Analogator learns to make analogies by example.
problem Developing a computer program to learn analogies.
method Connectionist approach using a recurrent network architecture trained to divide scenes into figure and ground.
result Analogator can make new analogies between novel situations.
Analog method solves portfolio optimization problems faster and more efficiently.
problem Accurate covariance matrix estimation and fast optimal portfolio selection for financial applications.
method Two-step process using equilibrium propagation and analog Hopfield networks.
result Fully analog pipeline calculates optimal portfolios in energy-efficient manner.
Analog arrays speed up ConvNets by parallelizing kernel matrix training.
problem Early ConvNets struggle with analog arrays due to small kernel matrices.
method Replicate kernel matrix on multiple analog arrays, training in parallel.
result Analog arrays achieve high acceleration factors (16-128) for ConvNets.
This thesis optimizes neuromorphic systems by slowing down their dynamics, improving performance.
problem Timescale mismatch between analog neuromorphic circuits and real-time sensory inputs.
method Proposes and tests solutions to slow down the dynamics of spiking neural networks.
result Spiking neural networks on analog neuromorphic systems can achieve significant performance boosts.
Fault-tolerant neural networks inspired by biological error correction codes.
problem Achieving reliable computation with unreliable neurons.
method Using biological error correction codes from grid cells in the mammalian cortex to develop a fault-tolerant neural network.
result Noisy biological neurons operate below a fault-tolerance threshold, suggesting a mechanism for reliable computation in the brain.
Defines an odd analog of Plamenevskaya's invariant for transverse links.
problem No specific problem stated; focuses on extending an invariant.
method Defines and analyzes an odd analog invariant in Khovanov homology.
result The odd analog invariant is an invariant of transverse links with similar properties.
EC^2-VAE generates music analogies by disentangling pitch and rhythm representations.
problem Disentangling music representations for generating creative analogies.
method Explicitly-constrained variational autoencoder (EC^2-VAE) for disentangling pitch and rhythm representations.
result EC^2-VAE enables the generation of music analogies by borrowing representations from different pieces.
Improves RNN performance under noisy computations.
problem Power and speed limitations in deep learning with noisy analog circuits.
method Deep Noise Injection training to robustify RNN weights/biases.
result Trained RNNs show more consistent performance under noisy inference.
Hierarchical spiking networks resist physical distortions for neuromorphic computing.
problem Distortions in physical neuromorphic implementations of spiking networks.
method Used hierarchical leaky integrate-and-fire neurons to create robust spiking networks.
result Hierarchical spiking networks are robust to physical distortions.
Analog deep learning shows promise but faces scalability challenges.
problem Bottlenecks in deep neural networks' calculation and optimization.
method Evaluation of eight analog deep learning methodologies.
result Analog deep learning has potential for consumer-level applications but scalability remains an issue.
The Spencer cohomology of certain graded Lie superalgebras are completely computed. This cohomology is interpreted as analogs of Riemann and Penrose tensors on supermanifolds. The results make it manifest that there is no simple generalization of Borel-Weil-Bott's theorem for Lie superalgebras.
New method uses surrogate gradients to train efficient spiking networks on neuromorphic hardware.
problem Training high-performing spiking networks on analog neuromorphic hardware is challenging due to device mismatch and lack of efficient algorithms.
method Introduces a general in-the-loop learning framework based on surrogate gradients.
result Learning self-corrects for device mismatch, resulting in competitive spiking network performance.
Bayesian optimization with neural networks improves analog circuit synthesis efficiency.
problem Analog circuit synthesis optimization with improved efficiency.
method Bayesian optimization using neural networks to learn and predict circuit parameters.
result Neural-network-based Gaussian process model provides more accurate predictions and accelerates optimization.
New method finds analogies from product descriptions to spur innovation.
problem Finding useful analogies in large, messy repositories.
method Crowdsourcing and recurrent neural networks to extract purpose and mechanism vector representations.
result Learned vectors allow for higher precision and recall of analogies.
Paper proposes a training framework for deploying DNNs on analog NVM crossbars, achieving significant efficiency gains.
problem Challenges in deploying deep learning models on microcontrollers due to limited compute and memory resources.
method Developed a training algorithm to eliminate tuning and propose unipolar-weighted matrices to reduce crossbar area and simplify hardware.
result Achieved up to 92.91% accuracy with 2-bit crossbars and up to 45% energy reduction.
