Matrix Factorization with Neural Networks
The factorization of a large matrix into the product of two matrices is an important mathematical problem encountered in many tasks, ranging from dictionary learning to machine learning. Statistical physics can provide on the one hand theoretical limits on the possibility of factorizing matrices in the limit of infinite size, and also practical algorithms. While this program has been successful in the case of finite rank matrices, the regime of extensive rank (scaling linearly with the dimension of the matrix) turns out to be much harder. This talk will describe a new approach to matrix factorization that maps it to neural network models of associative memory: each pattern found in the associative memory corresponds to one factor of the matrix decomposition. A detailed theoretical analysis of this new approach shows that matrix factorization in the extensive rank regime is possible when the rank is below a certain threshold. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-01-03. Recording duration: 00:44:31.
Associative memory of structured knowledge
A long standing challenge in biological and artificial intelligence is to understand how new knowledge can be constructed from known building blocks in a way that is amenable for computation by neuronal circuits. Here we focus on the task of storage and recall of structured knowledge in long-term memory. Specifically, we ask how recurrent neuronal networks can store and retrieve multiple knowledge structures. We model each structure as a set of binary relations between events and attributes (attributes may represent e.g., temporal order, spatial location, role in semantic structure), and map each structure to a distributed neuronal activity pattern using a vector symbolic architecture (VSA) scheme. We then use associative memory plasticity rules to store the binarized patterns as fixed points in a recurrent network. By a combination of signal-to-noise analysis and numerical simulations, we demonstrate that our model allows for efficient storage of these knowledge structures, such that the memorized structures as well as their individual building blocks (e.g., events and attributes) can be subsequently retrieved from partial retrieving cues. We show that long-term memory of structured knowledge relies on a new principle of computation beyond the memory basins. Finally, we show that our model can be extended to store sequences of memories as single attractors.
Functional segregation of rostral and caudal hippocampus in associative memory
It has long been established that the hippocampus plays a crucial role for episodic memory. As opposed to the modular approach, now it is generally assumed that being a complex structure, the HC performs multiplex interconnected functions, whose hierarchical organization provides basis for the higher cognitive functions such as semantics-based encoding and retrieval. However, the «where, when and how» properties of distinct memory aspects within and outside the HC are still under debate. Here we used a visual associative memory task as a probe to test the hypothesis about the differential involvement of the rostral and caudal portions of the human hippocampus in memory encoding, recognition and associative recall. In epilepsy patients implanted with stereo-EEG, we show that at retrieval the rostral HC is selectively active for recognition memory, whereas the caudal HC is selectively active for the associative memory. Low frequency desynchronization and high frequency synchronization characterize the temporal dynamic in encoding and retrieval. Therefore, we describe here anatomical segregation in the hippocampal contributions to associative and recognition memory.
NMC4 Short Talk: Multiscale and extended retrieval of associative memory structures in a cortical model of local-global inhibition balance
Inhibitory neurons take on many forms and functions. How this diversity contributes to memory function is not completely known. Previous formal studies indicate inhibition differentiated by local and global connectivity in associative memory networks functions to rescale the level of retrieval of excitatory assemblies. However, such studies lack biological details such as a distinction between types of neurons (excitatory and inhibitory), unrealistic connection schemas, and non-sparse assemblies. In this study, we present a rate-based cortical model where neurons are distinguished (as excitatory, local inhibitory, or global inhibitory), connected more realistically, and where memory items correspond to sparse excitatory assemblies. We use this model to study how local-global inhibition balance can alter memory retrieval in associative memory structures, including naturalistic and artificial structures. Experimental studies have reported inhibitory neurons and their sub-types uniquely respond to specific stimuli and can form sophisticated, joint excitatory-inhibitory assemblies. Our model suggests such joint assemblies, as well as a distribution and rebalancing of overall inhibition between two inhibitory sub-populations – one connected to excitatory assemblies locally and the other connected globally – can quadruple the range of retrieval across related memories. We identify a possible functional role for local-global inhibitory balance to, in the context of choice or preference of relationships, permit and maintain a broader range of memory items when local inhibition is dominant and conversely consolidate and strengthen a smaller range of memory items when global inhibition is dominant. This model therefore highlights a biologically-plausible and behaviourally-useful function of inhibitory diversity in memory.
On places and borders in the brain
While various forms of cells have been found in relation to the hippocampus cognitive map and navigation system, how these cells are formed and what is read from them is still a mystery. In the current lecture I will talk about several projects which tackle these issues. First, I will show how the formation of border cells in the coginitive map is related to a coordinate transformation, second I will discuss the interaction between the reward system (VTA) and the hippocampus. Finally I will describe a project using place cells as a proxy for associative memory for assessing deficits in Alzheimer’s disease.