Hamidou Tembine

Hamidou Tembine

Classical game-theoretic solution concepts assume that agents' internal representations remain causally linked to external states. In generative machine intelligence, this assumption fails: semantic representations can decouple from physical reality, stabilizing into self-reinforcing, operationally robust configurations. This paper introduces the risk-sensitive mean-field-type \emph{Causal Mirage Equilibrium} (CME), a solution refined concept formalizing endogenous epistemic decoupling within a risk-sensitive mean-field-type game. Unlike Nash, Bayesian, self-confirming, or robust equilibria, CME stabilizes detached semantic representation manifolds rather than optimization strategies or observational beliefs. To quantify this phenomenon, we define a dimensionless parameter, the \emph{mirage intensity} which measures semantic detachment as the ratio of an agent's endogenous reinforcement-confidence product to its causally grounded reality alignment. Under compactness, convexity, and continuity assumptions on the game primitives, we prove the existence of an CME using the Kakutani-Glicksberg-Fan fixed-point theorem on the space of joint probability measures. We establish a non-linear mirage bifurcation theorem: when endogenous reinforcement dominates causal grounding, the unique grounded fixed point becomes unstable, giving rise to a stable invariant manifold of ungrounded states. Our results demonstrate that synthetic consensus and causally detached semantic configurations are not transient optimization anomalies, but structurally stable, risk-aware attractors generated by recursive autoregressive dynamics.

Hamidou Tembine, Quanyan Zhu, Tamer Basar

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function described by a Hamilton-Jacobi-Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics.

Quanyan Zhu, Hamidou Tembine, Tamer Basar

Learning algorithms are essential for the applications of game theory in a networking environment. In dynamic and decentralized settings where the traffic, topology and channel states may vary over time and the communication between agents is impractical, it is important to formulate and study games of incomplete information and fully distributed learning algorithms which for each agent requires a minimal amount of information regarding the remaining agents. In this paper, we address this major challenge and introduce heterogeneous learning schemes in which each agent adopts a distinct learning pattern in the context of games with incomplete information. We use stochastic approximation techniques to show that the heterogeneous learning schemes can be studied in terms of their deterministic ordinary differential equation (ODE) counterparts. Depending on the learning rates of the players, these ODEs could be different from the standard replicator dynamics, (myopic) best response (BR) dynamics, logit dynamics, and fictitious play dynamics. We apply the results to a class of security games in which the attacker and the defender adopt different learning schemes due to differences in their rationality levels and the information they acquire.

Quanyan Zhu, Hamidou Tembine, Tamer Basar

In this paper, we formulate an evolutionary multiple access channel game with continuous-variable actions and coupled rate constraints. We characterize Nash equilibria of the game and show that the pure Nash equilibria are Pareto optimal and also resilient to deviations by coalitions of any size, i.e., they are strong equilibria. We use the concepts of price of anarchy and strong price of anarchy to study the performance of the system. The paper also addresses how to select one specifc equilibrium solution using the concepts of normalized equilibrium and evolutionary stable strategies. We examine the long-run behavior of these strategies under several classes of evolutionary game dynamics such as Brown-von Neumann-Nash dynamics, and replicator dynamics.

Kody J. H. Law, Hamidou Tembine, Raul Tempone

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Legland etal. (2011) is extended to non-Gaussian state space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence $κ$ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF when the dimension $d<2κ$. The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which exists for both DMFEnKF and standard EnKF. Numerical results support and extend the theory.

Quanyan Zhu, Hamidou Tembine, Tamer Basar

In this paper, we formulate an evolutionarymultiple access control game with continuousvariable actions and coupled constraints. We characterize equilibria of the game and show that the pure equilibria are Pareto optimal and also resilient to deviations by coalitions of any size, i.e., they are strong equilibria. We use the concepts of price of anarchy and strong price of anarchy to study the performance of the system. The paper also addresses how to select one specific equilibrium solution using the concepts of normalized equilibrium and evolutionarily stable strategies. We examine the long-run behavior of these strategies under several classes of evolutionary game dynamics, such as Brown-von Neumann-Nash dynamics, Smith dynamics and replicator dynamics. In addition, we examine correlated equilibrium for the single-receiver model. Correlated strategies are based on signaling structures before making decisions on rates. We then focus on evolutionary games for hybrid additive white Gaussian noise multiple access channel with multiple users and multiple receivers, where each user chooses a rate and splits it over the receivers. Users have coupled constraints determined by the capacity regions. Building upon the static game, we formulate a system of hybrid evolutionary game dynamics using G-function dynamics and Smith dynamics on rate control and channel selection, respectively. We show that the evolving game has an equilibrium and illustrate these dynamics with numerical examples.

