Paper explores how knowledge distillation transfers inductive biases between models.
problem Transferring inductive biases between models for tasks with limited data.
method Knowledge distillation applied to models with different inductive biases (LSTMs vs. Transformers, CNNs vs. MLPs).
result Effect of inductive biases is transferred through knowledge distillation, impacting both performance and solution characteristics.
We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson generalization of the reduction of symplectic manifolds with symmetry. Having as basic tools the equivariant momentum maps of Poisson actions, the double group of a Poisson-Lie group and the reduction of Poisson manifold…
New methods for CI testing under model misspecification.
problem Challenges in CI testing with misspecified models.
method Proposes new approximations and upper bounds for testing errors of regression-based CI tests.
result Introduces the Rao-Blackwellized Predictor Test (RBPT) robust against misspecified inductive biases.
We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the structure of these orbits. In fact, each coadjoint orbit of such a group is obtained b…
Most existing works on disentangled representation learning are solely built upon an marginal independence assumption: all factors in disentangled representations should be statistically independent. This assumption is necessary but definitely not sufficient for the disentangled representations without additional induc…
Paper simplifies and proves Bahri-Xu conjecture for various cases.
problem Universal inequality for p points in R^m
method Simplified conjecture, inductive conditions, reduction to basic case m=1
result Proved conjecture for m=1 with arbitrary p, and for p=4,5 and m≥2
New method stabilizes machine learning for physics-informed inverse problems.
problem Reconstructing physical quantities from PDE-compliant measurements.
method Physics-informed learning with smooth inductive bias.
result PDE operators stabilize variance and prevent overfitting in fixed dimensions.
Conditional Random Fields (CRFs) are undirected graphical models, a special case of which correspond to conditionally-trained finite state machines. A key advantage of these models is their great flexibility to include a wide array of overlapping, multi-granularity, non-independent features of the input. In face of thi…
Improved stability and generalization for blackbox learned optimizers.
problem Stability and generalization issues in blackbox learned optimizers.
method Investigation using dynamical systems, modifications to optimizer architecture and meta-training procedure.
result Improved stability and generalization of learned optimizers.
We consider the problem of quickest change-point detection in data streams. Classical change-point detection procedures, such as CUSUM, Shiryaev-Roberts and Posterior Probability statistics, are optimal only if the change-point model is known, which is an unrealistic assumption in typical applied problems. Instead we p…
Study shows different trajectory prediction models generalize better under OoD conditions.
problem Comparing trajectory prediction models' robustness across different datasets.
method Training models on Argoverse 2 and testing on Waymo Open Motion, and vice versa, with various augmentation strategies.
result Smallest model with highest inductive bias performs best in OoD generalization.
New diagnostic tool for assessing approximate Bayesian inference.
problem Assessing the trustworthiness of approximate Bayesian inference.
method Reframe the problem in terms of incompatible conditional distributions and use Gibbs priors.
result The diagnostic tool can discover the inductive bias in various Bayesian models and approximations.
Interpolated-MLPs control inductive bias for better performance in low-compute tasks.
problem Low-compute performance gap between MLPs and CNNs.
method Introduced Interpolated MLP (I-MLP) approach to control inductive bias incrementally.
result Continuous logarithmic relationship between inductive bias and performance in low-compute tasks.
New method quantifies inductive bias for machine learning tasks.
problem Quantifying the amount of inductive bias in machine learning models.
method Estimates inductive bias by modeling loss distribution of random hypotheses.
result Higher dimensional tasks require greater inductive bias.
Causal reasoning has been an indispensable capability for humans and other intelligent animals to interact with the physical world. In this work, we propose to endow an artificial agent with the capability of causal reasoning for completing goal-directed tasks. We develop learning-based approaches to inducing causal kn…
One-layer transformers can't solve induction heads task efficiently.
problem Solving the induction heads task efficiently with one-layer transformers.
method Communication complexity argument showing exponential size requirement.
result No one-layer transformer can solve the induction heads task efficiently.
OTI extends OTP for inductive semi-supervised learning.
problem Inductive semi-supervised learning for out-of-sample data.
method Optimal transport-based approach extended to inductive tasks.
result OTI outperforms state-of-the-art methods in experiments.
