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Leveraging 3D information within Multimodal Large Language Models (MLLMs) has recently shown significant advantages for indoor scene understanding. However, existing methods, including those using explicit ground-truth 3D positional encoding and those grafting external 3D foundation models for implicit geometry, struggle with the trade-off in 2D-3D representation fusion, leading to suboptimal deployment. To this end, we propose 3D-Implicit Depth Emergence, a method that reframes 3D perception as an emergent property derived from geometric self-supervision rather than explicit encoding. Our core insight is the Implicit Geometric Emergence Principle: by strategically leveraging privileged geometric supervision through mechanisms like a fine-grained geometry validator and global representation constraints, we construct an information bottleneck. This bottleneck forces the model to maximize the mutual information between visual features and 3D structures, allowing 3D awareness to emerge naturally within a unified visual representation. Unlike existing approaches, our method enables 3D perception to emerge implicitly, disentangling features in dense regions and, crucially, eliminating d

Neural networks often have identifiable computational structures - components of the network which perform an interpretable algorithm or task - but the mechanisms by which these emerge and the best methods for detecting these structures are not well understood. In this paper we investigate the emergence of computational structure in a transformer-like model trained to simulate the physics of a particle system, where the transformer's attention mechanism is used to transfer information between particles. We show that (a) structures emerge in the attention heads of the transformer which learn to detect particle collisions, (b) the emergence of these structures is associated to degenerate geometry in the loss landscape, and (c) the dynamics of this emergence follows a power law. This suggests that these components are governed by a degenerate "effective potential". These results have implications for the convergence time of computational structure within neural networks and suggest that the emergence of computational structure can be detected by studying the dynamics of network components.

Recent developments have shown that some semiclassical spacetimes cannot emerge from a traditional application of the rules of holography, prompting proposals for restoring their emergence with "observer rules". In this paper, we propose a general semiclassical diagnostic of such failures of emergence, and of the extent to which observer rules can fix them. Our diagnostic is the presence of certain "evanescent" quantum extremal surfaces, which are distinguished by an upper bound on their area rather than their generalized entropy. In particular, the generalized entropy of an evanescent QES may be large: even though its area term must be small, its bulk entanglement term is unconstrained. This feature is explained by an operational distinction between classical and quantum connectivity in semiclassical gravity, or equivalently between the two summands of the generalized entropy.

Many systems of interest exhibit nested emergent layers with their own rules and regularities, and our knowledge about them seems naturally organised around these levels. This paper proposes that this type of hierarchical emergence arises as a result of underlying symmetries. By combining principles from information theory, group theory, and statistical mechanics, one finds that dynamical processes that are equivariant with respect to a symmetry group give rise to emergent macroscopic levels organised into a hierarchy determined by the subgroups of the symmetry. The same symmetries happen to also shape Bayesian beliefs, yielding hierarchies of abstract belief states that can be updated autonomously at different levels of resolution. These results are illustrated in Hopfield networks and Ehrenfest diffusion, showing that familiar macroscopic quantities emerge naturally from their symmetries. Together, these results suggest that symmetries provide a fundamental mechanism for emergence and support a structural correspondence between objective and epistemic processes, making feasible inferential problems that would otherwise be computationally intractable.

Large language models have emergent capabilities that come unexpectedly at scale, but we need a theoretical framework to explain why and how they emerge. We prove that language models are actually non-ergodic systems while providing a mathematical framework based on Stuart Kauffman's theory of the adjacent possible (TAP) to explain capability emergence. Our resource-constrained TAP equation demonstrates how architectural, training, and contextual constraints interact to shape model capabilities through phase transitions in semantic space. We prove through experiments with three different language models that capacities emerge through discrete transitions guided by constraint interactions and path-dependent exploration. This framework provides a theoretical basis for understanding emergence in language models and guides the development of architectures that can guide capability emergence.

An enduring challenge in contagion theory is that the pathways contagions follow through social networks exhibit emergent complexities that are difficult to predict using network structure. Here, we address this challenge by developing a causal modeling framework that (i) simulates the possible network pathways that emerge as contagions spread and (ii) identifies which edges and nodes are most impactful on diffusion across these possible pathways. This yields a surprising discovery. If people require exposure to multiple peers to adopt a contagion (a.k.a., 'complex contagions'), the pathways that emerge often only work in one direction. In fact, the more complex a contagion is, the more asymmetric its paths become. This emergent directedness problematizes canonical theories of how networks mediate contagion. Weak ties spanning network regions - widely thought to facilitate mutual influence and integration - prove to privilege the spread contagions from one community to the other. Emergent directedness also disproportionately channels complex contagions from the network periphery to the core, inverting standard centrality models. We demonstrate two practical applications. We show th

