Topic: dimensionality reduction

Researchers and practitioners will discuss mathematical foundations of data science, including high-dimensional geometry, dimensionality reduction, scalable algorithms, uncertainty and machine learning. The conference takes place in person at the Salt Palace Convention Center on 16–20 November 2026. Early rates run through 19 October; abstract and travel-support deadlines have passed. Registration also covers the co-located SIAM Imaging Science and Data Mining conferences.

Learning induces changes in neural activity over slow timescales. These changes can be summarized by restructuring neural population data into a three-dimensional array or tensor, of size neurons by time points by trials. Classic dimensionality reduction methods often assume that neural representations are constrained to a fixed low-dimensional latent subspace. Consequently, this view does not capture how the latent subspace could evolve over learning, nor how high-dimensional neural activity could emerge over learning. Furthermore, the link between these empirically-observed changes in neural

Learning in neural circuits manifests via slow changes in activity driving behaviour changes. Uncovering how the coordination of plasticity mechanisms found in the brain leads to such changes is a difficult problem, chiefly because we do not have access to the synaptic parameters underlying neural computation. Nevertheless, as neural population recording techniques improve and experiments track changes in neural dynamics over long durations, finer details about plastic changes could be inferred by observing and characterizing changes in neural activity. In this work, we present a step towards

Predictive modeling and dimensionality reduction of functional neuroimaging data have provided rich information about the representations and functional architectures of the human brain. While these approaches have been effective in many cases, we will discuss how neglecting the internal dynamics of the brain (e.g., spontaneous activity, global dynamics, effective connectivity) and its underlying computational principles may hinder our progress in understanding and modeling brain functions. By reexamining evidence from our previous and ongoing work, we will propose new hypotheses and direction

The understanding of the stroke lesions’ consequences is limited, and it relies mostly on behavioral reports and mere descriptive correlational information from neuroimaging techniques. Using functional magnetic resonance imaging, it has been shown that the functional synchronization between distinct regions of the brain, referred to as functional connectivity, is disrupted by stroke. Nevertheless, this kind of data is usually large and high-dimensional. Extracting useful information from the vast amount of information afforded by brain networks remains a great challenge so, in order to make s

Brains often infer low-dimensional features from high-dimensional input. For example, during visual processing a picture captured by the retina is processed hierarchically through the ventral stream, which gradually infers higher-level features encoded by the lower number of neurons. However, it is still unclear how neural networks learn to perform such tasks. Hebbian Learning (HL), a local form of plasticity that uses pre- and postsynaptic activity to change synaptic efficacy, has been used extensively in receptive field models, sparse coding, independent and principal component analysis, an

Behavior results from neural computations that occur at the level of populations of neurons, and understanding how a given computation produces a particular behavior requires a characterization of how distinct signals interact and evolve. For example, in motor cortex, discrete reaches are generated by a combination of ‘preparatory’ and ‘execution-related’ signals. While the number of computationally-relevant signals is much lower than the number of neurons in a population – and is therefore amenable to dimensionality-reduction methods – standard techniques, like principal components analysis,

A central goal in neuroscience is to understand how orchestrated computations in the brain arise from the properties of single neurons and networks of such neurons. Answering this question requires theoretical advances that shine light into the ‘black box’ of representations in neural circuits. In this talk, we will demonstrate theoretical approaches that help describe how cognitive and behavioral task implementations emerge from the structure in neural populations and from biologically plausible neural networks. First, we will introduce an analytic theory that connects geometric structures th

Technological advances have increased the availability of recordings from large populations of neurons across multiple brain areas. Coupling these recordings with dimensionality reduction techniques, recent work has led to new proposals for how populations of neurons can send and receive signals selectively and flexibly. Advancement of these proposals depends, however, on untangling the bidirectional, parallel communication between neuronal populations. Because our current data analytic tools struggle to achieve this task, we have recently validated and presented a novel dimensionality reducti

Many networks in the brain are sparsely connected, and the brain eliminates synapses during development and learning. How could the brain decide which synapses to prune? In a recurrent network, determining the importance of a synapse between two neurons is a difficult computational problem, depending on the role that both neurons play and on all possible pathways of information flow between them. Noise is ubiquitous in neural systems, and often considered an irritant to be overcome. In the first part of this talk, I will suggest that noise could play a functional role in synaptic pruning, allo

Animals make decisions based on high-dimensional sensory inputs. Obtaining their low-dimensional disentangled representations, ideally in an unsupervised manner, is essential for straightforward downstream information processing. Although the machine learning field has developed useful nonlinear dimensionality reduction methods such as t-distributed stochastic neighbor embedding (t-SNE) [1], their implementation in simple biological circuits remains unclear. Here, we develop a biologically plausible dimensionality reduction algorithm compatible with t-SNE. The proposed algorithm, named Hebbian

Recent studies have proposed that neural circuits have a $\textit{task manifold}$: i.e., a subset of the neural state-space to which neural activity is confined as an animal performs a task [1]. Thus, discovering and characterising these manifolds and their associated dynamics from experimental data can shed light on the neural computations unfolding within the brain during various cognitive tasks. Yet, common manifold discovery methods often do not take into account that neural data is generated by an underlying dynamical system. To address this, we first derive a general class of manifolds t

Most mammalian species present topological maps of preference for the ori- entation of edges in their early visual cortex. However, despite the evidence that evolution has favoured topological map organisation in most species, a clear explanation for the functional role of such maps is lacking. Traditional approaches based on wiring minimisation are incomplete, showing how topology can reduce metabolic costs, but only after assuming a functional role of short- ranged like-tuned connectivity. In this work, we claim that topological maps are for reducing the complexity of the propagated informat