A new learning framework uses a teacher to guide learners through rounds of exposure to data.
problem Computational intractability of supervised learning.
method Curricular phases with a teacher guiding exposure to data.
result Simple learners can acquire complex concepts efficiently from examples.
Introduces semi-abelian generalized complex structures.
problem Deformation theory of abelian complex structures.
method Definition and examples of semi-abelian generalized complex structures.
result Illustration of new concept with examples.
Average-case information complexity for learning is bounded, revealing only O(d) bits for most concepts.
problem Understanding the average-case information leakage in learning algorithms for concept classes.
method Developed a learning algorithm that reveals O(d) bits of information for most concepts in a class of VC-dimension d.
result Most concepts in the class do not require large amounts of information leakage, revealing only O(d) bits on average.
We developed a caching method to speed up concept learning in complex knowledge bases.
problem Complex concept learning requires many instance retrieval calls, increasing runtime.
method Semantics-aware caching that links concepts to instances via crisp set operations.
result Our cache reduces concept retrieval and learning runtime by an order of magnitude.
A new approach switches between simple and complex models to handle concept drifts in regression tasks.
problem Handling concept drifts in regression models to maintain accurate predictions over time.
method Error Intersection Approach: switches between simple and complex models based on drift detection.
result The Error Intersection Approach significantly outperforms baselines in handling concept drifts in a real-world taxi demand dataset.
Researchers apply concept-based explainability to EEG data.
problem Understanding the internal states of complex EEG transformer models.
method Concept Activation Vectors (CAVs) adapted for EEG data, using externally labeled datasets and anatomically defined concepts.
result Both approaches to concept formation yield valuable insights into EEG model representations.
Energy-based models can generate complex images by combining simpler concepts.
problem Generating natural images that satisfy complex logical combinations of concepts.
method Energy-based models combine probability distributions of simpler concepts to generate compositions.
result Energy-based models can generate images that satisfy conjunctions, disjunctions, and negations of concepts.
Minimal learning agents can infer unobserved variables in complex environments.
problem How to infer unobserved variables in complex environments using minimal learning agents.
method Concrete operational definition of abstract concepts, minimal architecture supporting abstraction, reinforcement learning.
result Minimal learning agents can infer the existence of unobserved variables.
We develop an alternative approach to Degenerate complex Monge-Ampère equations on compact Kähler manifolds based on the concept of viscosity solutions and compare systematically viscosity concepts with pluripotential theoretic ones. We generalize to the Kähler case a theorem due to Dinew and Zhang in the projective ca…
System solves a significant fraction of Bongard problems using visual features and pragmatic reasoning.
problem Solving Bongard problems with intelligent vision systems.
method Image processing, symbolic visual vocabulary, Bayesian inference, pragmatic reasoning.
result Good agreement between induced concepts and Bongard's solutions.
Study learning and refutation in non-interactive LDP, showing sample complexity equivalence.
problem Characterize sample complexity for learning and refutation in non-interactive LDP.
method Characterize sample complexity for agnostic PAC learning in non-interactive LDP protocols.
result Optimal sample complexity for any concept class is captured by the approximate γ2~norm of a natural matrix associated with the class. ECBMs unify concept-based interpretations in deep learning models.
problem Suboptimal final accuracy and lack of concept interaction and conditional dependencies.
method ECBMs use a set of neural networks to define joint energy, enabling concept correction and conditional dependency quantification.
result ECBMs achieve higher accuracy and richer concept interpretations compared to state-of-the-art methods.
The increasing interest in complex networks research has been a consequence of several intrinsic features of this area, such as the generality of the approach to represent and model virtually any discrete system, and the incorporation of concepts and methods deriving from many areas, from statistical physics to sociolo…
Script Geometry offers a new approach to discrete differential geometry.
problem Classic approaches to discrete differential geometry have limitations.
method Script Geometry uses complexes of cells and minimality conditions called tightness.
result Script Geometry provides an equivalence to the Poincare lemma and new function theory.
This work improves interpretability in deep learning models by introducing a two-level concept discovery framework.
problem High complexity and lack of interpretability in deep learning models, especially for safety-critical tasks.
method Concept Bottleneck Models (CBMs) framework combining vision-language models and data-driven coarse-to-fine concept selection.
result The proposed framework outperforms recent CBM approaches and provides a principled interpretability.
