3,217 research outputs found
Computational techniques to interpret the neural code underlying complex cognitive processes
Advances in large-scale neural recording technology have significantly improved the
capacity to further elucidate the neural code underlying complex cognitive processes.
This thesis aimed to investigate two research questions in rodent models. First, what
is the role of the hippocampus in memory and specifically what is the underlying
neural code that contributes to spatial memory and navigational decision-making.
Second, how is social cognition represented in the medial prefrontal cortex at the
level of individual neurons. To start, the thesis begins by investigating memory and
social cognition in the context of healthy and diseased states that use non-invasive
methods (i.e. fMRI and animal behavioural studies). The main body of the thesis
then shifts to developing our fundamental understanding of the neural mechanisms
underpinning these cognitive processes by applying computational techniques to ana lyse stable large-scale neural recordings. To achieve this, tailored calcium imaging
and behaviour preprocessing computational pipelines were developed and optimised
for use in social interaction and spatial navigation experimental analysis. In parallel,
a review was conducted on methods for multivariate/neural population analysis. A
comparison of multiple neural manifold learning (NML) algorithms identified that non linear algorithms such as UMAP are more adaptable across datasets of varying noise
and behavioural complexity. Furthermore, the review visualises how NML can be
applied to disease states in the brain and introduces the secondary analyses that
can be used to enhance or characterise a neural manifold. Lastly, the preprocessing
and analytical pipelines were combined to investigate the neural mechanisms in volved in social cognition and spatial memory. The social cognition study explored
how neural firing in the medial Prefrontal cortex changed as a function of the social
dominance paradigm, the "Tube Test". The univariate analysis identified an ensemble
of behavioural-tuned neurons that fire preferentially during specific behaviours such
as "pushing" or "retreating" for the animal’s own behaviour and/or the competitor’s
behaviour. Furthermore, in dominant animals, the neural population exhibited greater
average firing than that of subordinate animals. Next, to investigate spatial memory,
a spatial recency task was used, where rats learnt to navigate towards one of three
reward locations and then recall the rewarded location of the session. During the
task, over 1000 neurons were recorded from the hippocampal CA1 region for five rats
over multiple sessions. Multivariate analysis revealed that the sequence of neurons encoding an animal’s spatial position leading up to a rewarded location was also active
in the decision period before the animal navigates to the rewarded location. The result
posits that prospective replay of neural sequences in the hippocampal CA1 region
could provide a mechanism by which decision-making is supported
Complexity & wormholes in holography
Holography has proven to be a highly successful approach in studying quantum gravity, where a non-gravitational quantum field theory is dual to a quantum gravity theory in one higher dimension. This doctoral thesis delves into two key aspects within the context of holography: complexity and wormholes. In Part I of the thesis, the focus is on holographic complexity. Beginning with a brief review of quantum complexity and its significance in holography, the subsequent two chapters proceed to explore this topic in detail. We study several proposals to quantify the costs of holographic path integrals. We then show how such costs can be optimized and match them to bulk complexity proposals already existing in the literature. In Part II of the thesis, we shift our attention to the study of spacetime wormholes in AdS/CFT. These are bulk spacetime geometries having two or more disconnected boundaries. In recent years, such wormholes have received a lot of attention as they lead to interesting implications and raise important puzzles. We study the construction of several simple examples of such wormholes in general dimensions in the presence of a bulk scalar field and explore their implications in the boundary theory
Deep Learning Techniques for Electroencephalography Analysis
