Agents learn spatial structure without supervision.
problem Understanding spatial knowledge in autonomous agents.
method Sensorimotor predictive scheme applied to various agents and exploration types.
result Agents can learn egocentric spatial structure without supervision.
New method fits low-rank models for egocentrically sampled networks.
problem Statistical modeling of egocentrically sampled partial networks.
method Graph spectral properties-based approach for low-rank models.
result Consistent recovery of missing subnetworks for sparse networks.
Link prediction in networks is typically accomplished by estimating or ranking the probabilities of edges for all pairs of nodes. In practice, especially for social networks, the data are often collected by egocentric sampling, which means selecting a subset of nodes and recording all of their edges. This sampling mech…
Body-worn cameras are now commonly used for logging daily life, sports, and law enforcement activities, creating a large volume of archived footage. This paper studies the problem of classifying frames of footage according to the activity of the camera-wearer with an emphasis on application to real-world police body-wo…
Framework for continual object recognition in egocentric settings.
problem Recognizing objects in a cold-start, open-world setting with limited supervision.
method Memory-based incremental framework using time and space persistence, similarity, and active learning.
result Feasibility of open-world, generic object recognition with complete user supervision.
High-throughput 3D control training system achieves 100,000 FPS.
problem Lack of efficient, single-machine reinforcement learning systems.
method Sample Factory combines asynchronous sampling and off-policy correction.
result Achieves 100,000 FPS on 3D control problems without sacrificing sample efficiency.
We consider tackling a single-agent RL problem by distributing it to n learners. These learners, called advisors, endeavour to solve the problem from a different focus. Their advice, taking the form of action values, is then communicated to an aggregator, which is in control of the system. We show that the local plan…
Framework learns portable representations for diverse tasks.
problem Creating task-independent abstract representations for diverse environments.
method Autonomously learns portable representations in egocentric space.
result Portable representations enable task-independent planning and transfer.
Understanding how images of objects and scenes behave in response to specific ego-motions is a crucial aspect of proper visual development, yet existing visual learning methods are conspicuously disconnected from the physical source of their images. We propose to exploit proprioceptive motor signals to provide unsuperv…
A new algorithm reduces communication costs for collaborative decision-making across clients.
problem Collaborative decision-making with sparse rewards and heterogeneous contexts.
method Federated Lasso algorithm for sparse linear contextual bandits.
result Achieves near-optimal regret with logarithmic communication costs.
Inertial information processing plays a pivotal role in ego-motion awareness for mobile agents, as inertial measurements are entirely egocentric and not environment dependent. However, they are affected greatly by changes in sensor placement/orientation or motion dynamics, and it is infeasible to collect labelled data …
The ability to transfer in reinforcement learning is key towards building an agent of general artificial intelligence. In this paper, we consider the problem of learning to simultaneously transfer across both environments (ENV) and tasks (TASK), probably more importantly, by learning from only sparse (ENV, TASK) pairs …
Bertrand framed surfaces defined in Euclidean 3-space with applications.
problem Defining and characterizing Bertrand framed surfaces.
method Using moving frames to define Bertrand framed surfaces and analyzing their caustics and involutes.
result Conditions for caustics and involutes to be inverse operations of framed surfaces.
Quaternionic frames' admissibility and homotopy proven.
problem Existence and interpolation of quaternionic frames.
method Interpreting frames as adjoint orbits.
result Spaces of quaternionic frames are path-connected.
Introduces hyperbolic generalized framed surfaces and their properties.
problem None explicitly stated; focuses on introducing new geometric objects.
method Generalization of hyperbolic framed surfaces and curves.
result Established conditions for a surface to be a hyperbolic generalized framed base surface and explored their singularities.
