The stochastic block model (SBM) has long been studied in machine learning and network science as a canonical model for clustering and community detection. In the recent years, new developments have demonstrated the presence of threshold phenomena for this model, which have set new challenges for algorithms. For the detection problem in symmetric SBMs, Decelle et al. conjectured that the so-called Kesten-Stigum (KS) threshold can be achieved efficiently. This was proved for two communities, but remained open for three and more communities. We prove this conjecture here, obtaining a general result that applies to arbitrary SBMs with linear size communities. The developed algorithm is a linearized acyclic belief propagation (ABP) algorithm, which mitigates the effects of cycles while provably achieving the KS threshold in O(n ln n) time. This extends prior methods by achieving universally the KS threshold while reducing or preserving the computational complexity. ABP is also connected to a power iteration method on a generalized nonbacktracking operator, formalizing the spectral-message passing interplay described in Krzakala et al., and extending results from Bordenave et al.

What computational structure are we building into large language models when we train them on next-token prediction? Here, we present evidence that this structure is given by the meta-dynamics of belief updating over hidden states of the data- generating process. Leveraging the theory of optimal prediction, we anticipate and then find that belief states are linearly represented in the residual stream of transformers, even in cases where the predicted belief state geometry has highly nontrivial fractal structure. We investigate cases where the belief state geometry is represented in the final residual stream or distributed across the residual streams of multiple layers, providing a framework to explain these observations. Furthermore we demonstrate that the inferred belief states contain information about the entire future, beyond the local next-token prediction that the transformers are explicitly trained on.

This monograph presents a modular cognitive architecture for artificial intelligence grounded in the formal modeling of belief as structured semantic state. Belief states are defined as dynamic ensembles of linguistic expressions embedded within a navigable manifold, where operators enable assimilation, abstraction, nullification, memory, and introspection. Drawing from philosophy, cognitive science, and neuroscience, we develop a layered framework that enables self-regulating epistemic agents capable of reflective, goal-directed thought. At the core of this framework is the epistemic vacuum: a class of semantically inert cognitive states that serves as the conceptual origin of belief space. From this foundation, the Null Tower arises as a generative structure recursively built through internal representational capacities. The theoretical constructs are designed to be implementable in both symbolic and neural systems, including large language models, hybrid agents, and adaptive memory architectures. This work offers a foundational substrate for constructing agents that reason, remember, and regulate their beliefs in structured, interpretable ways.

Despite efforts to better understand the constraints that operate on single-step parallel (aka "package", "multiple") revision, very little work has been carried out on how to extend the model to the iterated case. A recent paper by Delgrande & Jin outlines a range of relevant rationality postulates. While many of these are plausible, they lack an underlying unifying explanation. We draw on recent work on iterated parallel contraction to offer a general method for extending serial iterated belief revision operators to handle parallel change. This method, based on a family of order aggregators known as TeamQueue aggregators, provides a principled way to recover the independently plausible properties that can be found in the literature, without yielding the more dubious ones.

Goal Recognition (GR) is the problem of recognizing an agent's objectives based on observed actions. Recent data-driven approaches for GR alleviate the need for costly, manually crafted domain models. However, these approaches can only reason about a pre-defined set of goals, and time-consuming training is needed for new emerging goals. To keep this model-learning automated while enabling quick adaptation to new goals, this paper introduces GRAML: Goal Recognition As Metric Learning. GRAML uses a Siamese network to treat GR as a deep metric learning task, employing an RNN that learns a metric over an embedding space, where the embeddings for observation traces leading to different goals are distant, and embeddings of traces leading to the same goals are close. This metric is especially useful when adapting to new goals, even if given just one example observation trace per goal. Evaluated on a versatile set of environments, GRAML shows speed, flexibility, and runtime improvements over the state-of-the-art GR while maintaining accurate recognition.

Theory of Mind is a fundamental cognitive ability that underpins human social behavior, enabling individuals to infer the beliefs, intentions, and knowledge of others. In this paper, we propose BeliefNest, an open-source simulator designed to support research on collaborative behavior in embodied agents endowed with Theory of Mind capabilities. Recent advances in embodied agents powered by large language models (LLMs) have shown promising progress. However, there is still no platform that can explicitly represent nested belief states and integrate them with action generation mechanisms. BeliefNest addresses this gap by providing a flexible simulation framework that incorporates both hierarchical belief structures and prompt generation support. BeliefNest offers the following features: Explicit representation of nested belief states, as studied in Theory of Mind, using hierarchical simulators (see Section 3) Support for prompt generation based on each belief state, enabling the design and evaluation of methods for agent control with LLMs (see Section 5) Integration with the Minecraft environment, which is widely used in LLM agent research [1-4], and support for open-domain tasks In this paper, we describe the design and functionality of BeliefNest and demonstrate its effectiveness through experiments on false-belief tasks.

Forgetting a specific belief revision episode may not erase information because the other revisions may provide or entail the same information. Whether it does was proved coNP-hard for sequences of two arbitrary lexicographic revisions or arbitrarily long lexicographic Horn revisions. A polynomial algorithm is presented for the case of two lexicographic Horn revision. Heterogeneous sequences, including revisions other than lexicographic, were proved to belong in Delta2. Their previously proved coNP-hardness is enhanced to Dp-hardness.

This work introduces belief injection, a proactive epistemic control mechanism for artificial agents whose cognitive states are structured as dynamic ensembles of linguistic belief fragments. Grounded in the Semantic Manifold framework, belief injection directly incorporates targeted linguistic beliefs into an agent's internal cognitive state, influencing reasoning and alignment proactively rather than reactively. We delineate various injection strategies, such as direct, context-aware, goal-oriented, and reflective approaches, and contrast belief injection with related epistemic control mechanisms, notably belief filtering. Additionally, this work discusses practical applications, implementation considerations, ethical implications, and outlines promising directions for future research into cognitive governance using architecturally embedded belief injection.

Traditional logic-based belief revision research focuses on designing rules to constrain the behavior of revision operators. Frameworks have been proposed to characterize iterated revision rules, but they are often too loose, leading to multiple revision operators that all satisfy the rules under the same belief condition. In many practical applications, such as safety critical ones, it is important to specify a definite revision operator to enable agents to iteratively revise their beliefs in a deterministic way. In this paper, we propose a novel framework for iterated belief revision by characterizing belief information through preference relations. Semantically, both beliefs and new evidence are represented as belief algebras, which provide a rich and expressive foundation for belief revision. Building on traditional revision rules, we introduce additional postulates for revision with belief algebra, including an upper-bound constraint on the outcomes of revision. We prove that the revision result is uniquely determined given the current belief state and new evidence. Furthermore, to make the framework more useful in practice, we develop a particular algorithm for performing the proposed revision process. We argue that this approach may offer a more predictable and principled method for belief revision, making it suitable for real-world applications.

We examine belief filtering as a mechanism for the epistemic control of artificial agents, focusing on the regulation of internal cognitive states represented as linguistic expressions. This mechanism is developed within the Semantic Manifold framework, where belief states are dynamic, structured ensembles of natural language fragments. Belief filters act as content-aware operations on these fragments across various cognitive transitions. This paper illustrates how the inherent interpretability and modularity of such a linguistically-grounded cognitive architecture directly enable belief filtering, offering a principled approach to agent regulation. The study highlights the potential for enhancing AI safety and alignment through structured interventions in an agent's internal semantic space and points to new directions for architecturally embedded cognitive governance.