In this thesis we design deep learning techniques for training deep neural networks on electroencephalography (EEG) data and in particular on two problems, namely EEG-based motor imagery decoding and EEG-based affect recognition, addressing challenges associated with them. Regarding the problem of motor imagery (MI) decoding, we first consider the various kinds of domain shifts in the EEG signals, caused by inter-individual differences (e.g. brain anatomy, personality and cognitive profile). These domain shifts render multi-subject training a challenging task and impede robust cross-subject generalization. We build a two-stage model ensemble architecture and propose two objectives to train it, combining the strengths of curriculum learning and collaborative training. Our subject-independent experiments on the large datasets of Physionet and OpenBMI, verify the effectiveness of our approach. Next, we explore the utilization of the spatial covariance of EEG signals through alignment techniques, with the goal of learning domain-invariant representations. We introduce a Riemannian framework that concurrently performs covariance-based signal alignment and data augmentation, while training a convolutional neural network (CNN) on EEG time-series. Experiments on the BCI IV-2a dataset show that our method performs superiorly over traditional alignment, by inducing regularization to the weights of the CNN. We also study the problem of EEG-based affect recognition, inspired by works suggesting that emotions can be expressed in relative terms, i.e. through ordinal comparisons between different affective state levels. We propose treating data samples in a pairwise manner to infer the ordinal relation between their corresponding affective state labels, as an auxiliary training objective. We incorporate our objective in a deep network architecture which we jointly train on the tasks of sample-wise classification and pairwise ordinal ranking. We evaluate our method on the affective datasets of DEAP and SEED and obtain performance improvements over deep networks trained without the additional ranking objective
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
Recommended from our members
Interpretable Machine Learning Architectures for Efficient Signal Detection with Applications to Gravitational Wave Astronomy
Deep learning has seen rapid evolution in the past decade, accomplishing tasks that were previously unimaginable. At the same time, researchers strive to better understand and interpret the underlying mechanisms of the deep models, which are often justifiably regarded as "black boxes". Overcoming this deficiency will not only serve to suggest better learning architectures and training methods, but also extend deep learning to scenarios where interpretability is key to the application. One such scenario is signal detection and estimation, with gravitational wave detection as a specific example, where classic methods are often preferred for their interpretability. Nonetheless, while classic statistical detection methods such as matched filtering excel in their simplicity and intuitiveness, they can be suboptimal in terms of both accuracy and computational efficiency. Therefore, it is appealing to have methods that achieve ``the best of both worlds'', namely enjoying simultaneously excellent performance and interpretability.
In this thesis, we aim to bridge this gap between modern deep learning and classic statistical detection, by revisiting the signal detection problem from a new perspective. First, to address the perceived distinction in interpretability between classic matched filtering and deep learning, we state the intrinsic connections between the two families of methods, and identify how trainable networks can address the structural limitations of matched filtering. Based on these ideas, we propose two trainable architectures that are constructed based on matched filtering, but with learnable templates and adaptivity to unknown noise distributions, and therefore higher detection accuracy. We next turn our attention toward improving the computational efficiency of detection, where we aim to design architectures that leverage structures within the problem for efficiency gains. By leveraging the statistical structure of class imbalance, we integrate hierarchical detection into trainable networks, and use a novel loss function which explicitly encodes both detection accuracy and efficiency. Furthermore, by leveraging the geometric structure of the signal set, we consider using signal space optimization as an alternative computational primitive for detection, which is intuitively more efficient than covering with a template bank. We theoretical prove the efficiency gain by analyzing Riemannian gradient descent on the signal manifold, which reveals an exponential improvement in efficiency over matched filtering. We also propose a practical trainable architecture for template optimization, which makes use of signal embedding and kernel interpolation.