Study of generalized Bishop frames on curves in 4D space.
problem Understanding frames on curves in 4D space.
method Introducing and studying four types of generalized Bishop frames on curves in E4. result Every regular curve in E4 admits all four types of generalized Bishop frames. We demonstrate that effortlessly accessible digital records of behavior such as Facebook Likes can be obtained and utilized to automatically distinguish a wide range of highly delicate personal traits including: life satisfaction, cultural ethnicity, political views, age, gender and personality traits. The analysis pre…
The main drawback of the Frenet frame is that it is undefined at those points where the curvature is zero. Further- more, in the case of planar curves, the Frenet frame does not agree with the standard framing of curves in the plane. The main drawback of the Bishop frame is that the principle normal vector N is not in …
New framed moves extend classical knot theory results.
problem Extending classical knot theory to framed braids.
method Introduced framed versions of L-moves, Hilden, Pure Hilden groups, and framed versions of the Birman theorem.
result Proved a framed version of the Birman theorem for framed links in plat representation.
Study on Bertrand lightcone framed curves in Lorentz-Minkowski 3-space.
problem Analyzing mixed types of curves with singular points in Lorentz-Minkowski 3-space.
method Using lightcone frame to consider Bertrand types for lightcone framed curves.
result Existence conditions of Bertrand lightcone framed curves in all cases.
The paper extends BPS invariants for framed knots and links.
problem Investigating BPS invariants for framed knots and links.
method Using the dual A-polynomial and framing change formula, the paper extends the relationship between algebraic curves and BPS invariants to framed knots and links.
result Explicit formulas for extremal A-polynomials and BPS invariants of framed knots, and numerical calculations for framed Whitehead links and Borromean rings.
Simply connected spaces of tight frames identified.
problem Understanding the connectivity of spaces of tight frames.
method Viewing tight frames as elements of Stiefel manifolds and identifying simply connected spaces.
result Spaces of tight frames, including finite unit-norm tight frames, are simply connected.
Gradient descent constructs tight fusion frames.
problem Constructing tight fusion frames from prescribed subspaces.
method Gradient descent and symplectic geometry.
result Gradient descent can be used to construct tight fusion frames.
New invariants defined for framed knots and links.
problem Defining invariants for framed knots and links.
method Introducing birack brackets and categorifying their multiset.
result Quiver-valued invariant defined for framed knots and links.
Study reveals LLM personas have two distinct components: frame-robust aggregated traits and frame-dependent geometric features.
problem Evaluation of LLM personas via psychometric questionnaires discards within-instance correlation structure.
method Constructed within-instance correlation matrices from IPIP-50 responses and analyzed geometry on SPD manifolds under manipulated question orderings.
result Persona expression comprises two dissociable components: aggregated features (Big Five scores) and geometric features (SPD manifold).
It is now much easier than ever before to produce videos. While the ubiquitous video data is a great source for information discovery and extraction, the computational challenges are unparalleled. Automatically summarizing the videos has become a substantial need for browsing, searching, and indexing visual content. Th…
Higher-dimensional Milnor frames are characterized and contrasted with 3D Heisenberg and 4D nilpotent Lie algebras.
problem Characterizing higher-dimensional Milnor frames and their properties.
method Definition and classification of higher-dimensional Milnor frames and their relationship to known Lie algebras.
result Higher-dimensional Milnor frames are isomorphic to direct sums of 3D Heisenberg and 4D nilpotent Lie algebras and an abelian Lie algebra.
Canonical framings and stable framings for the tangent bundle of a spin 3-manifold are introduced, and illustrated by a number of familiar examples. Methods for constructing canonical framings, and for comparing them with other naturally defined framings, are discussed.
Study on focal surfaces of lightcone framed surfaces in Lorentz-Minkowski 3-space.
problem Investigate differential geometry properties of focal surfaces of lightcone framed surfaces.
method Introduced lightcone frame to define lightcone framed surfaces, then investigated their differential geometry properties.
result Investigated differential geometry properties of focal surfaces of lightcone framed surfaces.
The paper shows that random frames have full spark with high probability.
problem The probability of a random frame having full spark.
method Relating frame spaces to toric symplectic manifolds to analyze geometric and spectral properties.
result The probability of a random frame having full spark is one.
The paper connects hyperbolic spinors to non-null framed curves in Minkowski 3-space.
problem Understanding geometric properties of non-null framed curves.
method Developed new adapted frames for non-null framed curves and investigated their hyperbolic spinor representations.
result Found geometric results and interpretations for non-null framed curves.