The origin of agriculture represents a major evolutionary transition and a paradigmatic example of how complex collective behaviors emerge from simple interactions. Here we introduce an artificial society of reinforcement learning agents embedded in a dynamic ecological environment to identify general principles underlying this transition. Within this system, agricultural practices emerge spontaneously - without explicit instruction - through the coupled dynamics of learning and environmental modification. We show that this transition is governed by four key ingredients: individual planning through the valuation of delayed rewards, social vulnerability to cheaters, stabilization via social learning, and an emergent lock-in effect that renders agriculture effectively irreversible once established. In particular, we demonstrate that social learning acts as a "firewall" that suppresses cheater invasion and enables the propagation of successful strategies, leading to sustained population growth and nonlinear amplification of domesticated resources. Together, these results reveal universal mechanisms linking individual decision-making, social interactions, and ecological feedbacks. More

We examine the logical structure of the emergence of classical stochasticity for a quantum system governed by a Pauli-type master equation. It is well-known that while such equations describe the evolution of probabilities, they do not automatically justify classical reasoning based on the assumption that the system exists in a definite state at intermediate times. On the other hand, we show that this assumption is crucial for the standard calculation of stochastic times such as the persistent time and the time of first arrivals. We then consider examples of single particles, bosons, and fermions in the so-called ultradecoherence limit to illustrate how classical stochasticity may emerge from quantum mechanics.

The remarkable success of Large Language Models (LLMs) in generative tasks has raised fundamental questions about the nature of their acquired capabilities, which often appear to emerge unexpectedly without explicit training. This paper examines the emergent properties of Deep Neural Networks (DNNs) through both theoretical analysis and empirical observation, addressing the epistemological challenge of "creation without understanding" that characterises contemporary AI development. We explore how the neural approach's reliance on nonlinear, stochastic processes fundamentally differs from symbolic computational paradigms, creating systems whose macro-level behaviours cannot be analytically derived from micro-level neuron activities. Through analysis of scaling laws, grokking phenomena, and phase transitions in model capabilities, I demonstrate that emergent abilities arise from the complex dynamics of highly sensitive nonlinear systems rather than simply from parameter scaling alone. My investigation reveals that current debates over metrics, pre-training loss thresholds, and in-context learning miss the fundamental ontological nature of emergence in DNNs. I argue that these systems

The modern Everett interpretation of quantum mechanics describes an emergent multiverse. The goal of this paper is to provide a perspicuous characterisation of how the multiverse emerges making use of a recent account of (weak) ontological emergence. This will be cashed out with a case study that identifies decoherence as the mechanism for emergence. The greater metaphysical clarity enables the rebuttal of critiques due to Baker (2007) and Dawid and Thébault (2015) that cast the emergent multiverse ontology as incoherent; responses are also offered to challenges to the Everettian approach from Maudlin (2010) and Monton (2013).

In this perspective article, we discuss the scenario of dynamically emergent correlation (DEC) arising in classical and quantum noninteracting systems when they are subjected to a common fluctuating stochastic environment. The key property of such systems is that the strong correlations between different particles emerge from the dynamics and not from built-in interactions. In many cases, these strong correlations persist even at long times in the stationary state. Computing observables explicitly for such strongly correlated states in general is very hard. Remarkably, the stationary states in several models of DEC exhibit an interesting analytical structure that allows to compute physical observables, despite being strongly correlated. Recent experiments on trapped colloidal particles have established that these DEC in the stationary state can in fact be measured. DEC is a rapidly emerging domain of strongly correlated out-of-equilibrium statistical physics, with both theoretical and experimental, as well as classical and quantum, components.

Emergent communication, or emergent language, is the field of research which studies how human language-like communication systems emerge de novo in deep multi-agent reinforcement learning environments. The possibilities of replicating the emergence of a complex behavior like language have strong intuitive appeal, yet it is necessary to complement this with clear notions of how such research can be applicable to other fields of science, technology, and engineering. This paper comprehensively reviews the applications of emergent communication research across machine learning, natural language processing, linguistics, and cognitive science. Each application is illustrated with a description of its scope, an explication of emergent communication's unique role in addressing it, a summary of the extant literature working towards the application, and brief recommendations for near-term research directions.

Symbol grounding (Harnad, 1990) describes how symbols such as words acquire their meanings by connecting to real-world sensorimotor experiences. Recent work has shown preliminary evidence that grounding may emerge in (vision-)language models trained at scale without using explicit grounding objectives. Yet, the specific loci of this emergence and the mechanisms that drive it remain largely unexplored. To address this problem, we introduce a controlled evaluation framework that systematically traces how symbol grounding arises within the internal computations through mechanistic and causal analysis. Our findings show that grounding concentrates in middle-layer computations and is implemented through the aggregate mechanism, where attention heads aggregate the environmental ground to support the prediction of linguistic forms. This phenomenon replicates in multimodal dialogue and across architectures (Transformers and state-space models), but not in unidirectional LSTMs. Our results provide behavioral and mechanistic evidence that symbol grounding can emerge in language models, with practical implications for predicting and potentially controlling the reliability of generation.