Paper reviews neuromorphic engineering features and compares analog vs digital systems.
problem Lack of consensus and unclear features in neuromorphic engineering.
method Review of recent work, comparison of machine learning accelerator chips.
result Analog processing and reduced bit precision architectures offer best efficiencies.
Paper tackles noisy neural networks and proposes a method to enhance their robustness.
problem Noisy neural networks struggle with random continuous noise in weights.
method Knowledge distillation combined with noise injection during training.
result Models achieve up to twice greater noise tolerance.
We constructed an analog electrical circuit which generates fluctuations in which probability density function has power law tails. In the circuit fluctuations with an arbitrary exponent of the power law can be obtained by adjusting the resistance. With this low cost circuit the random fluctuations which have the simil…
Novel algorithm for privacy-preserving distributed learning in analog domain.
problem Privacy-preserving distributed learning over analog data.
method Proposes a novel algorithm for analog data, leveraging real/complex number representation and information-theoretic security metrics.
result Demonstrates a fundamental trade-off between privacy and accuracy in analog domain distributed learning.
I survey methods from differential geometry, algebraic geometry and representation theory relevant for the permanent v. determinant problem from computer science, an algebraic analog of the P v. NP problem.
AnEn uses past analogs for weather forecasting, but this work replaces the dataset with deep generative models.
problem Memory and computational costs for storing and searching historical data.
method Deep generative models to replace historical data and analogs search.
result Generative models reduce memory and computational costs significantly.
Study noise in inference to improve accuracy and security.
problem Noise in inference affects deep learning systems' accuracy and security.
method Noise-injected training and voting method for improving accuracy; defensive architecture for adversarial attacks.
result Significant improvement in accuracy and robustness against attacks.
A new SNN learning algorithm for energy-efficient VLSI circuits.
problem Designing energy-efficient SNNs for VLSI implementation.
method Temporal coding, analog VLSI, resistive memory.
result Classification accuracy comparable to state-of-the-art temporal coding SNN algorithms.
Computes mapping class groups of 4-manifolds with boundary.
problem Computing mapping class groups for 4-manifolds with boundary.
method Topological and smooth methods applied to compact, simply connected 4-manifolds.
result Description of topological and stable smooth mapping class groups.
Analog forecasting uses local dynamics to predict chaotic systems.
problem Theoretical connections between analog forecasting and dynamical systems are overlooked.
method Local approximations of the system's dynamics, linear regression, and estimation of analog forecasting errors.
result Analog forecasting performances are highly linked to the local Jacobian matrix of the flow map.
New formula for dual knots using involutions.
problem Understanding dual knots and their transformations.
method Involutive analog of knot surgery formula.
result Computed local equivalence class for involutive dual knots.
We investigate the analogy between the large N expansion in normal matrix models and the asymptotic expansion of the determinant of the Hilb map, appearing in the study of critical metrics on complex manifolds via projective embeddings. This analogy helps to understand the geometric meaning of the expansion of matrix m…
ADR helps LLMs find and use historical analogies for foresight analysis.
problem LLMs struggle to find relevant historical analogies due to surface-level matching.
method Proposes CANA framework with mechanism alignment and cross-analogy confirmation.
result CANA improves historical analogy generation by up to 10%.
Analog methods improve forecast accuracy in complex models.
problem Improving forecast accuracy in complex models like Lorenz-96.
method Constructing analogs using variational autoencoders for ensemble data assimilation.
result Constructed analogs perform as well as a full ensemble square root filter.
We obtain formulas for the first and second cohomology groups of a general current Lie algebra with coefficients in the "current" module, and apply them to compute structure functions for manifolds of loops with values in compact Hermitian symmetric spaces.
Lattice cohomology, defined by Némethi in (arXiv:0709.0841), is an invariant of negative definite plumbed 3-manifolds which conjecturally computes the Heegaard Floer homology HF^+. We prove a surgery exact triangle for the lattice cohomology analogous to the one for HF^+. This is a step towards comparing these two inva…
The paper evaluates the probability distributions of analog-to-target distances for multiple analogs.
problem Understanding the performance of analog applications through the distribution of distances to target states.
method Theoretical analysis and numerical experiments using dynamical systems theory.
result The size of the catalog and dimensionality affect the probability distributions of the K-best analogs.
