The measurement of time is central to intelligent behavior.

Neural Information Processing Systems http://nips.cc/

Taylor's formula holds significant importance in function representation, such as solving differential difference equations, ordinary differential equations, partial differential equations, and further promotes applications in visual perception, complex control, fluid mechanics, weather forecasting and thermodynamics. However, the Taylor's formula suffers from the curse of dimensionality and error propagation during derivative computation in discrete situations. In this paper, we propose a new discrete differential operator to estimate derivatives and to represent continuous smooth function locally using the Vandermonde coefficient matrix derived from truncated Taylor series. Our method simultaneously computes all derivatives of orders less than the number of sample points, inherently mitigating error propagation. Utilizing equidistant uniform sampling, it achieves high-order accuracy while alleviating the curse of dimensionality. We mathematically establish rigorous error bounds for both derivative estimation and function representation, demonstrating tighter bounds for lower-order derivatives. We extend our method to the two-dimensional case, enabling its use for multivariate derivative calculations. Experiments demonstrate the effectiveness and superiority of the proposed method compared to the finite forward difference method for derivative estimation and cubic spline and linear interpolation for function representation. Consequently, our technique offers broad applicability across domains such as vision representation, feature extraction, fluid mechanics, and cross-media imaging.

After reading the Author Feedback: The authors addressed and responded to all my concerns in an extensive manner. This is an interesting well-thought contribution, and I am happy to increase my score. Summary: In this paper, the authors investigate how deep reinforcement learning agents with distinct architectures (mainly, feed-forward vs. recurrent) learn to solve an interval timing task analogous to a time reproduction task widely used in the human timing literature, implemented in a virtual psychophysics lab (PsychLab/DeepMind lab). Briefly, in each trial the agent has to measure the time interval between a "ready" and "set" cue, and wait for the same duration before responding by moving their virtual gaze inside a "go" target; with the goal that the duration between the "set" cue and the "go" response should match the interval between "ready" and "set". Time intervals during training are drawn from a discrete uniform distribution.

Large language models (LLMs) demonstrate promising translation performance among various natural languages. However, many LLMs especially the open-sourced ones, such as BLOOM and LLaMA, are English-dominant and support only dozens of natural languages, making the potential of LLMs on language translation less explored. In this work, we present BigTranslate which adapts LLaMA that covers only 20 languages and enhances it with multilingual translation capability on more than 100 languages. BigTranslate is built upon LLaMA-13B and it is optimized in three steps. First, we continue training LLaMA with massive Chinese monolingual data. Second, we continue training the model with a large-scale parallel dataset that covers 102 natural languages. Third, we instruct-tune the foundation model with multilingual translation instructions, leading to our BigTranslate model. The preliminary experiments on multilingual translation show that BigTranslate performs comparably with ChatGPT and Google Translate in many languages and even outperforms ChatGPT in 8 language pairs. We release the BigTranslate model and hope it can advance the research progress.

The measurement of time is central to intelligent behavior. We know that both animals and artificial agents can successfully use temporal dependencies to select actions. In artificial agents, little work has directly addressed (1) which architectural components are necessary for successful development of this ability, (2) how this timing ability comes to be represented in the units and actions of the agent, and (3) whether the resulting behavior of the system converges on solutions similar to those of biology. Here we studied interval timing abilities in deep reinforcement learning agents trained end-to-end on an interval reproduction paradigm inspired by experimental literature on mechanisms of timing. We characterize the strategies developed by recurrent and feedforward agents, which both succeed at temporal reproduction using distinct mechanisms, some of which bear specific and intriguing similarities to biological systems. These findings advance our understanding of how agents come to represent time, and they highlight the value of experimentally inspired approaches to characterizing agent abilities.