We study the topological and differentiable singularities of the configuration space C(Γ) of a mechanical linkage Γin d-dimensional Euclidean space, defining an inductive sufficient condition to determine when a configuration is singular. We show that this condition holds for generic singularities, provide a mechanical…
Masking diffusion outperforms other discrete diffusion models by incorporating jump times into the model.
problem Improving the performance of discrete diffusion models.
method Conditioning on the jump schedule of discrete Markov processes.
result Schedule-conditioned discrete diffusion (SCUD) models outperform classical and masking diffusion models.
This thesis explores supervised classification methods using Bayesian and exchangeability theories.
problem Assigning objects into predefined classes using training data and auxiliary information.
method Bayesian inductive theories and exchangeabilities (de Finetti and partition exchangeability).
result Optimal classifiers for different scenarios of object features and categories.
Strong inductive biases prevent harmless interpolation in overparameterized models.
problem Understanding the conditions under which overparameterized models can interpolate noise without overfitting.
method Theoretical analysis of high-dimensional kernel regression and deep neural networks, focusing on the role of inductive biases.
result The strength of an estimator's inductive bias determines whether interpolation is harmless or requires fitting noise for good generalization.
Deep ResNets favor low bottleneck rank with proper hyperparameters.
problem Understanding the inductive bias of deep neural networks.
method Computed minimum-norm weights of a deep linear ResNet.
result Deep nonlinear ResNets have an inductive bias towards minimizing bottleneck rank.
Physics-informed GCRL tackles sparse feedback learning with hybrid dynamics.
problem Sparse feedback learning with high-dimensional, hybrid, or contact-dependent dynamics.
method Introduces physics-informed inductive biases into goal-conditioned value learning.
result Contact-rich manipulation tasks degrade existing Pi-GCRL methods.
This research formalizes inductive generalization and proposes a new learning paradigm called Inductive Learning.
problem Generalization from easy to hard tasks, especially out-of-domain generalization.
method Formalizes inductive generalization, introduces Inductive Learning, and outlines steps to adapt techniques for learning model successors.
result A new learning paradigm (Inductive Learning) that emphasizes induction and universal properties of learning and computation.
We introduce several methods to define the self-inductance of a single loop as the regularization of divergent integrals which we obtain by applying Neumann (or Weber) formula for the mutual inductance of a pair of loops to the case when two loops are identical.
We introduce the notion of large scale inductive dimension for asymptotic resemblance spaces. We prove that the large scale inductive dimension and the asymptotic dimensiongrad are equal in the class of r-convex metric spaces. This class contains the class of all geodesic metric spaces and all finitely generated groups…
If p:Y→X is an unramified covering map between two compact oriented surfaces of genus at least two, then it is proved that the embedding map, corresponding to p, from the Teichmüller space T(X), for X, to T(Y) actually extends to an embedding between the Thurston compactification of the tw…
The dominant paradigm for relation prediction in knowledge graphs involves learning and operating on latent representations (i.e., embeddings) of entities and relations. However, these embedding-based methods do not explicitly capture the compositional logical rules underlying the knowledge graph, and they are limited …
The paper explores methods to better estimate treatment effects by leveraging shared structure in potential outcomes.
problem Estimating treatment effects when outcomes may vary widely and existing methods often assume heterogeneity.
method Investigates and compares three learning strategies: regularization, reparametrization, and a multi-task architecture.
result All three approaches improve upon existing baselines, providing insights into their relative strengths.
Novel framework for Bayesian reinforcement learning infers value function distributions.
problem Bayesian reinforcement learning's challenges in inferring value function distributions.
method Inferential Induction framework for Bayesian reinforcement learning, developing Bayesian Backwards Induction algorithm.
result Proposed algorithm is competitive with state-of-the-art methods.
Noise affects the effectiveness of interpolating models, especially those with strong inductive biases.
problem The impact of noise on interpolating models with strong inductive biases.
method Analyzing linear and classification models with sparse ground truths, proving fast rates for interpolators.
result Strong inductive biases can lead to faster but noisier interpolators, contrary to intuition.
