arXiv research

Study how actions affect perception in embodied agents using group theory.

PeL separates sensory interface optimization from decision learning.

Deep learning, computational neuroscience, and cognitive science have overlapping goals related to understanding intelligence such that perception and behaviour can be simulated in computational systems. In neuroimaging, machine learning methods have been used to test computational models of sensory information process…

Agents acting in the natural world aim at selecting appropriate actions based on noisy and partial sensory observations. Many behaviors leading to decision mak- ing and action selection in a closed loop setting are naturally phrased within a control theoretic framework. Within the framework of optimal Control Theory, o…

New method decomposes sensory information from neurons into specific stimuli and features.

We consider a scenario where the aim of a group of agents is to perform the optimal coverage of a region according to a sensory function. In particular, centroidal Voronoi partitions have to be computed. The difficulty of the task is that the sensory function is unknown and has to be reconstructed on line from noisy me…

No real-world reward function is perfect. Sensory errors and software bugs may result in RL agents observing higher (or lower) rewards than they should. For example, a reinforcement learning agent may prefer states where a sensory error gives it the maximum reward, but where the true reward is actually small. We formal…

Objects are represented in sensory systems by continuous manifolds due to sensitivity of neuronal responses to changes in physical features such as location, orientation, and intensity. What makes certain sensory representations better suited for invariant decoding of objects by downstream networks? We present a theory…

Algorithm balances learning and coverage for multi-robots over unknown fields.

Large language models predict human sensory judgments across multiple modalities.

The paper develops models to understand sensory coding and cortical topography.

Deep reinforcement learning (DRL) has shown incredible performance in learning various tasks to the human level. However, unlike human perception, current DRL models connect the entire low-level sensory input to the state-action values rather than exploiting the relationship between and among entities that constitute t…

Unsupervised learning requiring only raw data is not only a fundamental function of the cerebral cortex, but also a foundation for a next generation of artificial neural networks. However, a unified theoretical framework to treat sensory inputs, synapses and neural activity together is still lacking. The computational …

Deep active inference learns policies from sensory inputs.

Graph Convolutional Networks improve prosthetic sensation interpretation.

Constellation learns group-level visual relationships for abstract reasoning.

New algebraic structures on manifolds generalize supergeometry concepts.

Each element of the commutator subgroup of a group can be represented as a product of commutators. The minimal number of factors in such a product is called the commutator length of the element. The commutator length of a group is defined as the supremum of commutator lengths of elements of its commutator subgroup. We …

Sensor fusion has wide applications in many domains including health care and autonomous systems. While the advent of deep learning has enabled promising multi-modal fusion of high-level features and end-to-end sensor fusion solutions, existing deep learning based sensor fusion techniques including deep gating architec…

Doodles link to commutator identities in a 2-sphere.

Study on deformation cohomology for braided commutative structures.

Examining singularities of commuting vector fields on submanifolds.

Study on infinite-type surfaces shows stable commutator length is continuous and defines open subgroups.

An increasing number of sensors on mobile, Internet of things (IoT), and wearable devices generate time-series measurements of physical activities. Though access to the sensory data is critical to the success of many beneficial applications such as health monitoring or activity recognition, a wide range of potentially …

New proof and description of commutator subgroups for free and surface groups.

Formulae for non-symmetric connections derived from covariant derivatives.

This work investigates how a naive agent can acquire its own body image in a self-supervised way, based on the predictability of its sensorimotor experience. Our working hypothesis is that, due to its temporal stability, an agent's body produces more consistent sensory experiences than the environment, which exhibits a…

The paper studies Riemannian metrics on Lie groups with specific commutator subgroups.

Homotopy commutativity in quasitoric manifolds depends on polytope structure and characteristic matrix type.

Covariance is shown as a commutator in random variable calculus.

Every homeomorphism of Euclidean space is a commutator of two homeomorphisms.

We show that solutions of Thurston equation on triangulated 3-manifolds in a commutative ring carry topological information. We also introduce a homogeneous Thurston equation and a commutative ring associated to triangulated 3-manifolds.

For an autonomous agent to fulfill a wide range of user-specified goals at test time, it must be able to learn broadly applicable and general-purpose skill repertoires. Furthermore, to provide the requisite level of generality, these skills must handle raw sensory input such as images. In this paper, we propose an algo…

Tensor models decode human perception and memory using SPO triples.

We show that the mapping class group of any closed connected orientable surface of genus at least five is generated by only two commutators, and if the genus is three or four, by three commutators.

This paper studies nonlinear representation learning dynamics beyond the NTK regime.

We give new upper bounds on the stable commutator lengths of Dehn twists in mapping class groups and new lower bounds on the stable commutator lengths of Dehn twists in hyperelliptic mapping class groups. In particular, we show that the stable commutator lengths of Dehn twists about a nonseparating and a separating cur…

Survey on invariant quasimorphisms and their relation to stable commutator length.

Paper proves non-compact inaudibility of symmetry and commutativity.

Animals need to devise strategies to maximize returns while interacting with their environment based on incoming noisy sensory observations. Task-relevant states, such as the agent's location within an environment or the presence of a predator, are often not directly observable but must be inferred using available sens…

In this paper, we introduce a new commuting condition between the structure Jacobi operator and symmetric (1,1)-type tensor field $T$, that is, $R_ξφT=TR_ξφ$, where $T=A$ or $T=S$ for Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians. By using simultaneous diagonalzation for commuting symmetric operators…

Multimodal sensory data resembles the form of information perceived by humans for learning, and are easy to obtain in large quantities. Compared to unimodal data, synchronization of concepts between modalities in such data provides supervision for disentangling the underlying explanatory factors of each modality. Previ…

We introduce the notion of commuting Ricci tensor for real hypersurfaces in the complex quadric $Q^m = SO_{m+2}/SO_mSO_2$ . It is shown that the commuting Ricci tensor gives that the unit normal vector field $N$ becomes $\frak A$-principal or $\frak A$-isotropic. Then according to each case, we give a complete classifi…

The paper defines constraints for commuting endomorphisms in generalized tangent bundles.

Let $WB_n$ be the welded (or loop) braid group on n strands, $n \geq 3$. We investigate commutator subgroup of $WB_n$. We prove that the commutator subgroup $WB_n'$ is finitely generated and Hopfian. We show that $WB_n'$ is perfect if and only if $n \geq 5$. We also compute finite presentation for $FWB_n'$, the commuta…

An arbitrary homomorphism between groups is nonincreasing for stable commutator length, and there are infinitely many (injective) homomorphisms between free groups which strictly decrease the stable commutator length of some elements. However, we show in this paper that a random homomorphism between free groups is almo…

For any group, there is a natural (pseudo-)norm on the vector space B1 of real (group) 1-boundaries, called the stable commutator length norm. This norm is closely related to, and can be thought of as a relative version of, the Gromov (pseudo)-norm on (ordinary) homology. We show that for a free group, the unit ball of…

The paper finds commutator formulas for Gradient Ricci Shrinker metrics and applies them to linear stability.