We deal with smooth real manifolds as well as complex analytic manifolds as well. It is well known that the concept of star product is powerful enough to produce all Poisson structures on real manifolds. According to [BdM] it is not known whether holomorphic star products exist on complex analytic manifolds. The main p…
A theory for approximating complex concepts with simple decision trees.
problem Approximating complex concepts with simple decision trees.
method Introducing interpretable approximations, studying binary concept approximation by decision trees.
result A trichotomy of cases for approximating a binary concept by decision trees based on a simple class.
This paper is devoted to dualization of paracompactness to the coarse category via the concept of R-disjointness. Property A of G.Yu can be seen as a coarse variant of amenability via partitions of unity and leads to a dualization of paracompactness via partitions of unity. On the other hand, finite decomposition com…
PAC learning sample complexity is decidable with finite support bounds.
problem Determining the exact sample complexity for PAC learning concepts.
method Observation and proof of decidability with a-priori bounds.
result Sample complexity can be exactly determined for various concepts with finite support bounds.
Paper shows SGD can learn RNNs efficiently for certain functions.
problem Understanding what concept class RNNs can learn and how efficiently.
method Vanilla stochastic gradient descent (SGD) approach.
result RNNs can learn some functions efficiently with polynomial complexity in input length.
Study on teaching complexity in graphs, proving hardness and tractability.
problem Computing the minimum number of examples per concept for teaching.
method Classical and parameterized complexity analysis, NP-hardness, upper and lower bounds, fixed-parameter tractability.
result Nearly complete understanding of teaching complexity in graphs.
The abstract aims to generalize classical curve concepts to uniquely define complex curves.
problem Lack of sufficient information to distinguish between different curves.
method Generalizing classical concepts of curvature and torsion to higher algebraic curvatures.
result Each analytic branch of a complex curve is uniquely defined by higher algebraic curvatures.
Concepts simplify complex models for better understanding.
problem Difficulty in generating understandable explanations for high-dimensional tabular datasets with correlated variables.
method Introduces concepts as groupings of correlated variables and embeds them in a surrogate decision tree.
result Improvement in human interpretability of surrogates without sacrificing accuracy and fidelity.
This paper explores Khovanov adequacy in knot theory.
problem Understanding Khovanov homology and its adequacy.
method Using independence complexes and homotopy type calculations.
result Khovanov adequacy is explored within the context of independence complexes and homotopy type of extreme spectra.
Improved multi-group learning with group-realizable concepts.
problem Enhancing multi-group learning efficiency.
method Empirical risk minimization over group-realizable concepts.
result Improved sample complexity in group-realizable settings.
Single spiking neuron outperforms ConvNets in counting weakly labeled concepts.
problem Counting weakly labeled concepts in MNIST task.
method Improved gradient-based local learning rule for leaky integrate and fire model.
result Single spiking neuron outperforms conventional ConvNets in MNIST counting task.
Net2Vec maps filters to vectors to reveal complex concept encoding.
problem Understanding how deep neural networks encode semantic concepts.
method Net2Vec framework that maps semantic concepts to vectorial embeddings based on filter responses.
result Multiple filters are often required to code for a concept, and filters help encode multiple concepts.
New method for visualizing high-level concepts in generative models.
problem Challenges in evaluating and visualizing concepts in generative models.
method Introduces a method to compute concept saliency maps for latent representations of known or novel high-level concepts.
result Concept saliency maps highlight input features important for high-level concepts.
Defines explanations for classifier outcomes using causal concepts.
problem Understanding classifier outcomes in a causal context.
method Proposes a new definition of explanation based on causality, compares it with existing notions, and evaluates it experimentally.
result Experimental evaluation shows the new definition's effectiveness on financial datasets.
Learn conditional averages in PAC framework for better predictions.
problem Learning average labels over neighborhoods in unknown concept class.
method Characterization of learnability using combinatorial parameters.
result Complete characterization and sample complexity bounds.
Study expands multiclass classification models with new rates and partial concept classes.
problem Multiclass classification with a bounded number of labels under various conditions.
method Extends traditional PAC model to distribution-dependent and data-dependent learning rates, characterizes optimal rates for universal and partial concept classes.
result Characterizes three types of learning rates (exponential, linear, arbitrarily slow) for fixed distributions and complexity measures for partial concept classes.
