We investigate multi-agent imitation learning (IL) within the framework of mean field games (MFGs), considering the presence of time-varying correlated signals. Existing MFG IL algorithms assume demonstrations are sampled from Mean Field Nash Equilibria (MFNE), limiting their adaptability to real-world scenarios. For example, in the traffic network equilibrium influenced by public routing recommendations, recommendations introduce time-varying correlated signals into the game, not captured by MFNE and other existing correlated equilibrium concepts. To address this gap, we propose Adaptive Mean Field Correlated Equilibrium (AMFCE), a general equilibrium incorporating time-varying correlated signals. We establish the existence of AMFCE under mild conditions and prove that MFNE is a subclass of AMFCE. We further propose Correlated Mean Field Imitation Learning (CMFIL), a novel IL framework designed to recover the AMFCE, accompanied by a theoretical guarantee on the quality of the recovered policy. Experimental results, including a real-world traffic flow prediction problem, demonstrate the superiority of CMFIL over state-of-the-art IL baselines, highlighting the potential of CMFIL in understanding large population behavior under correlated signals.

Parallels between the signal processing tasks and biological neurons lead to an understanding of the principles of self-organized optimization of input signal recognition. In the present paper, we discuss such similarities among biological and technical systems. We propose the addition to the well-known STDP synaptic plasticity rule to directs the weight modification towards the state associated with the maximal difference between the background noise and correlated signals. The principle of physically constrained weight growth is used as a basis for such control of the modification of the weights. It is proposed, that biological synaptic straight modification is restricted by the existence and production of bio-chemical 'substances' needed for plasticity development. In this paper, the information about the noise-to-signal ratio is used to control such a substances' production and storage and to drive the neuron's synaptic pressures towards the state with the best signal-to-noise ratio. Several experiments with different input signal regimes are considered to understand the functioning of the proposed approach.

Biological neurons have adaptive nature and perform complex computations involving the filtering of redundant information. Such processing is often associated with Bayesian inference. Yet most common models of neural cells, including biologically plausible, such as Hodgkin-Huxley or Izhikevich do not possess predictive dynamics on the level of a single cell. The modern rules of synaptic plasticity or interconnections weights adaptation also do not provide grounding for the ability of neurons to adapt to the ever-changing input signal intensity. While natural neuron synaptic growth is precisely controlled and restricted by protein supply and recycling, weight correction rules such as widely used STDP are efficiently unlimited in change rate and scale. In the present article, we will introduce new mechanics of interconnection between neuron firing rate homeostasis and weight change by means of STDP growth bounded by abstract protein reserve, controlled by the intracellular optimization algorithm. We will show, how these cellular dynamics help neurons to filter out the intense signals to help neurons keep a stable firing rate. We will also examine that such filtering does not affect the ability of neurons to recognize the correlated inputs in unsupervised mode. Such an approach might be used in the machine learning domain to improve the robustness of AI systems. Modern neural networks and deep learning systems still lack the generalization and self-learning abilities of natural brains. Also, deep neural nets (DNN) need a lot of labeled data. Being tuned for one particular task and dataset DNNs may not perform so well in real practical application. These are major obstructions in the widespread implementation of deep learning systems for practical use [1]. Yet, training of SNN still needs to be improved to be widely used.

In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding of a numerical algorithm into a neural network form, resulting in a substantial reduction of the computational complexity. In this paper, we consider the recovery of a target signal with the aid of a correlated signal, the so-called side information (SI), and propose a deep unfolding model that incorporates SI. The proposed model is used to learn coupled representations of correlated signals from different modalities, enabling the recovery of multimodal data at a low computational cost. As such, our work introduces the first deep unfolding method with SI, which actually comes from a different modality. We apply our model to reconstruct near-infrared images from undersampled measurements given RGB images as SI. Experimental results demonstrate the superior performance of the proposed framework against single-modal deep learning methods that do not use SI, multimodal deep learning designs, and optimization algorithms.