Reaching consensus and convergence to equilibrium are two major challenges of multi-agent systems. Although each has attracted significant attention, relatively few studies address both challenges at the same time. This paper examines the connection between the notions of consensus and equilibrium in a multi-agent system where multiple interacting sub-populations coexist. We argue that consensus can be seen as an intricate component of intra-population stability, whereas equilibrium can be seen as encoding inter-population stability. We show that smooth fictitious play, a well-known learning model in game theory, can achieve both consensus and convergence to equilibrium in diverse multi-agent settings. Moreover, we show that the consensus formation process plays a crucial role in the seminal thorny problem of equilibrium selection in multi-agent learning.

Belief systems are rarely globally consistent, yet effective reasoning often persists locally. We propose a novel graph-theoretic framework that cleanly separates credibility--external, a priori trust in sources--from confidence--an internal, emergent valuation induced by network structure. Beliefs are nodes in a directed, signed, weighted graph whose edges encode support and contradiction. Confidence is obtained by a contractive propagation process that mixes a stated prior with structure-aware influence and guarantees a unique, stable solution. Within this dynamics, we define reasoning zones: high-confidence, structurally balanced subgraphs on which classical inference is safe despite global contradictions. We provide a near-linear procedure that seeds zones by confidence, tests balance using a parity-based coloring, and applies a greedy, locality-preserving repair with Jaccard de-duplication to build a compact atlas. To model belief change, we introduce shock updates that locally downscale support and elevate targeted contradictions while preserving contractivity via a simple backtracking rule. Re-propagation yields localized reconfiguration-zones may shrink, split, or collapse--without destabilizing the entire graph. We outline an empirical protocol on synthetic signed graphs with planted zones, reporting zone recovery, stability under shocks, and runtime. The result is a principled foundation for contradiction-tolerant reasoning that activates classical logic precisely where structure supports it.

Reaching consensus and convergence to equilibrium are two major challenges of multi-agent systems. Although each has attracted significant attention, relatively few studies address both challenges at the same time. This paper examines the connection between the notions of consensus and equilibrium in a multi-agent system where multiple interacting sub-populations coexist. We argue that consensus can be seen as an intricate component of intra-population stability, whereas equilibrium can be seen as encoding inter-population stability. We show that smooth fictitious play, a well-known learning model in game theory, can achieve both consensus and convergence to equilibrium in diverse multi-agent settings. Moreover, we show that the consensus formation process plays a crucial role in the seminal thorny problem of equilibrium selection in multi-agent learning.

We propose MToMnet - a Theory of Mind (ToM) neural network for predicting beliefs and their dynamics during human social interactions from multimodal input. ToM is key for effective nonverbal human communication and collaboration, yet, existing methods for belief modelling have not included explicit ToM modelling or have typically been limited to one or two modalities. MToMnet encodes contextual cues (scene videos and object locations) and integrates them with person-specific cues (human gaze and body language) in a separate MindNet for each person. Inspired by prior research on social cognition and computational ToM, we propose three different MToMnet variants: two involving fusion of latent representations and one involving re-ranking of classification scores. We evaluate our approach on two challenging real-world datasets, one focusing on belief prediction, while the other examining belief dynamics prediction. Our results demonstrate that MToMnet surpasses existing methods by a large margin while at the same time requiring a significantly smaller number of parameters. Taken together, our method opens up a highly promising direction for future work on artificial intelligent systems that can robustly predict human beliefs from their non-verbal behaviour and, as such, more effectively collaborate with humans.

Humans talk in free-form while negotiating the expressed meanings or common ground. Despite the impressive conversational abilities of the large generative language models, they do not consider the individual differences in contextual understanding in a shared situated environment. In this work, we propose MindDial, a novel conversational framework that can generate situated free-form responses to negotiate common ground. We design an explicit mind module that can track three-level beliefs -- the speaker's belief, the speaker's prediction of the listener's belief, and the common belief based on the gap between the first two. Then the speaking act classification head will decide to continue to talk, end this turn, or take task-related action. We augment a common ground alignment dataset MutualFriend with belief dynamics annotation, of which the goal is to find a single mutual friend based on the free chat between two agents. Experiments show that our model with mental state modeling can resemble human responses when aligning common ground meanwhile mimic the natural human conversation flow. The ablation study further validates the third-level common belief can aggregate information of the first and second-order beliefs and align common ground more efficiently.

