emergent phase transitions in sparsity, which we characterize analytically. With few parameters and much conditional independence, our proposed framework provides natural baseline models for causal inference in relational data.

We prove that mild solutions to the stochastic heat equation with superlinear accretive forcing and polynomially growing multiplicative noise cannot explode under two sets of assumptions. The first set of assumptions allows both the deterministic forcing and multiplicative noise terms to grow polynomially, as long as the multiplicative noise is sufficiently larger. The second set of assumptions imposes an Osgood condition on the deterministic forcing and allows the multiplicative noise to grow polynomially. In both cases, the multiplicative noise cannot grow faster than $u^{\frac{3}{2}}$, as this would cause explosion.

A popular method for Neural Architecture Search (NAS) is based on growing networks via small local changes to the network's architecture called network morphisms. These methods start with a small seed network and progressively grow the network by adding new neurons in an automated way. However, it remains a challenge to efficiently determine which parts of the network are best to grow. Here we propose a NAS method for growing a network by using a Gauss-Newton approximation of the loss function to efficiently learn and evaluate candidate network morphisms. We compare our method with state of the art NAS methods for CIFAR-10 and CIFAR-100 classification tasks, and conclude our method learns similar quality or better architectures at a smaller computational cost.

An amoeba is a tree together with instructions how to iteratively grow trees by adding paths of a fixed length $\ell$. This paper analyses such a growth process. An amoeba is mortal if all versions of the process are finite, and it is immortal if they are all infinite. We obtain some necessary and some sufficient conditions for mortality. In particular, for growing caterpillars in the case $\ell=1$ we characterize mortal amoebas. We discuss variations of the mortality concept, conjecture that some of them are equivalent, and support this conjecture for $\ell\in\{1,2\}$.

Biological lifeforms can heal, grow, adapt, and reproduce -- abilities essential for sustained survival and development. In contrast, robots today are primarily monolithic machines with limited ability to self-repair, physically develop, or incorporate material from their environments. While robot minds rapidly evolve new behaviors through AI, their bodies remain closed systems, unable to systematically integrate material to grow or heal. We argue that open-ended physical adaptation is only possible when robots are designed using a small repertoire of simple modules. This allows machines to mechanically adapt by consuming parts from other machines or their surroundings and shed broken components. We demonstrate this principle on a truss modular robot platform. We show how robots can grow bigger, faster, and more capable by consuming materials from their environment and other robots. We suggest that machine metabolic processes like those demonstrated here will be an essential part of any sustained future robot ecology.

We introduce a new model of correlated randomly growing graphs and study the fundamental questions of detecting correlation and estimating aspects of the correlated structure. The model is simple and starts with any model of randomly growing graphs, such as uniform attachment (UA) or preferential attachment (PA). Given such a model, a pair of graphs $(G_1, G_2)$ is grown in two stages: until time $t_{\star}$ they are grown together (i.e., $G_1 = G_2$), after which they grow independently according to the underlying growth model. We show that whenever the seed graph has an influence in the underlying graph growth model---this has been shown for PA and UA trees and is conjectured to hold broadly---then correlation can be detected in this model, even if the graphs are grown together for just a single time step. We also give a general sufficient condition (which holds for PA and UA trees) under which detection is possible with probability going to $1$ as $t_{\star} \to \infty$. Finally, we show for PA and UA trees that the amount of correlation, measured by $t_{\star}$, can be estimated with vanishing relative error as $t_{\star} \to \infty$.

Most models that try to explain economic growth indicate exponential growth paths. In recent years, however, a lively discussion has emerged considering the validity of this notion. In the empirical literature dealing with drivers of economic growth, the majority of articles is based upon an implicit assumption of exponential growth. Few scholarly articles have addressed this issue so far. In order to shed light on this issue, we estimate autoregressive integrated moving average time series models based on Gross Domestic Product Per Capita data for 18 mature economies from 1960 to 2013. We compare the adequacy of linear and exponential growth models and conduct several robustness checks. Our fndings cast doubts on the widespread belief of exponential growth and suggest a deeper discussion on alternative economic grow theories.

Within the framework of general relativity, it can be shown that gravitational waves are radiated with the merger of massive compact objects. Such gravitational wave signals are observed on Earth on various detectors, in particular, on Laser Interferometer Gravitational Wave Observatory (LIGO) and Virgo. During the operation of these detectors, many events have been detected. Those events are associated with the merger of massive compact objects, however, the nature of some merging objects has not yet been reliably established. This work considers nontopological solitons of dark matter -- Q-balls, as candidates for the role of massive compact objects. In this work one of the simplest models of Q-balls, the mechanism of their birth during a phase transition in the early Universe and the mechanism of their mass gaining during the evolution of the Universe, which is based on their mutual merger, are considered. As a result, it is analyzed whether Q-balls of dark matter can grow to the mass gap masses and be candidates for the role of massive compact objects.