Elham Rostami, Taous-Meriem Laleg-Kirati, Hamidou Tembine

We study training-free flow matching between two Gaussian mixture models (GMMs) using explicit velocity fields that transport one mixture into the other over time. Our baseline approach constructs component-wise Gaussian paths with affine velocity fields satisfying the continuity equation, which yields to a closed-form surrogate for the pairwise kinetic transport cost. In contrast to the exact Gaussian Wasserstein cost, which relies on matrix square-root computations, the surrogate admits a simple analytic expression derived from the kinetic energy of the induced flow. We then analyze how closely this surrogate approximates the exact cost. We prove second-order agreement in a local commuting regime and derive an explicit cubic error bound in the local commuting regime. To handle nonlocal regimes, we introduce a path-splitting strategy that localizes the covariance evolution and enables piecewise application of the bound. We finally compare the surrogate with an exact construction based on the Gaussian Wasserstein geodesic and summarize the results in a practical regime map showing when the surrogate is accurate and the exact method is preferable.

Daryl Noupa Yongueng, Hamidou Tembine

Normalization is a key point in transformer training . In Dynamic Tanh (DyT), the author demonstrated that Tanh can be used as an alternative layer normalization (LN) and confirmed the effectiveness of the idea. But Tanh itself faces orthogonality, linearity and distortion problems. Due to that, his proposition cannot be reliable. So we propose a Holonorm (hn) which has residual connections and nonlinearity. Holonorm is suitable for replacing Tanh in the context of normalization. Although the HoloNorm expression could be similar to the softsign function in dimension one, softsign is a componentwise function which is not good for tensors and vectors of great dimension. Holonorm preserves the orthogonality, the direction, the invertibility of the signal. Holonorm is also a suitable metric, maps all vectors into the open unit ball. This prevents exploding activations and improves stability in deep Transformer models. In this work, we have meticulously examined the normalization in transformers and say that Holonorm, a generalized form of softsign function suited as a normalization function first.Second, defined between 0 and 1 hn serves as a percentage, and $1 - \text{Holonorm}$ is its complement, making it better understandable in evaluating a model.

Hamidou Tembine

This article develops an intergenerational mean-field-type game (MFTG) to model Mali's and neighbouring countries multi-actor conflict ecosystem, which includes formal state forces, traditional hunters, nonstate militias, jihadists, criminal networks, civil societies, and international proxies. Each decision-maker (agent, a group of agents or representative agent) is defined by a type, state, information structure, and action, with payoffs dependent not only on individual decisions but also on the evolving distribution of all agents' profiles. The model reveals that cycles of violence can persist across multiple generations due to the embedded presence of retaliatory types such as revenger child-soldiers whose trauma-conditioned best-responses favor conflict, and whose behavior reinforces intergenerational transmission of violence. The model also captures the strategic exploitation of institutional fragility by war entrepreneurs who profit from sustained instability through arms sales, militia contracting, and unregistered market mediation. These actors inject minimal resources to trigger profitable escalations, turning latent tensions into self-reinforcing violence economies. We show that in the absence of structural counterincentives, peaceful strategies are non-absorbing, and violence remains dynamically rewarding for war entrepreneurs. However, by embedding incentive-compatible, information-adaptive transfers directly into instantaneous payoffs, rewarding verifiable peacebuilding and penalizing aggression, it is possible to shift the mean-field-type equilibrium distribution intergenerationally toward more peaceful types and drive systemic de-escalation. We also discuss about the funding and the real implementation of such mechanisms in the field.

Allahsera Auguste Tapo, Ali Traore, Sidy Danioko et al.

In the last 5 years, the availability of large audio datasets in African countries has opened unlimited opportunities to build machine intelligence (MI) technologies that are closer to the people and speak, learn, understand, and do businesses in local languages, including for those who cannot read and write. Unfortunately, these audio datasets are not fully exploited by current MI tools, leaving several Africans out of MI business opportunities. Additionally, many state-of-the-art MI models are not culture-aware, and the ethics of their adoption indexes are questionable. The lack thereof is a major drawback in many applications in Africa. This paper summarizes recent developments in machine intelligence in Africa from a multi-layer multiscale and culture-aware ethics perspective, showcasing MI use cases in 54 African countries through 400 articles on MI research, industry, government actions, as well as uses in art, music, the informal economy, and small businesses in Africa. The survey also opens discussions on the reliability of MI rankings and indexes in the African continent as well as algorithmic definitions of unclear terms used in MI.