We study the dynamics of belief formation on multiple interconnected topics in networks of agents with a shared belief system. We establish sufficient conditions and necessary conditions under which sustained oscillations of beliefs arise on the network in a Hopf bifurcation and characterize the role of the communication graph and the belief system graph in shaping the relative phase and amplitude patterns of the oscillations. Additionally, we distinguish broad classes of graphs that exhibit such oscillations from those that do not.

The effect of population heterogeneity in multi-agent learning is practically relevant but remains far from being well-understood. Motivated by this, we introduce a model of multi-population learning that allows for heterogeneous beliefs within each population and where agents respond to their beliefs via smooth fictitious play (SFP).We show that the system state -- a probability distribution over beliefs -- evolves according to a system of partial differential equations akin to the continuity equations that commonly desccribe transport phenomena in physical systems. We establish the convergence of SFP to Quantal Response Equilibria in different classes of games capturing both network competition as well as network coordination. We also prove that the beliefs will eventually homogenize in all network games. Although the initial belief heterogeneity disappears in the limit, we show that it plays a crucial role for equilibrium selection in the case of coordination games as it helps select highly desirable equilibria. Contrary, in the case of network competition, the resulting limit behavior is independent of the initialization of beliefs, even when the underlying game has many distinct Nash equilibria.

Humans possess a unique social cognition capability; nonverbal communication can convey rich social information among agents. In contrast, such crucial social characteristics are mostly missing in the existing scene understanding literature. In this paper, we incorporate different nonverbal communication cues (e.g., gaze, human poses, and gestures) to represent, model, learn, and infer agents' mental states from pure visual inputs. Crucially, such a mental representation takes the agent's belief into account so that it represents what the true world state is and infers the beliefs in each agent's mental state, which may differ from the true world states. By aggregating different beliefs and true world states, our model essentially forms "five minds" during the interactions between two agents. This "five minds" model differs from prior works that infer beliefs in an infinite recursion; instead, agents' beliefs are converged into a "common mind". Based on this representation, we further devise a hierarchical energy-based model that jointly tracks and predicts all five minds. From this new perspective, a social event is interpreted by a series of nonverbal communication and belief dynamics, which transcends the classic keyframe video summary. In the experiments, we demonstrate that using such a social account provides a better video summary on videos with rich social interactions compared with state-of-the-art keyframe video summary methods.

Most mobile robots follow a modular sense-planact system architecture that can lead to poor performance or even catastrophic failure for visual inertial navigation systems due to trajectories devoid of feature matches. Planning in belief space provides a unified approach to tightly couple the perception, planning and control modules, leading to trajectories that are robust to noisy measurements and disturbances. However, existing methods handle uncertainties as costs that require manual tuning for varying environments and hardware. We therefore propose a novel trajectory optimization formulation that incorporates inequality constraints on uncertainty and a novel Augmented Lagrangian based stochastic differential dynamic programming method in belief space. Furthermore, we develop a probabilistic visibility model that accounts for discontinuities due to feature visibility limits. Our simulation tests demonstrate that our method can handle inequality constraints in different environments, for holonomic and nonholonomic motion models with no manual tuning of uncertainty costs involved. We also show the improved optimization performance in belief space due to our visibility model.

Animal behavior is not driven simply by its current observations, but is strongly influenced by internal states. Estimating the structure of these internal states is crucial for understanding the neural basis of behavior. In principle, internal states can be estimated by inverting behavior models, as in inverse model-based Reinforcement Learning. However, this requires careful parameterization and risks model-mismatch to the animal. Here we take a data-driven approach to infer latent states directly from observations of behavior, using a partially observable switching semi-Markov process. This process has two elements critical for capturing animal behavior: it captures non-exponential distribution of times between observations, and transitions between latent states depend on the animal's actions, features that require more complex non-markovian models to represent. To demonstrate the utility of our approach, we apply it to the observations of a simulated optimal agent performing a foraging task, and find that latent dynamics extracted by the model has correspondences with the belief dynamics of the agent. Finally, we apply our model to identify latent states in the behaviors of monkey performing a foraging task, and find clusters of latent states that identify periods of time consistent with expectant waiting. This data-driven behavioral model will be valuable for inferring latent cognitive states, and thereby for measuring neural representations of those states.