Estimating Scale-Invariant Future in Continuous Time

Foundations of a temporal RL

Recent advances in neuroscience and psychology show that the brain has access to timelines of both the past and the future. Spiking across populations of neurons in many regions of the mammalian brain maintains a robust temporal memory, a neural timeline of the recent past. Behavioral results demonstrate that people can estimate an extended temporal model of the future, suggesting that the neural timeline of the past could extend through the present into the future. This paper presents a mathematical framework for learning and expressing relationships between events in continuous time. We assume that the brain has access to a temporal memory in the form of the real Laplace transform of the recent past. Hebbian associations with a diversity of synaptic time scales are formed between the past and the present that record the temporal relationships between events. Knowing the temporal relationships between the past and the present allows one to predict relationships between the present and the future, thus constructing an extended temporal prediction for the future. Both memory for the past and the predicted future are represented as the real Laplace transform, expressed as the firing rate over populations of neurons indexed by different rate constants s. The diversity of synaptic timescales allows for a temporal record over the much larger time scale of trial history. In this framework, temporal credit assignment can be assessed via a Laplace temporal difference. The Laplace temporal difference compares the future that actually follows a stimulus to the future predicted just before the stimulus was observed. This computational framework makes a number of specific neurophysiological predictions and, taken together, could provide the basis for a future iteration of RL that incorporates temporal memory as a fundamental building block.

Scanning a compressed ordered representation of the future

Several authors have suggested a deep symmetry between the psychological processes that underlie our ability to remember the past and make predictions about the future. The judgment of recency (JOR) task measures temporal order judgments for the past by presenting pairs of probe stimuli; participants choose the probe that was presented more recently. We performed a short-term relative JOR task and introduced a novel judgment of imminence (JOI) task to study temporal order judgments for the future. In the JOR task, participants were presented with a sequence of stimuli and asked to choose which of two probe stimuli was presented closer to the present. In the JOI task, participants were trained on a probabilistic sequence. After training, the sequence was interrupted with probe stimuli. Participants were asked to choose which of two probe stimuli was expected to be presented closer to the present. Replicating prior work on JOR, we found that RT results supported a backward self-terminating search model operating on a temporally organized representation of the past. We also showed that RT distributions are consistent with this model and that the temporally organized representation is compressed. Critically, results for the JOI task probing expectations of the future suggest a forward self-terminating search model operating on a temporally organized representation of the future. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Time Is of the Essence: Neural Codes, Synchronies, Oscillations, Architectures

Time is of the essence in how neural codes, synchronies, and oscillations might function in encoding, representation, transmission, integration, storage, and retrieval of information in brains. This Hypothesis and Theory article examines observed and possible relations between codes, synchronies, oscillations, and types of neural networks they require. Toward reverse-engineering informational functions in brains, prospective, alternative neural architectures incorporating principles from radio modulation and demodulation, active reverberant circuits, distributed content-addressable memory, signal-signal time-domain correlation and convolution operations, spike-correlation-based holography, and self-organizing, autoencoding anticipatory systems are outlined. Synchronies and oscillations are thought to subserve many possible functions: sensation, perception, action, cognition, motivation, affect, memory, attention, anticipation, and imagination. These include direct involvement in coding attributes of events and objects through phase-locking as well as characteristic patterns of spike latency and oscillatory response. They are thought to be involved in segmentation and binding, working memory, attention, gating and routing of signals, temporal reset mechanisms, inter-regional coordination, time discretization, time-warping transformations, and support for temporal wave-interference based operations. A high level, partial taxonomy of neural codes consists of channel, temporal pattern, and spike latency codes. The functional roles of synchronies and oscillations in candidate neural codes, including oscillatory phase-offset codes, are outlined. Various forms of multiplexing neural signals are considered: time-division, frequency-division, code-division, oscillatory-phase, synchronized channels, oscillatory hierarchies, polychronous ensembles. An expandable, annotative neural spike train framework for encoding low- and high-level attributes of events and objects is proposed. Coding schemes require appropriate neural architectures for their interpretation. Time-delay, oscillatory, wave-interference, synfire chain, polychronous, and neural timing networks are discussed. Some novel concepts for formulating an alternative, more time-centric theory of brain function are discussed. As in radio communication systems, brains can be regarded as networks of dynamic, adaptive transceivers that broadcast and selectively receive multiplexed temporally-patterned pulse signals. These signals enable complex signal interactions that select, reinforce, and bind common subpatterns and create emergent lower dimensional signals that propagate through spreading activation interference networks. If memory traces share the same kind of temporal pattern forms as do active neuronal representations, then distributed, holograph-like content-addressable memories are made possible via temporal pattern resonances.

A temporal record of the past with a spectrum of time constants in the monkey entorhinal cortex

Episodic memory is believed to be intimately related to our experience of the passage of time. Indeed, neurons in the hippocampus and other brain regions critical to episodic memory code for the passage of time at a range of timescales. The origin of this temporal signal, however, remains unclear. Here, we examined temporal responses in the entorhinal cortex of macaque monkeys as they viewed complex images. Many neurons in the entorhinal cortex were responsive to image onset, showing large deviations from baseline firing shortly after image onset but relaxing back to baseline at different rates. This range of relaxation rates allowed for the time since image onset to be decoded on the scale of seconds. Further, these neurons carried information about image content, suggesting that neurons in the entorhinal cortex carry information about not only when an event took place but also, the identity of that event. Taken together, these findings suggest that the primate entorhinal cortex uses a spectrum of time constants to construct a temporal record of the past in support of episodic memory.

Time-conjunctive representations of future events

It is widely accepted that people can predict the relative imminence of future events. However, it is unknown whether the timing of future events is represented using only a "strength-like" estimate or if future events are represented conjunctively with their position on a mental timeline. We examined how people judge temporal relationships among anticipated future events using the novel Judgment of Anticipated Co-Occurrence (JACO) task. Participants were initially trained on a stream of letters sampled from a probabilistically repeating sequence. During test trials, the stream was interrupted with pairs of probe letters and the participants' task was to choose the probe letter they expected to appear in the stream during a lagged target window 4-6 items (4.3-8.5 s) in the future. Participants performed above chance as they gained experience with the task. Because the correct item was sometimes the more imminent probe letter and other times the less imminent probe letter, these results rule out the possibility that participants relied solely on thresholding a strength-like estimate of temporal imminence. Rather, these results suggest that participants held (1) temporally organized predictions of the future letters in the stream, (2) a temporal estimate of the lagged target window, and (3) some means to compare the two and evaluate their temporal alignment. Response time increased with the lag to the more imminent probe letter, suggesting that participants accessed the future sequentially in a manner that mirrors scanning processes previously proposed to operate on memory representations in the short-term judgment of recency task.

Bayesian nonparametric models characterize instantaneous strategies in a competitive dynamic game

Previous studies of strategic social interaction in game theory have predominantly used games with clearly-defined turns and limited choices. Yet, most real-world social behaviors involve dynamic, coevolving decisions by interacting agents, which poses challenges for creating tractable models of behavior. Here, using a game in which humans competed against both real and artificial opponents, we show that it is possible to quantify the instantaneous dynamic coupling between agents. Adopting a reinforcement learning approach, we use Gaussian Processes to model the policy and value functions of participants as a function of both game state and opponent identity. We found that higher-scoring participants timed their final change in direction to moments when the opponent's counter-strategy was weaker, while lower-scoring participants less precisely timed their final moves. This approach offers a natural set of metrics for facilitating analysis at multiple timescales and suggests new classes of experimental paradigms for assessing behavior.