Hamidou Tembine

As multimodal machine intelligence systems started achieving average animal-level and average human-level fluency in many measurable tasks in processing images, language, and sound, they began to exhibit a new class of cognitive aberrations: machine mirages. These include delusion, illusion, confabulation, hallucination, misattribution error, semantic drift, semantic compression, exaggeration, causal inference failure, uncanny valley of perception, bluffing-patter-bullshitting, cognitive stereotypy, pragmatic misunderstanding, hypersignification, semantic reheating-warming, simulated authority effect, fallacious abductive leap, contextual drift, referential hallucination, semiotic Frankenstein effect, calibration failure, spurious correlation, bias amplification, concept drift sensitivity, misclassification under uncertainty, adversarial vulnerability, overfitting, prosodic misclassification, accent bias, turn boundary failure, semantic boundary confusion, noise overfitting, latency-induced decision drift, ambiguity collapse and other forms of error that mimic but do not replicate human or animal fallibility. This article presents some of the errors and argues that these failures must be explicitly defined and systematically assessed. Understanding machine mirages is essential not only for improving machine intelligence reliability but also for constructing a multiscale ethical, co-evolving intelligence ecosystem that respects the diverse forms of life, cognition, and expression it will inevitably touch.

Jian Gao, Deep Chakraborty, Hamidou Tembine et al.

We propose a nonparallel data-driven emotional speech conversion method. It enables the transfer of emotion-related characteristics of a speech signal while preserving the speaker's identity and linguistic content. Most existing approaches require parallel data and time alignment, which is not available in most real applications. We achieve nonparallel training based on an unsupervised style transfer technique, which learns a translation model between two distributions instead of a deterministic one-to-one mapping between paired examples. The conversion model consists of an encoder and a decoder for each emotion domain. We assume that the speech signal can be decomposed into an emotion-invariant content code and an emotion-related style code in latent space. Emotion conversion is performed by extracting and recombining the content code of the source speech and the style code of the target emotion. We tested our method on a nonparallel corpora with four emotions. Both subjective and objective evaluations show the effectiveness of our approach.

Brian Powers, Michalis Smyrnakis, Hamidou Tembine

Although the definition of what empathetic preferences exactly are is still evolving, there is a general consensus in the psychology, science and engineering communities that the evolution toward players' behaviors in interactive decision-making problems will be accompanied by the exploitation of their empathy, sympathy, compassion, antipathy, spitefulness, selfishness, altruism, and self-abnegating states in the payoffs. In this article, we study one-shot bimatrix games from a psychological game theory viewpoint. A new empathetic payoff model is calculated to fit empirical observations and both pure and mixed equilibria are investigated. For a realized empathy structure, the bimatrix game is categorized among four generic class of games. Number of interesting results are derived. A notable level of involvement can be observed in the empathetic one-shot game compared the non-empathetic one and this holds even for games with dominated strategies. Partial altruism can help in breaking symmetry, in reducing payoff-inequality and in selecting social welfare and more efficient outcomes. By contrast, partial spite and self-abnegating may worsen payoff equity. Empathetic evolutionary game dynamics are introduced to capture the resulting empathetic evolutionarily stable strategies under wide range of revision protocols including Brown-von Neumann-Nash, Smith, imitation, replicator, and hybrid dynamics. Finally, mutual support and Berge solution are investigated and their connection with empathetic preferences are established. We show that pure altruism is logically inconsistent, only by balancing it with some partial selfishness does it create a consistent psychology.

Hamidou Tembine, Raul Tempone, Pedro Vilanova

In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the Banach-Picard iteration converges with geometrical convergence rate. When the best reply map is not a contraction, Ishikawa-based learning is proposed. The algorithm is shown to behave well for Lipschitz continuous and pseudo-contractive maps. However, the convergence rate is still unsatisfactory. Several acceleration techniques are presented. We explain how cognitive users can improve the convergence rate based only on few number of measurements. The methodology provides nice properties in mean field games where the payoff function depends only on own-action and the mean of the mean-field (first moment mean-field games). A learning framework that exploits the structure of such games, called, mean-field learning, is proposed. The proposed mean-field learning framework is suitable not only for games but also for non-convex global optimization problems. Then, we introduce mean-field learning without feedback and examine the convergence to equilibria in beauty contest games, which have interesting applications in financial markets. Finally, we provide a fully distributed mean-field learning and its speedup versions for satisfactory solution in wireless networks. We illustrate the convergence rate improvement with numerical examples.