Researchers mapped CNNs to resistive devices for training, overcoming noise and bound limitations.
problem Training deep CNNs with resistive cross-point devices.
method Mapped CNN layers to RPU arrays, implemented noise and bound management techniques, and digitally programmable update management.
result Successfully applied RPU concept for training CNNs, enabling broader applicability.
Approximates smooth surfaces using Laguerre geometry meshes.
problem Approximating smooth surfaces in Laguerre geometry.
method Using Laguerre meshes composed of quadrilaterals, cones, and spherical faces.
result Laguerre conjugate nets and directions for surface approximation.
Cyclidic nets are introduced as discrete analogs of curvature line parametrized surfaces and orthogonal coordinate systems. A 2-dimensional cyclidic net is a piecewise smooth C1-surface built from surface patches of Dupin cyclides, each patch being bounded by curvature lines of the supporting cyclide. An explicit de…
Survey on approximability of graph embeddings and related problems.
problem Determining when graphs can be embedded in the plane without intersections.
method Criteria for approximability by embeddings and van Kampen obstruction.
result Completeness of the van Kampen obstruction for approximability by embeddings.
Approximates surfaces using Laguerre geometry with spherical faces.
problem Approximating smooth surfaces using Laguerre geometry.
method Using Laguerre conjugate nets and spherical faces to approximate surfaces.
result Laguerre conjugate nets provide a method for surface approximation.
New method uses analogy kernel for better object ranking.
problem Improving object ranking in preference learning.
method Introduces analogy kernel based on analogical proportions.
result Experimental results show competitive predictive accuracy.
We formulate and prove an analog of the Hopf Index Theorem for Riemannian foliations. We compute the basic Euler characteristic of a closed Riemannian manifold as a sum of indices of a non-degenerate basic vector field at critical leaf closures. The primary tool used to establish this result is an adaptation to foliati…
We prove in a simple and coordinate-free way the equivalence bteween the classical definitions of the mass or the center of mass of an asymptotically flat manifold and their alternative definitions depending on the Ricci tensor and conformal Killing fields. This enables us to prove an analogous statement in the asympto…
Computes Vafa-Witten invariants of 3-manifolds.
problem Computing invariants of 3-manifolds.
method Explicit computations using Vafa-Witten theory.
result Explicit invariants computed for specific 3-manifolds.
A novel Gradient-Based Multiple Access algorithm for distributed learning over fading channels.
problem Distributed learning over multiple access fading channels.
method Gradient-Based Multiple Access (GBMA) algorithm, using analog gradients and common shaping waveforms.
result GBMA can approach the convergence rate of centralized gradient descent in large networks.
Computes derivatives of sections in vector bundles using Lie derivatives.
problem Computing time derivatives of sections in natural vector bundles.
method Extending a lemma to compute Lie derivatives of sections of natural vector bundles.
result Computed derivatives of sections in vector bundles using Lie derivatives.
Researchers compute c-projective symmetry algebras for Kähler surfaces.
problem Understanding symmetries in Kähler surfaces.
method Defined and analyzed c-projective vector fields and computed their symmetries.
result Computed c-projective symmetry algebras for Kähler surfaces with essential c-projective vector fields.
We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkahler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to q…
We present a graph manifold analog of the Jankins-Neumann classification of Seifert fibered spaces over S2 admitting taut foliations, providing a finite recursive formula to compute the L-space Dehn-filling interval for any graph manifold with torus boundary. As an application of a generalization of this result to F…
Complexity of counting homomorphisms in 3-manifold invariants is hard.
problem Computational complexity of counting homomorphisms in 3-manifold invariants.
method Study the action of the mapping class group on homomorphisms, using combinatorial topological quantum field theory.
result Proving #P-completeness of counting homomorphisms for closed 3-manifolds and knot complements. We show that the recently introduced L1TV functional can be used to explicitly compute the flat norm for co-dimension one boundaries. While this observation alone is very useful, other important implications for image analysis and shape statistics include a method for denoising sets which are not boundaries or which ha…