We demonstrate the performance of all proposed architectures on the task of gravitational wave detection in astrophysics, where matched filtering is the current method of choice. The architectures are also widely applicable to general signal or pattern detection tasks, which we exemplify with the handwritten digit recognition task using the template optimization architecture. Together, we hope the this work useful to scientists and engineers seeking machine learning architectures with high performance and interpretability, and contribute to our understanding of deep learning as a whole
Optimal decay for solutions of the Teukolsky equation on the Kerr metric for the full subextremal range |a| < M
We derive the large time asymptotics of initially regular and localized
solutions of the Teukolsky equation on the exterior of a subextremal Kerr black
hole for any half integer spin. More precisely, we obtain the leading order
term (predicted by Price's law) in the large time regime assuming that the
initial data have compact support and have enough (but finite) Sobolev
regularity. For initial data with less spatial decay (typically decaying like
r^{--1--} with (0, 1)), we prove that the solution has a
pointwise decay of order t^{--1----s--|s|+} on spatially compact
regions. In the proof, we adopt the spectral point of view and make use of
recent advances in microlocal analysis and non elliptic Fredholm theory which
provide a robust framework to study linear operators on black hole type
spacetimes
Data-assisted modeling of complex chemical and biological systems
Complex systems are abundant in chemistry and biology; they can be multiscale, possibly high-dimensional or stochastic, with nonlinear dynamics and interacting components. It is often nontrivial (and sometimes impossible), to determine and study the macroscopic quantities of interest and the equations they obey. One can only (judiciously or randomly) probe the system, gather observations and study trends. In this thesis, Machine Learning is used as a complement to traditional modeling and numerical methods to enable data-assisted (or data-driven) dynamical systems. As case studies, three complex systems are sourced from diverse fields: The first one is a high-dimensional computational neuroscience model of the Suprachiasmatic Nucleus of the human brain, where bifurcation analysis is performed by simply probing the system. Then, manifold learning is employed to discover a latent space of neuronal heterogeneity. Second, Machine Learning surrogate models are used to optimize dynamically operated catalytic reactors. An algorithmic pipeline is presented through which it is possible to program catalysts with active learning. Third, Machine Learning is employed to extract laws of Partial Differential Equations describing bacterial Chemotaxis. It is demonstrated how Machine Learning manages to capture the rules of bacterial motility in the macroscopic level, starting from diverse data sources (including real-world experimental data). More importantly, a framework is constructed though which already existing, partial knowledge of the system can be exploited. These applications showcase how Machine Learning can be used synergistically with traditional simulations in different scenarios: (i) Equations are available but the overall system is so high-dimensional that efficiency and explainability suffer, (ii) Equations are available but lead to highly nonlinear black-box responses, (iii) Only data are available (of varying source and quality) and equations need to be discovered. For such data-assisted dynamical systems, we can perform fundamental tasks, such as integration, steady-state location, continuation and optimization. This work aims to unify traditional scientific computing and Machine Learning, in an efficient, data-economical, generalizable way, where both the physical system and the algorithm matter
Hyperbolic Image-Text Representations
Visual and linguistic concepts naturally organize themselves in a hierarchy,
where a textual concept ``dog'' entails all images that contain dogs. Despite
being intuitive, current large-scale vision and language models such as CLIP do
not explicitly capture such hierarchy. We propose MERU, a contrastive model
that yields hyperbolic representations of images and text. Hyperbolic spaces
have suitable geometric properties to embed tree-like data, so MERU can better
capture the underlying hierarchy in image-text data. Our results show that MERU
learns a highly interpretable representation space while being competitive with
CLIP's performance on multi-modal tasks like image classification and
image-text retrieval.Comment: Technical repor
Robust Estimation of Surface Curvature Information from Point Cloud Data
This paper surveys and evaluates some popular state of the art methods for
algorithmic curvature and normal estimation. In addition to surveying existing
methods we also propose a new method for robust curvature estimation and
evaluate it against existing methods thus demonstrating its superiority to
existing methods in the case of significant data noise. Throughout this paper
we are concerned with computation in low dimensional spaces (N < 10) and
primarily focus on the computation of the Weingarten map and quantities that
may be derived from this; however, the algorithms discussed are theoretically
applicable in any dimension. One thing that is common to all these methods is
their basis in an estimated graph structure. For any of these methods to work
the local geometry of the manifold must be exploited; however, in the case of
point cloud data it is often difficult to discover a robust manifold structure
underlying the data, even in simple cases, which can greatly influence the
results of these algorithms. We hope that in pushing these algorithms to their
limits we are able to discover, and perhaps resolve, many major pitfalls that
may affect potential users and future researchers hoping to improve these
methodsComment: 16 pages, 13 figure
FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundles
Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way that the base space accounts for the large scale topology, while the fibers account for the local geometry. This allows one to reduce the dimensionality of the fibers, while preserving the large scale topology. We formalize this point of view and, as an application, we describe a dimensionality reduction algorithm based on topological inference for vector bundles. The algorithm takes as input a dataset together with an initial representation in Euclidean space, assumed to recover part of its large scale topology, and outputs a new representation that integrates local representations obtained through local linear dimensionality reduction. We demonstrate this algorithm on examples coming from dynamical systems and chemistry. In these examples, our algorithm is able to learn topologically faithful embeddings of the data in lower target dimension than various well known metric-based dimensionality reduction algorithms
- …