How to design optimal brain stimulation to modulate phase-amplitude coupling?

Objective. Phase-amplitude coupling (PAC), the coupling of the amplitude of a faster brain rhythm to the phase of a slower brain rhythm, plays a significant role in brain activity and has been implicated in various neurological disorders. For example, in Parkinson’s disease, PAC between the beta (13–30 Hz) and gamma (30–100 Hz) rhythms in the motor cortex is exaggerated, while in Alzheimer’s disease, PAC between the theta (4–8 Hz) and gamma rhythms is diminished. Modulating PAC (i.e. reducing or enhancing PAC) using brain stimulation could therefore open new therapeutic avenues. However, while it has been previously reported that phase-locked stimulation can increase PAC, it is unclear what the optimal stimulation strategy to modulate PAC might be. Here, we provide a theoretical framework to narrow down the experimental optimisation of stimulation aimed at modulating PAC, which would otherwise rely on trial and error. Approach. We make analytical predictions using a Stuart–Landau model, and confirm these predictions in a more realistic model of coupled neural populations. Main results. Our framework specifies the critical Fourier coefficients of the stimulation waveform which should be tuned to optimally modulate PAC. Depending on the characteristics of the amplitude response curve of the fast population, these components may include the slow frequency, the fast frequency, combinations of these, as well as their harmonics. We also show that the optimal balance of energy between these Fourier components depends on the relative strength of the endogenous slow and fast rhythms, and that the alignment of fast components with the fast rhythm should change throughout the slow cycle. Furthermore, we identify the conditions requiring to phase-lock stimulation to the fast and/or slow rhythms. Significance. Together, our theoretical framework lays the foundation for guiding the development of innovative and more effective brain stimulation aimed at modulating PAC for therapeutic benefit

Uncertainty-guided learning with scaled prediction errors in the basal ganglia

To accurately predict rewards associated with states or actions, the variability of observations has to be taken into account. In particular, when the observations are noisy, the individual rewards should have less influence on tracking of average reward, and the estimate of the mean reward should be updated to a smaller extent after each observation. However, it is not known how the magnitude of the observation noise might be tracked and used to control prediction updates in the brain reward system. Here, we introduce a new model that uses simple, tractable learning rules that track the mean and standard deviation of reward, and leverages prediction errors scaled by uncertainty as the central feedback signal. We show that the new model has an advantage over conventional reinforcement learning models in a value tracking task, and approaches a theoretic limit of performance provided by the Kalman filter. Further, we propose a possible biological implementation of the model in the basal ganglia circuit. In the proposed network, dopaminergic neurons encode reward prediction errors scaled by standard deviation of rewards. We show that such scaling may arise if the striatal neurons learn the standard deviation of rewards and modulate the activity of dopaminergic neurons. The model is consistent with experimental findings concerning dopamine prediction error scaling relative to reward magnitude, and with many features of striatal plasticity. Our results span across the levels of implementation, algorithm, and computation, and might have important implications for understanding the dopaminergic prediction error signal and its relation to adaptive and effective learning

Sequential Memory with Temporal Predictive Coding

Forming accurate memory of sequential stimuli is a fundamental function of biological agents. However, the computational mechanism underlying sequential memory in the brain remains unclear. Inspired by neuroscience theories and recent successes in applying predictive coding (PC) to \emph{static} memory tasks, in this work we propose a novel PC-based model for \emph{sequential} memory, called \emph{temporal predictive coding} (tPC). We show that our tPC models can memorize and retrieve sequential inputs accurately with a biologically plausible neural implementation. Importantly, our analytical study reveals that tPC can be viewed as a classical Asymmetric Hopfield Network (AHN) with an implicit statistical whitening process, which leads to more stable performance in sequential memory tasks of structured inputs. Moreover, we find that tPC exhibits properties consistent with behavioral observations and theories in neuroscience, thereby strengthening its biological relevance. Our work establishes a possible computational mechanism underlying sequential memory in the brain that can also be theoretically interpreted using existing memory model frameworks.Comment: 37th Conference on Neural Information Processing Systems (NeurIPS 2023

Expressions for Bayesian confidence of drift diffusion observers in fluctuating stimuli tasks

