Improved TSC with BOSS and SP techniques.
problem Comparing BOP and BOSS for time series classification.
method Deconstructed and measured components of BOP and BOSS, adapted CV techniques.
result SP with BOSS significantly more accurate than benchmarks.
Study approximates operator learning for PDEs using Fourier multipliers.
problem Approximating operator behavior for PDE simulations.
method Approximation of operator symbols in Fourier domain using semi-norms.
result Identifies conditions for achieving predefined approximation error.
The paper connects quantum 6 j 6j 6 j -symbols to tetrahedra volumes via discrete Fourier transforms.
problem Understanding the asymptotic behavior of quantum 6 j 6j 6 j -symbols and their relation to 3-manifold invariants. method Proposing and proving a conjecture linking discrete Fourier transforms of quantum 6 j 6j 6 j -symbols to the volumes of deeply truncated tetrahedra. result Supporting evidence for the conjecture in specific cases, with numerical calculations for larger dihedral angles.
EPSTE: A geometric token and deep learning approach to estimating transfer entropy in neuroimaging time series
problem Inferring directed interactions between neural systems from EEG and MEG
method Reframing TE estimation as a learnable problem operating on structured symbolic representations
result EPSTE achieves near-perfect recovery of ground-truth directed structure and significantly lower absolute error than the baseline
QABBA improves time series storage efficiency while preserving shape information.
problem Efficient storage and shape preservation of time series data.
method Quantized symbolic time series approximation (QABBA) using ABBA technique.
result QABBA achieves a new state-of-the-art on Monash regression dataset.
Improved scalability of BOSS ensemble for time series classification.
problem Non-trivial scalability issues in BOSS and WEASEL.
method Random selection of classifiers, ensembling techniques, and build time reduction.
result Significant reduction in build time with minimal accuracy loss.
Symbolic regression finds simple formulas for implied volatility.
problem Discovering accurate parametric representations for implied volatility.
method Symbolic regression to find analytic formulas from market data.
result Symbolic regression identifies compact parametrizations with competitive fitting performance.
Bayesian symbolic regression automates model discovery from data.
problem Learning closed-form mathematical models from data using heuristic methods.
method Probabilistic approach to symbolic regression, connecting to information theory and statistical physics.
result Probabilistic approach provides model plausibility and performance guarantees.
New IT representation improves symbolic regression approximations.
problem Finding better approximations to real-world data sets.
method Evolutionary Algorithm with IT representation using only mutation.
result IT representation finds better approximations than traditional methods.
Neural networks learn symbolic structure to perform compositional tasks.
problem How neural networks perform well on compositional tasks without explicit representations.
method ROLE analysis to uncover symbolic structure in recurrent neural networks.
result Neural networks converge to solutions that implicitly represent symbolic structure.
Symbolic regression constructs smooth value functions for reinforcement learning.
problem Function approximators in reinforcement learning are black-box models with hyper-parameter tuning.
method Symbolic regression methods for constructing smooth value functions in the form of analytic expressions.
result Symbolic regression methods yield well-performing policies and are compact and mathematically tractable.
ABBA creates a new symbolic time series representation based on Brownian bridge.
problem Representing time series data in a compact, symbolic form.
method Adaptive polygonal chain approximation followed by mean-based clustering.
result ABBA outperforms other representations in preserving time series shape information.
We show that the index of an elliptic Fourier integral operator associated to a contact diffeomorphism φ φ φ of cosphere bundles of two Riemannian manifolds X and Y is given by ∫ B ∗ X A ^ ( T ∗ X ) exp θ − ∫ B ∗ Y A ^ ( T ∗ Y ) exp θ \int_{B^*X}\hat{A}(T^*X)\expθ - \int_{B^*Y}\hat{A}(T^*Y)\expθ ∫ B ∗ X A ^ ( T ∗ X ) exp θ − ∫ B ∗ Y A ^ ( T ∗ Y ) exp θ . Here B ∗ B^* B ∗ stands for the unit coball bundle and θ θ θ is a certain characteristic…
VaSST uses soft symbolic trees for probabilistic symbolic regression.
problem Efficiently recover symbolic expressions from noisy data.
method Variational inference with soft symbolic trees.
result Superior performance in structural recovery and predictive accuracy.
Shape-constrained symbolic regression improves model extrapolation with prior knowledge.
problem Improving model extrapolation with prior knowledge in symbolic regression.
method Shape-constrained symbolic regression using evolutionary algorithms with interval arithmetic.
result Models with shape constraints have improved extrapolation but lower accuracy on test sets.
