Mathematical Modeling seminars

There is a fundamental tension between storing discrete traces of individual experiences, which allows recall of particular moments in our past without interference, and extracting regularities across these experiences, which supports generalization and prediction in similar situations in the future. One influential proposal for how the brain resolves this tension is that it separates the processes anatomically into Complementary Learning Systems, with the hippocampus rapidly encoding individual episodes and the neocortex slowly extracting regularities over days, months, and years. But this does not explain our ability to learn and generalize from new regularities in our environment quickly, often within minutes. We have put forward a neural network model of the hippocampus that suggests that the hippocampus itself may contain complementary learning systems, with one pathway specializing in the rapid learning of regularities and a separate pathway handling the region’s classic episodic memory functions. This proposal has broad implications for how we learn and represent novel information of specific and generalized types, which we test across statistical learning, inference, and category learning paradigms. We also explore how this system interacts with slower-learning neocortical memory systems, with empirical and modeling investigations into how the hippocampus shapes neocortical representations during sleep. Together, the work helps us understand how structured information in our environment is initially encoded and how it then transforms over time.

In the current virtual journal club Dr Di Luca will present findings from a series of psychophysical investigations where he measured sensitivity and bias in the perception of the timing of stimuli. He will present how improved detection with longer sequences and biases in reporting isochrony can be accounted for by optimal statistical predictions. Among his findings was also that the timing of stimuli that occasionally deviate from a regularly paced sequence is perceptually distorted to appear more regular. Such change depends on whether the context these sequences are presented is also regular. Dr Di Luca will present a Bayesian model for the combination of dynamically updated expectations, in the form of a priori probability, with incoming sensory information. These findings contribute to the understanding of how the brain processes temporal information to shape perceptual experiences.

The predictive map hypothesis provides a promising framework to model representations in the hippocampal formation. I will introduce a tractable implementation of a predictive map called the successor representation (SR), before presenting data showing that rats and humans display SR-like navigational choices on a novel open-field maze. Next, I will show how such a predictive map could be implemented using spatial representations found in the hippocampal formation, before finally presenting how such learning might be well approximated by phenomena that exist in the spatial memory system - namely spike-timing dependent plasticity and theta phase precession.

From a workout at the gym to helping a colleague with their work, everyday we make decisions about whether we are willing to exert effort to obtain some sort of benefit. Increases in how effortful actions and cognitive processes are perceived to be has been linked to clinically severe impairments to motivation, such as apathy and fatigue, across many neurological and psychiatric conditions. However, the vast majority of neuroscience research has focused on understanding the benefits for acting, the rewards, and not on the effort required. As a result, the computational and neural mechanisms underlying how effort is processed are poorly understood. How do we compute how effortful we perceive a task to be? How does this feed into our motivation and decisions of whether to act? How are such computations implemented in the brain? and how do they change in different environments? I will present a series of studies examining these questions using novel behavioural tasks, computational modelling, fMRI, pharmacological manipulations, and testing in a range of different populations. These studies highlight how the brain represents the costs of exerting effort, and the dynamic processes underlying how our sensitivity to effort changes as a function of our goals, traits, and socio-cognitive processes. This work provides new computational frameworks for understanding and examining impaired motivation across psychiatric and neurological conditions, as well as why all of us, sometimes, can’t be bothered.

To efficiently process sensory information, the brain relies on statistical regularities in the input. While generally improving the reliability of sensory estimates, this strategy also induces perceptual illusions that help reveal the underlying computational principles. Focusing on auditory and visual perception, in my talk I will describe how the brain exploits statistical regularities within and across the senses for the perception space, time and multisensory integration. In particular, I will show how results from a series of psychophysical experiments can be interpreted in the light of Bayesian Decision Theory, and I will demonstrate how such canonical computations can be implemented into simple and biologically plausible neural circuits. Finally, I will show how such principles of sensory information processing can be leveraged in virtual and augmented reality to overcome display limitations and expand human perception.

Environmental boundaries anchor cognitive maps that support memory. However, trapezoidal boundary geometry distorts the regular firing patterns of entorhinal grid cells proposedly providing a metric for cognitive maps. Here, we test the impact of trapezoidal boundary geometry on human spatial memory using immersive virtual reality. Consistent with reduced regularity of grid patterns in rodents and a grid-cell model based on the eigenvectors of the successor representation, human positional memory was degraded in a trapezoid compared to a square environment; an effect particularly pronounced in the trapezoid’s narrow part. Congruent with spatial frequency changes of eigenvector grid patterns, distance estimates between remembered positions were persistently biased; revealing distorted memory maps that explained behavior better than the objective maps. Our findings demonstrate that environmental geometry affects human spatial memory similarly to rodent grid cell activity — thus strengthening the putative link between grid cells and behavior along with their cognitive functions beyond navigation.