We introduce a new approach to modelling decision confidence, with the aim of enabling computationally cheap predictions while taking into account, and thereby exploiting, trial-by-trial variability in stochastically fluctuating stimuli. Using the framework of the drift diffusion model of decision making, along with time-dependent thresholds and the idea of a Bayesian confidence readout, we derive expressions for the probability distribution over confidence reports. In line with current models of confidence, the derivations allow for the accumulation of “pipeline” evidence that has been received but not processed by the time of response, the effect of drift rate variability, and metacognitive noise. The expressions are valid for stimuli that change over the course of a trial with normally-distributed fluctuations in the evidence they provide. A number of approximations are made to arrive at the final expressions, and we test all approximations via simulation. The derived expressions contain only a small number of standard functions, and require evaluating only once per trial, making trial-by-trial modelling of confidence data in stochastically fluctuating stimuli tasks more feasible. We conclude by using the expressions to gain insight into the confidence of optimal observers, and empirically observed patterns

Dopamine encoding of novelty facilitates efficient uncertainty-driven exploration

When facing an unfamiliar environment, animals need to explore to gain new knowledge about which actions provide reward, but also put the newly acquired knowledge to use as quickly as possible. Optimal reinforcement learning strategies should therefore assess the uncertainties of these action-reward associations and utilise them to inform decision making. We propose a novel model whereby direct and indirect striatal pathways act together to estimate both the mean and variance of reward distributions, and mesolimbic dopaminergic neurons provide transient novelty signals, facilitating effective uncertainty-driven exploration. We utilised electrophysiological recording data to verify our model of the basal ganglia, and we fitted exploration strategies derived from the neural model to data from behavioural experiments. We also compared the performance of directed exploration strategies inspired by our basal ganglia model with other exploration algorithms including classic variants of upper confidence bound (UCB) strategy in simulation. The exploration strategies inspired by the basal ganglia model can achieve overall superior performance in simulation, and we found qualitatively similar results in fitting model to behavioural data compared with the fitting of more idealised normative models with less implementation level detail. Overall, our results suggest that transient dopamine levels in the basal ganglia that encode novelty could contribute to an uncertainty representation which efficiently drives exploration in reinforcement learning

Hunger improves reinforcement-driven but not planned action

Human decisions can be reflexive or planned, being governed respectively by model-free and model-based learning systems. These two systems might differ in their responsiveness to our needs. Hunger drives us to specifically seek food rewards, but here we ask whether it might have more general effects on these two decision systems. On one hand, the model-based system is often considered flexible and context-sensitive, and might therefore be modulated by metabolic needs. On the other hand, the model-free system's primitive reinforcement mechanisms may have closer ties to biological drives. Here, we tested participants on a well-established two-stage sequential decision-making task that dissociates the contribution of model-based and model-free control. Hunger enhanced overall performance by increasing model-free control, without affecting model-based control. These results demonstrate a generalized effect of hunger on decision-making that enhances reliance on primitive reinforcement learning, which in some situations translates into adaptive benefits

Bayesian confidence in optimal decisions

The optimal way to make decisions in many circumstances is to track the difference in evidence collected in favour of the options. The drift diffusion model (DDM) implements this approach, and provides an excellent account of decisions and response times. However, existing DDM-based models of confidence exhibit certain deficits, and many theories of confidence have used alternative, non-optimal models of decisions. Motivated by the historical success of the DDM, we ask whether simple extensions to this framework might allow it to better account for confidence. Motivated by the idea that the brain will not duplicate representations of evidence, in all model variants decisions and confidence are based on the same evidence accumulation process. We compare the models to benchmark results, and successfully apply 4 qualitative tests concerning the relationships between confidence, evidence, and time, in a new preregistered study. Using computationally cheap expressions to model confidence on a trial-by-trial basis, we find that a subset of model variants also provide a very good to excellent account of precise quantitative effects observed in confidence data. Specifically, our results favour the hypothesis that confidence reflects the strength of accumulated evidence penalised by the time taken to reach the decision (Bayesian readout), with the penalty applied not perfectly calibrated to the specific task context. These results suggest there is no need to abandon the DDM or single accumulator models to successfully account for confidence reports

Universal Hopfield networks: a general framework for single-shot associative memory models

A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield networks (MCHNs), which possess close links with self-attention in machine learning. In this paper, we propose a general framework for understanding the operation of such memory networks as a sequence of three operations: similarity, separation, and projection. We derive all these memory models as instances of our general framework with differing similarity and separation functions. We extend the mathematical framework of Krotov et al (2020) to express general associative memory models using neural network dynamics with local computation, and derive a general energy function that is a Lyapunov function of the dynamics. Finally, using our framework, we empirically investigate the capacity of using different similarity functions for these associative memory models, beyond the dot product similarity measure, and demonstrate empirically that Euclidean or Manhattan distance similarity metrics perform substantially better in practice on many tasks, enabling a more robust retrieval and higher memory capacity than existing models