The paper proposes and proves asymptotic expansions for quantum invariants.
problem Quantum invariants and their expansions under varying metrics.
method Asymptotic expansion conjectures for relative Reshetikhin-Turaev, Turaev-Viro invariants and quantum 6j-symbols.
result Proved asymptotic expansions for special cases, showing geometric dependence on metrics.
Unified framework integrates symbolic planning and HRL for robust decision-making.
problem Combining reinforcement learning and symbolic planning for robust decision-making in dynamic environments.
method Integrates symbolic planning with hierarchical reinforcement learning to guide task execution and improve planning.
result Unified framework leads to rapid policy search and robust symbolic plans in complex domains.
Co-eye combines multiple symbolic representations to improve time series classification accuracy.
problem Challenges in time series classification due to domain diversity.
method Inspired by compound eyes, Co-eye uses multiple symbolic representations and hyper-parameterised lenses to classify time series data.
result Co-eye outperforms state-of-the-art techniques in accuracy and robustness across various domains.
Upper bound conjecture for Yokota invariant proved for polyhedral graphs.
problem Growth of Yokota invariant of polyhedral graphs
method Barrett's Fourier transform
result Proved upper bound conjecture for large family of examples
MARLeME extracts MARL models into symbolic models for better interpretability.
problem Improving interpretability and explainability of MARL systems.
method Develops a MARL model extraction library that approximates MARL systems with symbolic models.
result Enhanced understanding and inspection of MARL systems and agents.
Study evaluates clustering methods for Google Trends data.
problem Clustering high-dimensional, noisy time series data.
method Symbolic Aggregate Approximation (SAX), Enhanced SAX (eSAX), and Topological Data Analysis (TDA).
result TDA provides more balanced and meaningful groupings than SAX and eSAX.
We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in problems with large number of variables, we find that by constraini…
Paper closes neural-symbolic learning loop with grammar model and back-search algorithm.
problem Slow convergence in neural-symbolic learning due to error propagation issues.
method Introduces grammar model as symbolic prior and back-search algorithm for efficient error propagation.
result Significantly outperforms RL methods in performance, converging speed, and data efficiency.
Geometric symbols help compute heat invariants.
problem Computing heat invariants efficiently.
method Geometric symbol calculus of pseudodifferential operators.
result Efficient computation of heat invariants.
Deep neural network generates symbolic equations from data.
problem Lack of insight into underlying mappings from traditional deep learning.
method Combines deep learning flexibility with symbolic solutions.
result Accurately generates governing equations for dynamical systems.
For an arbitrary Riemannian manifold X X X and Hermitian vector bundles E E E and F F F over X X X we define the notion of the normal symbol of a pseudodifferential operator P P P from E E E to F F F . The normal symbol of P P P is a certain smooth function from the cotangent bundle T ∗ X T^*X T ∗ X to the homomorphism bundle H o m ( E , F ) Hom (E,F) H o m ( E , F ) and dep…
Based on the ideas of Optimal Control, we introduce the new basic characteristic of a bracket generating distribution, the Jacobi symbol. In contrast to the classical Tanaka symbol, the set of Jacobi symbols is discrete and classifiable. We give an explicit and unified algebraic procedure for the construction of the ca…
New algorithms improve time series classification accuracy and efficiency while enhancing interpretability.
problem Lack of interpretability in time series classification algorithms.
method Combining multiple resolutions and domains, using SEQL with greedy feature selection.
result SAX-SFA-SEQL achieves similar accuracy to state-of-the-art methods but with lower computational time.
In this paper we give formulae for the Dixmier trace and the noncommutative residue (also called Wodzicki's residue) of pseudo-differential operators by using the notion of global symbol. We consider both cases, compact manifolds with or without boundary. Our analysis on the Dixmier trace of invariant pseudo-differenti…
Symbolic knowledge in neural models can inadvertently make them more vulnerable to adversarial attacks.
problem Symbolic knowledge in neural models can make models more susceptible to adversarial attacks.
method Investigated deep probabilistic graphical models that incorporate symbolic knowledge and neural nets.
result Symbolic knowledge can propagate the negative effects of adversarial examples, making models more vulnerable.
Study light ray transform in pseudo-Euclidean space, derive inversion formula, and prove stability.
problem Analyzing light ray transform in pseudo-Euclidean space.
method Investigate normal operator, derive inversion formula, analyze as Fourier Integral Operator.
result Derive an inversion formula and prove stability estimates.