When making decision under risk, people often exhibit behaviours that classical economic theories cannot explain. Newer models that attempt to account for these ‘irrational’ behaviours often lack neuroscience bases and require the introduction of subjective and problem-specific constructs. Here, we present a decision-making model inspired by the prediction error signals and introspective neuronal replay reported in the brain. In the model, decisions are chosen based on ‘anticipated surprise’, defined by a nonlinear average of the differences between individual outcomes and a reference point. The reference point is determined by the expected value of the possible outcomes, which can dynamically change during the mental simulation of decision-making problems involving sequential stages. Our model elucidates the contribution of each stage to the appeal of available options in a decision-making problem. This allows us to explain several economic paradoxes and gambling behaviours. Our work could help bridge the gap between decision-making theories in economics and neurosciences.

I will begin by describing recent research taking a new, model-based approach to perceptual development. This approach uncovers fundamental changes in information processing underlying the protracted development of perception, action, and decision-making in childhood. For example, integration of multiple sensory estimates via reliability-weighted averaging – widely used by adults to improve perception – is often not seen until surprisingly late into childhood, as assessed by both behaviour and neural representations. This approach forms the basis for a newer question: the scope for the nervous system to deploy useful computations (e.g. reliability-weighted averaging) to optimise perception and action using newly-learned sensory signals provided by technology. Our initial model system is augmenting visual depth perception with devices translating distance into auditory or vibro-tactile signals. This problem has immediate applications to people with partial vision loss, but the broader question concerns our scope to use technology to tune in to any signal not available to our native biological receptors. I will describe initial progress on this problem, and our approach to operationalising what it might mean to adopt a new signal comparably to a native sense. This will include testing for its integration (weighted averaging) alongside the native senses, assessing the level at which this integration happens in the brain, and measuring the degree of ‘automaticity’ with which new signals are used, compared with native perception.

Behavioural measurements are often overlooked by computational neuroscientists, who prefer to focus on electrophysiological recordings or neuroimaging data. This attitude is largely due to perceived lack of depth/richness in relation to behavioural datasets. I will show how contemporary psychophysics can deliver extremely rich and highly constraining datasets that naturally interface with computational modelling. More specifically, I will demonstrate how psychophysics can be used to guide/constrain/refine computational models, and how models can be exploited to design/motivate/interpret psychophysical experiments. Examples will span a wide range of topics (from feature detection to natural scene understanding) and methodologies (from cascade models to deep learning architectures).

The idea that behavior results from a dynamic interplay between automatic and controlled processing underlies much of decision science, but has also generated considerable controversy. In this talk, I will highlight behavioral and neural data showing how recently-developed computational models of decision making can be used to shed new light on whether, when, and how decisions result from distinct processes operating at different timescales. Across diverse domains ranging from altruism to risky choice biases and self-regulation, our work suggests that a model of prioritized attentional sampling and evidence accumulation may provide an alternative explanation for many phenomena previously interpreted as supporting dual process models of choice. However, I also show how some features of the model might be taken as support for specific aspects of dual-process models, providing a way to reconcile conflicting accounts and generating new predictions and insights along the way.

The COINTOB (conditional intention and integration to bound) model provides a heuristic framework of processes in Libet-style experiments. The model is based on three assumptions. First, brain activation preceding conscious intentions in Libet-style experiments does not reflect an unconscious decision but rather the unfolding of a decision process. Second, the time of conscious decision (W) reflects the moment in time when the decision boundary is crossed. This interpretation of W is consistent with our apparent intuition that we decide in the moment we experience the conscious intention to act. Third, the decision process is configured by conscious intentions that participants form at the beginning of the experiment based on the experimental instruction. Brass and Mele discuss the model, conceptual background for it, and the model’s bearing on free will.

Humans spend a lifetime learning, storing and refining a repertoire of motor memories. However, it is unknown what principle underlies the way our continuous stream of sensori-motor experience is segmented into separate memories and how we adapt and use this growing repertoire. Here we develop a principled theory of motor learning based on the key insight that memory creation, updating, and expression are all controlled by a single computation – contextual inference. Unlike dominant theories of single-context learning, our repertoire-learning model accounts for key features of motor learning that had no unified explanation and predicts novel phenomena, which we confirm experimentally. These results suggest that contextual inference is the key principle underlying how a diverse set of experiences is reflected in motor behavior.