To predict and maximize future rewards in this ever-changing world, animals must be able to discover the temporal structure of stimuli and then anticipate or act correctly at the right time. However, we still lack a systematic understanding of the neural mechanisms of how animals perceive, maintain, and use time intervals ranging from hundreds of milliseconds to multi-seconds in working memory, the combination of time information with spatial information processing and decision making, and the reasons for the strong neuronal temporal signal even when animals performing tasks in which time information is not required. Here, we addressed these problems by training neural network models. We reveal that neural networks perceive time intervals through the evolution of population state along stereotypical trajectory, maintain time intervals by line attractor along which most neurons vary their activities monotonically with the duration of the maintained interval, and produce or compare time intervals by scaling the evolution velocity of population state. Time and non-time information is coded in subspaces orthogonal with each other, which facilitates generalizable decoding of time and non-time information. This is based on the network structure of multiple feedforward sequences that mutually excite or inhibit depending on whether their preferences of non-timing information are similar or not. Strong temporal signal in non-timing tasks arises from high temporal complexity of task, broad input tuning, multi-tasking and timing anticipation. Our work discloses fundamental computional principles of temporal processing, and is supported by and gives predictions to a number of experimental phenomena. Keywordsinterval timing | population coding | neural network model SignificanceTo understand the neural mechanisms for the brain to flexibly perceive, maintain and use time intervals ranging from hundreds of milliseconds to multi-seconds in working memory, and the formation of strong temporal signals in neuronal activity even when animals performing non-timing tasks, we trained neural network models. We found that neural networks perceive time intervals through states along stereotypical trajectory, maintain time intervals by attractor dynamics, and use the maintained time interval by scaling state evolution velocity. Time and non-time information is coded orthogonally, which facilitates decoding generalizability, based on the network structure of multiple interacting feedforward sequences. Strong temporal signal in nontiming tasks arises from high temporal complexity of task, broad input tuning, multi-tasking and timing anticipation.
Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional 'real' systems persist to be very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of partition function expansion and the concept of regiongraphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region-graph, such as belief-propagation and surveypropagation, are also derived rigorously.
In an iterated non-cooperative game, if all the players act to maximize their individual accumulated payoff, the system as a whole usually converges to a Nash equilibrium that poorly benefits any player. Here we show that such an undesirable destiny is avoidable in an iterated Rock-Paper-Scissors (RPS) game involving two rational players, X and Y. Player X has the option of proactively adopting a cooperation-trap strategy, which enforces complete cooperation from the rational player Y and leads to a highly beneficial and maximally fair situation to both players. That maximal degree of cooperation is achievable in such a competitive system with cyclic dominance of actions may stimulate further theoretical and empirical studies on how to resolve conflicts and enhance cooperation in human societies.
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