We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field Q ( − 3 ) \mathbb{Q}(\sqrt{-3}) Q ( − 3 ) , following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and Rédei's triple symbol, and describes the decomposition…
New technique finds globally optimal symbolic equations.
problem Finding globally optimal mathematical expressions.
method Formulated a mixed integer non-linear program (MINLP).
result Guaranteed global optimality in symbolic regression.
Researchers extend asymptotic analysis to Bergman projections with Gevrey weights.
problem Analyzing Bergman projections with Gevrey weights.
method Extending direct approach to semiclassical asymptotics to Gevrey weights using Fourier integral operators.
result Gevrey symbol amplitude of asymptotic Bergman projection with Gevrey weights and Gevrey-type growth rate.
A formula for Rademacher symbols in triangle groups is provided.
problem No specific problem stated; focuses on a mathematical formula.
method Presentation of an explicit formula for Rademacher symbols.
result Generalizes Ghys' proof of modular knot linking numbers.
The symbolic dynamics technique is well-known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully applied to time series generated by complex systems of much higher dimensionality. Ou…
Complex b b b - 6 j 6j 6 j symbols relate to hyperbolic tetrahedron volumes and determinants.
problem Analyzing asymptotics of complex b b b - 6 j 6j 6 j symbols. method Relating asymptotics to hyperbolic tetrahedron volumes and determinants.
result Complex b b b - 6 j 6j 6 j symbols' asymptotics linked to tetrahedron volumes and determinants. The paper classifies symbols of differential operators on vector bundles.
problem Classifying symbols of linear differential operators on vector bundles.
method Associated tuples of linear operators to non-degenerate symbols and used C. Procesi's results to find rational invariants and equivalence criteria.
result Generators for rational invariants and a criterion for symbol equivalence.
NeSS combines neural and symbolic approaches for better compositional generalization.
problem Lack of compositional generalization in deep learning models.
method NeSS uses a neural network to generate traces, executed by a symbolic stack machine with sequence manipulation.
result Achieves 100% generalization performance across multiple domains.
Defines transverse symbols for foliated manifolds and proves their K-homology class.
problem Transverse index theory for foliated manifolds.
method Using filtrations of tangent bundles, defining transverse symbols, and constructing equivariant KK-classes.
result Transversally Rockland operators yield a K-homology class and there is a Poincare duality result.
A new method for spotting symbols in CAD images reduces annotation costs and improves accuracy.
problem Challenging task of labeling symbols from CAD drawings.
method Pixel-wise point location via Progressive Gaussian Kernels (PGK) and local offset.
result The proposed method achieves good generalization on real-world CAD images.
Revel tackles safe exploration in RL with verified symbolic policies.
problem Computational infeasibility of verifying neural networks in RL learning loops.
method Two policy classes: neurosymbolic with approximate gradients and symbolic policies for efficient verification. Mirror descent over policies to safely update and project policies.
result Revel discovers policies that outperform prior approaches to verified exploration.
Paper proposes a bijective approach for signal/symbol translation using variational auto-encoders.
problem Extracting symbolic information from signals, especially in music, is challenging and non-generic.
method Turned into a density estimation task, using two variational auto-encoders with additive constraint.
result Bijective signal/symbol translation achieved, allowing both signal-to-symbol and symbol-to-signal inference.
The Wodzicki residue and the cut-off integral extend to classical symbol-valued forms. We show that they obey a Stokes' type property and that the extended Wodzicki residue can be interpreted as a complex residue like the ordinary one. In the case of cut-off integrals, Stokes' property (i.e. vanishing on exact forms) o…
Perceptor Gradients learns symbolic representations from raw data.
problem Learning transferable symbolic representations from raw data.
method Decomposes policy into perceptor network and task encoding program.
result Efficiently learns symbolic representations for control tasks.
In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform fast search, and recognition in very high dimensional spaces. The problem is ma…
Study compares symbolic and distributional methods for relational learning.
problem Comparing symbolic and distributional paradigms for relational learning.
method Comparison of representation learning and relational learning on various tasks.
result Preliminary results suggest possible indicators for choosing between approaches.
New SDA models for big data analysis using aggregated symbols.
problem Handling large and complex datasets efficiently.
method Developing likelihood functions for symbolic data based on underlying measurement-level data.
result Efficient analysis of big data through reduced distributional summaries.