Unsupervised machine translation---i.e., not assuming any cross-lingual supervision signal, whether a dictionary, translations, or comparable corpora---seems impossible, but nevertheless, Lample et al. (2018) recently proposed a fully unsupervised machine translation (MT) model. The model relies heavily on an adversari…
Endowing robots with human-like physical reasoning abilities remains challenging. We argue that existing methods often disregard spatio-temporal relations and by using Graph Neural Networks (GNNs) that incorporate a relational inductive bias, we can shift the learning process towards exploiting relations. In this work,…
The study identifies conditions for algorithms to have tight generalization bounds.
problem Understanding which algorithms have tight generalization bounds.
method Analyzing conditions that preclude tight generalization bounds and identifying stable algorithms.
result Stable algorithms have tight generalization bounds, while unstable ones do not.
Paper revises power theory using classical mechanics concepts.
problem Clarifying instantaneous power definitions for circuit elements.
method Defines power using classical mechanics concepts like velocity and momentum.
result General and compact expression for inductance, capacitance, and resistance powers.
In the first part of this series, we defined an equivariant index without assuming the group acting or the orbit space of the action to be compact. This allowed us to generalise an index of deformed Dirac operators, defined for compact groups by Braverman. In this paper, we investigate properties and applications of th…
This paper tackles data-efficient nonlinear control in Hamiltonian systems using symplectic geometry.
problem Data-efficient nonlinear control in Hamiltonian systems.
method Combines symplectic geometry, recurrence on energy level sets, and chain policies to solve target reachability problems.
result Data requirements depend on geometric and recurrence properties of the Hamiltonian, not the state dimension.
We consider controller-stopper problems in which the controlled processes can have jumps. The global filtration is represented by the Brownian filtration, enlarged by the filtration generated by the jump process. We assume that there exists a conditional probability density function for the jump times and marks given t…
New approach relaxes inductive biases of physics-inspired NNs for better performance.
problem Challenges in applying physics-inspired NNs to real-world systems.
method Examined and relaxed inductive biases of Hamiltonian NNs, improving performance on non-conservative systems.
result Improved performance on practical, non-conservative systems by relaxing inductive biases.
SGD-trained deep nets often generalize well due to a strong inductive bias towards low-error, low-complexity functions.
problem Understanding why overparameterized deep nets generalize well despite fitting training data perfectly.
method Empirical investigation of PSGD(f∣S) and PB(f∣S) for various architectures and datasets. result The probability of SGD-converging on a function consistent with training data correlates well with the Bayesian posterior probability of expressing that function.
Study links neural network inductive bias, feature learning, and generalization on Boolean functions.
problem Understanding how neural networks learn and generalize on Boolean data.
method End-to-end analysis of depth-2 discrete fully connected networks and DNF formulas, using Monte Carlo learning.
result Predictable training dynamics and interpretable features emerge, linking inductive bias and generalization.
This paper improves sample efficiency in noisy inductive matrix completion with side-information.
problem Improving sample efficiency in noisy inductive matrix completion with side-information.
method Nonconvex projected gradient descent algorithm with spectral initialization.
result Achieves linear convergence and stable recovery at a sample complexity governed by the effective side-information dimension.
Novel approach trains LLMs for inductive reasoning using probabilistic programs.
problem Training LLMs for inductive reasoning with sparse, ambiguous data.
method Program-based Posterior Training (PPT) using probabilistic inference.
result Significant improvement in estimation accuracy and alignment with human judgments.
We prove addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial.
ERM with f-divergence regularization yields unique solution.
problem Optimizing empirical risk with f-divergence. method Mild conditions on f lead to unique optimal measure. result Equivalence of ERM-fDR to different f-divergence regularization. Extends positive mass theorem to arbitrary dimensions using a new inductive scheme.
problem Overcoming singularities in the Schoen-Yau proof for arbitrary dimensions.
method Inductive scheme combining shielding principle, conformal blow-up, and Cheeger-Naber bound.
result Proof of positive mass theorem in arbitrary dimensions.
Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict inductively on new users/movies. In this paper, we study the problem of inductive matr…
I-BERT extends Transformer's self-attention to arbitrary input lengths.
problem Transformer models struggle with inductive generalization to unseen input lengths.
method Replaces positional encodings with a recurrent layer.
result I-BERT achieves state-of-the-art results on algorithmic tasks.