Related papers: Classification in Active Dimension 2 for Weighted …
We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the…
The ResNet architecture has been widely adopted in deep learning due to its significant boost to performance through the use of simple skip connections, yet the underlying mechanisms leading to its success remain largely unknown. In this…
We investigate the critical behavior of disordered systems transversely driven at a uniform and steady velocity. An intuitive argument predicts that the long-distance physics of $D$-dimensional driven disordered systems at zero temperature…
Studies of the dynamics of nonlinear recurrent neural networks often assume independent and identically distributed couplings, but large-scale connectomics data indicate that biological neural circuits exhibit markedly different…
Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal…
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…
A primitive type of two-dimensional dynamic system is introduced. It is shown that there is no decision procedure able to answer if such a dynamical system is ultimately zero.
For ambiguous queries, conventional retrieval systems are bound by two conflicting goals. On the one hand, they should diversify and strive to present results for as many query intents as possible. On the other hand, they should provide…
We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training…
Classification models are a key component of structural digital twin technologies used for supporting asset management decision-making. An important consideration when developing classification models is the dimensionality of the input, or…
Reproducibility of a deep-learning fully convolutional neural network is evaluated by training several times the same network on identical conditions (database, hyperparameters, hardware) with non-deterministic Graphics Processings Unit…
We investigate dynamics of deformable self-propelled particles with a repulsive interaction whose magnitude depends on the relative direction of elongation of a pair of particles. A collective motion of the particles appears in two…
Prior work argues that refusal in large language models is mediated by a single activation-space direction, enabling effective steering and ablation. We show that this account is incomplete. Across eleven categories of refusal and…
Interpreting the learning dynamics of neural networks can provide useful insights into how networks learn and the development of better training and design approaches. We present an approach to interpret learning in neural networks by…
It is shown that for any positive integer n there exists a subnormal weighted shift on a directed tree whose nth power is closed and densely defined while its (n + 1)th power has trivial domain. Similar result for composition operators in…
We study the dynamics of the one dimensional disordered trap model presenting a broad distribution of trapping times $p(\tau) \sim 1/\tau^{1+\mu}$, when an external force is applied from the very beginning at $t=0$, or only after a waiting…
We consider a single-species diffusion-limited annihilation reaction with reactants confined to a two-dimensional surface with one arbitrarily large dimension and the other comparable in size to interparticle distances. This situation could…
Agents affected by their own future states in a one-dimensional discrete dynamical system (1-DDS) can replicate two-dimensional images. It is shown that such replication requires a toroidal spacetime and three rules are needed to calculate…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…
Trainable activation functions, whose parameters are optimized alongside network weights, offer increased expressivity compared to fixed activation functions. Specifically, trainable activation functions defined as ratios of polynomials…