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Inference and inverse problems are closely related concepts, both fundamentally involving the deduction of unknown causes or parameters from observed data. Bayesian inference, a powerful class of methods, is often employed to solve a…
Variational Autoencoders (VAEs) are powerful generative models for learning latent representations. Standard VAEs generate dispersed and unstructured latent spaces by utilizing all dimensions, which limits their interpretability, especially…
Two-dimensional embeddings obtained from dimensionality reduction techniques such as MDS, t-SNE, or UMAP, are widely used to visualize high-dimensional data and support researchers in visually identifying clusters, outliers, and other…
In this work, we study value function approximation in reinforcement learning (RL) problems with high dimensional state or action spaces via a generalized version of representation policy iteration (RPI). We consider the limitations of…
Modern transformer-based encoder-decoder architectures struggle with reasoning tasks due to their inability to effectively extract relational information between input objects (data/tokens). Recent work introduced the Abstractor module,…
Do large language models (LLMs) represent concepts abstractly, i.e., independent of input format? We revisit Function Vectors (FVs), compact representations of in-context learning (ICL) tasks that causally drive task performance. Across…
Unsupervised learning of discrete representations in neural networks (NNs) from continuous ones is essential for many modern applications. Vector Quantisation (VQ) has become popular for this, in particular in the context of generative…
A main object of our study is multiset functions -- that is, permutation-invariant functions over inputs of varying sizes. Deep Sets, proposed by \cite{zaheer2017deep}, provides a \emph{universal representation} for continuous multiset…
This paper presents the Visual Place Cell Encoding (VPCE) model, a biologically inspired computational framework for simulating place cell-like activation using visual input. Drawing on evidence that visual landmarks play a central role in…
We present a formal and constructive simulation framework for nondeterministic finite automata (NFAs) using time-shared, depth-unrolled feedforward networks (TS-FFNs), i.e., acyclic unrolled computations with shared parameters that are…
Classification of time series data is an important task for many application domains. One of the best existing methods for this task, in terms of accuracy and computation time, is MiniROCKET. In this work, we extend this approach to provide…
Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or…
Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces,…
Self Organizing Map (SOM) has been applied into several classical modeling tasks including clustering, classification, function approximation and visualization of high dimensional spaces. The final products of a trained SOM are a set of…
How can neural networks perform so well on compositional tasks even though they lack explicit compositional representations? We use a novel analysis technique called ROLE to show that recurrent neural networks perform well on such tasks by…
The ability to recognize objects despite there being differences in appearance, known as Core Object Recognition, forms a critical part of human perception. While it is understood that the brain accomplishes Core Object Recognition through…
The increasing efficiency and compactness of deep learning architectures, together with hardware improvements, have enabled the complex and high-dimensional modelling of medical volumetric data at higher resolutions. Recently,…
One of the potential solutions for model interpretation is to train a surrogate model: a more transparent model that approximates the behavior of the model to be explained. Typically, classification rules or decision trees are used due to…
Variational Autoencoders (VAEs) provide a flexible and scalable framework for non-linear dimensionality reduction. However, in application domains such as genomics where data sets are typically tabular and high-dimensional, a black-box…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…