Improved agnostic learning time via Gaussian surface area analysis.
problem Learning polynomial threshold functions under Gaussian marginals.
method Improvement of polynomial degree required for approximation.
result Near optimal bounds on agnostic learning complexity.
In this paper, we introduce a new concept so called harmonic complex structure by using harmonic theory for vector bundle-valued differential forms. It is a new structure intermediates between complex structure and Kähler structure. From differential geometric viewpoint, it is a natural generalization of Kähler structu…
New bounds on query learning complexity for various concept classes.
problem Learning complexity in query learning models.
method Introducing new combinatorial quantities and proving lower and upper bounds.
result New and shorter proofs of efficient learnability for prominent examples.
Paper shows pre-training and transfer learning reduce sample complexity for neural networks.
problem Training high-dimensional supervised learning with limited labeled data.
method Study of single-layer neural networks via online stochastic gradient descent, considering concept shift.
result Pre-training and transfer learning reduce sample complexity by polynomial factors under general assumptions.
The Hodge theorem connects cohomology groups on compact Kähler manifolds.
problem Establishing a relationship between cohomology groups on compact Kähler manifolds.
method Proving the Hodge decomposition theorem on compact d-Kähler manifolds.
result Hodge decomposition theorem on compact d-Kähler manifolds.
Paper proposes SGP-Q for efficient online anomaly detection with concept drift adaptation.
problem Efficient online anomaly detection for time-series data with concept drift.
method Sparse Gaussian processes with Q-function (SGP-Q).
result SGP-Q achieves better anomaly detection results with concept drift adaptation.
Method makes non-interpretable models more intervenable.
problem Making non-interpretable models more understandable and controllable.
method Intervenability formalization and fine-tuning of black-box models.
result Fine-tuned black-box models are more intervenable and often better-calibrated.
Introduces Grassmann Distance Complexity to measure algebraic set nearest point problems.
problem Measuring complexity of finding nearest points in Grassmannian space.
method Uses Lipschitz critical point theory and o-minimal geometry.
result Establishes fundamental properties of GDC, including bounds and finiteness conditions.
TCAV uses CAVs to interpret deep learning models by testing for concept importance.
problem Interpreting deep learning models due to their complexity and opaque internal state.
method Testing with CAVs (TCAV) using directional derivatives to quantify concept importance.
result Shows how CAVs can be used to explore hypotheses and generate insights in image classification and medical applications.
Formalizes concepts as latent variables in hierarchical models for high-dimensional data.
problem Lack of formalization and theoretical insights for learning discrete concepts from high-dimensional data.
method Formalizes concepts as latent causal variables in a hierarchical model, formulates conditions for concept identification.
result Conditions for identifying latent hierarchical models in unsupervised data, handling complex structures and high-dimensional data.
Proposes SGShift to identify shifted features causing model performance degradation under concept shift.
problem Concept shift leading to miscalibration in ML models across domains.
method SGShift method for identifying sparse set of shifted features using feature selection and statistical tools.
result SGShift identifies shifted features more accurately than baseline methods, requires few samples in the shifted domain, and is robust to complex cases.
New method for simplifying complex 4D shapes with boundaries.
problem Complexity reduction in 4D shape analysis.
method Introducing pseudo-trisections and pseudo-bridge trisections.
result Existence and uniqueness of pseudo-trisections established.
Extracts salient concepts from CNNs for explaining deep neural networks.
problem Explaining the opaque behavior of deep neural networks in safety-critical domains.
method Uses autoencoders to extract salient concepts and builds a Bayesian causal model.
result Identifies and visualizes features influencing deep neural network classifications.
COMET learns concepts for few-shot learning, improving performance.
problem Few-shot learning challenges in machine learning.
method Meta-learning with human-interpretable concept dimensions.
result Significant improvement in 1-shot learning tasks.
Paper generalizes toric concepts to nonrational settings.
problem Nonrational toric structures.
method Algebraic geometry perspective.
result Reframed symplectic and complex toric quasifolds.
Characterizes alternating link exteriors using cubed complexes.
problem Understanding the structure of alternating link exteriors.
method Introducing signed BW cubed-complexes and characterizing their homeomorphism to link exteriors.
result Characterization of alternating link exteriors in terms of cubed complexes.
New approach for testable learning using moment matching and Rademacher complexity.
problem Replacing hard-to-verify distributional assumptions with testable ones.
method Moment matching and metric distances in probability.
result Improved sample complexity bounds for various concept classes and distributions.