Microbial ecosystems exhibit a surprising amount of functionally relevant diversity at all levels of taxonomic resolution, presenting a significant challenge for most modeling frameworks. A long-standing hope of theoretical ecology is that some patterns might persist despite community complexity -- or perhaps even emerge because of it. A deeper understanding of such "emergent simplicity" could enable new approaches for predicting the behaviors of the complex ecosystems in nature. However, the concept remains partly intuitive with no consistent definition, and most empirical examples described so far afford limited predictive power. Here, we propose an information-theoretic framework for defining and quantifying emergent simplicity in empirical data based on the ability of coarsened descriptions to predict community-level functional properties. Applying this framework to two published datasets, we demonstrate that all five properties measured across both experiments exhibit robust evidence of what we define as "emergent predictability": surprisingly, as community richness increases, simple compositional descriptions become more predictive. We show that standard theoretical models of

Transformer-like models for vision tasks have recently proven effective for a wide range of downstream applications such as segmentation and detection. Previous works have shown that segmentation properties emerge in vision transformers (ViTs) trained using self-supervised methods such as DINO, but not in those trained on supervised classification tasks. In this study, we probe whether segmentation emerges in transformer-based models solely as a result of intricate self-supervised learning mechanisms, or if the same emergence can be achieved under much broader conditions through proper design of the model architecture. Through extensive experimental results, we demonstrate that when employing a white-box transformer-like architecture known as CRATE, whose design explicitly models and pursues low-dimensional structures in the data distribution, segmentation properties, at both the whole and parts levels, already emerge with a minimalistic supervised training recipe. Layer-wise finer-grained analysis reveals that the emergent properties strongly corroborate the designed mathematical functions of the white-box network. Our results suggest a path to design white-box foundation models t

We explore the Emergence Proposal for the moduli metric and the gauge couplings in a concrete model with 7 saxionic and 7 axionic moduli fields, namely the compactification of the type IIA superstring on a 6-dimensional toroidal orbifold. We show that consistency requires integrating out precisely the 12 towers of light particle species arising from KK and string/brane winding modes and one asymptotically tensionless string up to the species scale. After pointing out an issue with the correct definition of the species scale in the presence of string towers, we carry out the emergence computation and find that the KK and winding modes indeed impose the classical moduli dependence on the one-loop corrections, while the emergent string induces moduli dependent logarithmic suppressions. The interpretation of these results for the Emergence Proposal are discussed revealing a couple of new and still not completely settled aspects.

In a recent paper arXiv:2409.01034, Gong et al. studied the disorder effects in nodal-knot semimetal through Wilson momentum-shell renormalization group (RG) method. They stated that various nodal-knot transitions emerge driven by disorders. However, we notice that there are serious problems in this paper. First, in this paper, the RG analysis is not performed in the momentum space around the Fermi surface but in an incorrect momentum space around the point $k=0$. Accordingly, the RG equations are completely unreliable. Second, the criterion for phase transition employed in this paper is invalid. Accroding to the criterion in this paper, we can find that the various phase transitions stated in this paper even emerge in clean nodal-knot semimetal system! Thus, the conclusions in this paper are unfounded.

We explore the necessary conditions for 1-form symmetries to emerge in the long-distance limit when they are explicitly broken at short distances. A minimal requirement is that there exist operators which become topological at long distances and that these operators have non-trivial correlation functions. These criteria are obeyed when the would-be emergent symmetry is spontaneously broken, or is involved in 't Hooft anomalies. On the other hand, confinement, i.e. a phase with unbroken 1-form symmetry, is nearly incompatible with the emergence of 1-form symmetries. We comment on some implications of our results for QCD as well as the idea of Higgs-confinement continuity.

Pragmatics is core to natural language, enabling speakers to communicate efficiently with structures like ellipsis and anaphora that can shorten utterances without loss of meaning. These structures require a listener to interpret an ambiguous form - like a pronoun - and infer the speaker's intended meaning - who that pronoun refers to. Despite potential to introduce ambiguity, anaphora is ubiquitous across human language. In an effort to better understand the origins of anaphoric structure in natural language, we look to see if analogous structures can emerge between artificial neural networks trained to solve a communicative task. We show that: first, despite the potential for increased ambiguity, languages with anaphoric structures are learnable by neural models. Second, anaphoric structures emerge between models 'naturally' without need for additional constraints. Finally, introducing an explicit efficiency pressure on the speaker increases the prevalence of these structures. We conclude that certain pragmatic structures straightforwardly emerge between neural networks, without explicit efficiency pressures, but that the competing needs of speakers and listeners conditions the d