Ego-CNN detects critical structures in graphs efficiently.
problem Lack of precise detection of critical structures in existing graph embedding models.
method Ego-CNN uses ego-convolutions at each layer and stacks them in an ego-centric way.
result Ego-CNN achieves comparable task performance to state-of-the-art models and can incorporate scale-free priors.
This note is dedicated to the study of a Hopf module structures on the space of framed chord diagrams and framed graphs. We also introduce a framed version of the chromatic polynomial and propose two methods to construct framed weight systems.
Clarifies Einstein-Cartan gravitation with Dirac spinor on generalized frame bundle.
problem Formulating Einstein-Cartan gravitation on a frame bundle.
method Integrates Dirac spinor into the Einstein-Cartan spacetime structure.
result Variational equations imply standard field equations under standard frame bundle condition.
Introduces formal frames for manifolds and their properties.
problem Understanding and generalizing frames and connections on manifolds.
method Introduces formal frames, canonical forms, and torsions.
result Equivalence of vanishing torsions to realizability of formal frames as ordinary frames.
Frame-spun knots are constructed by spinning a knot of lower dimension about a framed submanifold of S^n. We show that all frame-spun knots are slice (null-cobordant).
Generalized Frenet frames for singular space curves
problem Revisiting the Frenet frame for singular space curves
method Introducing a generalized Frenet frame and frame sequence
result Unified framework for Frenet and Bishop frames
Study of lightcone framed surfaces in Lorentz-Minkowski 3-space, focusing on curvature behavior.
problem Investigate differential geometric properties of lightcone framed surfaces.
method Introduced modified frame to study the properties of lightcone framed surfaces.
result Showed behavior of Gaussian and mean curvatures at lightlike and singular points.
Modified knotoids with framing and coframing for quantum invariants.
problem Defining and classifying knotoids with framing.
method Defining framed and biframed knotoids, showing topological correspondence, and constructing quantum invariants.
result Generalized quantum knotoid invariants constructed.
The paper studies circular evolutes and involutes of framed curves in Euclidean space.
problem Investigating properties of framed curves and their evolutes and involutes.
method Definition and analysis of circular evolutes and involutes of framed curves, properties of normal surfaces, and their relations.
result Circular evolutes and involutes of framed curves are opposite operations under suitable assumptions, similar to fronts in the Euclidean plane.
The generic singularities and bifurcations are classified for one-parameter families of curves with frames in a space form, the Euclidean space, the elliptic space or the hyperbolic space via projective geometry. Two kinds of frames are considered, adapted frames and osculating frames, in terms of certain differential …
The paper explores Parseval frames on vector bundles, proving their existence for certain cases.
problem Existence of Parseval frames on vector bundles.
method Using G-bundles and algebraic topology, the authors prove the existence of Parseval frames for orientable vector bundles and provide conditions for smaller size frames. result The existence of Parseval frames for orientable vector bundles and conditions for smaller size frames.
Quantizes neural networks using frame theory for improved accuracy.
problem Improving neural network efficiency and accuracy through quantization.
method Sigma-Delta (ΣΔ) quantization with finite unit-norm tight frames. result Error bound between original and quantized neural networks derived.
In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general the …
It is well-known that a knot in a contact manifold (M,C) transverse to a trivialized contact structure possesses the natural framing given by the first of the trivialization vectors along the knot. If the Euler class eC∈H2(M) of C is nonzero, then C is nontrvivializable and the natural framing of transvers…
Study on singular points of translation surfaces under linearly dependent conditions.
problem Investigate singular points of translation surfaces under linearly dependent conditions.
method Use theories of generalised framed surfaces and framed surfaces.
result Introduce translation generalised framed surfaces and investigate their singular points.
Paper proposes a CNN-based method for estimating intra frame bits and quality.
problem Efficient video delivery and bit allocation in video coding.
method Deep learning approach using CNNs trained on original frames and encoded distortions.
result Accurate estimation of intra frame bits and quality for better bit allocation.
Recent advances in video super-resolution have shown that convolutional neural networks combined with motion compensation are able to merge information from multiple low-resolution (LR) frames to generate high-quality images. Current state-of-the-art methods process a batch of LR frames to generate a single high-resolu…