New research shows common ID estimators in neural representations are inaccurate.
problem Inaccurate estimation of intrinsic dimensions in neural representations.
method Theoretical and empirical investigation of ID estimators in neural representations.
result Common ID estimators do not accurately reflect the true underlying ID of neural representations.
Neural networks benefit from intermediate representations, reducing sample complexity.
problem Understanding how neural networks leverage intermediate representations for hierarchical learning.
method Fixed, randomly initialized neural network as a representation function, compared with raw inputs and other trainable networks.
result Neural representations can achieve improved sample complexities compared to raw inputs, especially for low-rank polynomials.
Neural networks are mathematically represented via quiver representations.
problem Understanding how neural networks process data and create representations.
method Representing neural networks as quiver representations with activation functions.
result Neural networks' computations can be studied algebraically and geometrically.
A neural scene representation framework enforcing 3D transformations.
problem Learning 3D scene representations from images without 3D supervision.
method Introducing a loss enforcing equivariance of the scene representation with 3D transformations.
result Real-time neural rendering with comparable results to models requiring minutes for inference.
Equivariant neural networks use symmetry to interpret complex data.
problem Interpreting and understanding the behavior of equivariant neural networks.
method Decompose layers into simple representations and analyze nonlinear activation functions.
result Equivariant neural networks can be interpreted using a filtration generalizing Fourier series.
This work characterizes how data augmentation shapes neural representations.
problem Understanding the impact of data augmentation on neural network representations.
method Embedding neural network hidden representations into a metric space invariant to transformations, analyzing shape-space trajectories.
result Increasing data augmentation strength leads to well-behaved trajectories in the embedded space, and different augmentation types steer representations in distinct directions.
MSA compares neural representations' intrinsic geometry for better understanding.
problem Existing similarity measures fail to capture subtle distinctions between neural network solutions.
method Metric similarity analysis (MSA) using Riemannian geometry.
result MSA can disentangle features of neural computations and compare nonlinear dynamics.
Enhanced BCPNN learns hidden representations without labels.
problem Unsupervised learning of hierarchical representations in neural networks.
method Extended BCPNN architecture with local Hebbian learning mechanisms.
result Demonstrated capability for unsupervised learning of salient hidden representations.
Researchers analyze neural process architectures and their representational capacities.
problem Understanding what functions can be represented by different neural process architectures.
method Analyzing four types of neural process architectures: CNPs, ANPs, TNPs, and their latent variants.
result Prove these architectures form a strict hierarchy and characterize their representational capabilities.
Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can translate the problem of analyzing a complex neural network into that of analyzi…
RNNs compute by warping neural representations over time.
problem Understanding how RNNs perform task computations.
method Developed a Riemannian geometric framework to derive the manifold topology and geometry of RNNs.
result Dynamic warping is a fundamental feature of RNN computations.
GNNs learn graph representations, with new theory on their power and limitations.
problem Understanding the capabilities and limitations of GNNs.
method Theoretical analysis of GNNs, focusing on approximation and learning properties.
result New insights into the representation, generalization, and extrapolation of GNNs.
Deconfounds neural network representation similarity metrics to improve consistency and accuracy.
problem Confounding by population structure in similarity metrics like RSA and CKA.
method Covariate adjustment regression to adjust for confounders.
result Improves detection of semantically similar neural networks and consistency in transfer learning.
Algorithm removes spurious concepts from neural network representations without harming task performance.
problem Spurious correlations hinder neural network out-of-distribution generalization.
method Iterative algorithm that identifies two orthogonal subspaces in neural network representation.
result Algorithm outperforms existing methods on computer vision and natural language processing benchmarks.
DORA analyzes deep neural networks' internal representations to detect spurious correlations.
problem Detecting spurious correlations in deep neural networks' internal representations.
method DORA uses Extreme-Activation (EA) distance measure to assess representation similarities.
result Identifies internal representations capable of detecting spurious correlations.
The study analyzes neural network predictions of knot invariants and finds that braid representations work best.
problem Understanding and predicting knot invariants using neural networks.
method Investigated different knot representations and invariants, proposed a cosine similarity score.
result Braid representations are best for predicting knot invariants, and some invariants are easier to learn than others.
Neural nets learn robust geometric data representations.
problem Ensuring neural networks are robust to adversarial attacks.
method Topological Data Analysis via persistence diagrams, Lipschitz stability.
result Certified ε-robustness on ORBIT5K dataset. Modality-agnostic compression improves across diverse data types.
problem Efficiently compressing data across multiple modalities.
method Functional view of data, Implicit Neural Representation (INR), modality-agnostic latent representations, variational compression.
result Improved performance compared to existing methods, especially for diverse modalities.
New measures link neural representation geometry to decoding ability.
problem Understanding how neural representations relate to decoding ability.
method Showed that popular similarity measures can be interpreted from a decoding perspective.
result Proved that measures like CKA and CCA quantify alignment between optimal linear readouts.
Neural networks learn spectral representations for group composition.
problem Understanding structured emergence in neural network training.
method Lifting gradient flow to Fourier domain, proving convergence to irreducible representations.
result Neurons converge to single irreducible representations, cross-layer coefficients align.
We study how finite Bayesian neural networks adapt their hidden representations.
problem Understanding how finite Bayesian neural networks differ from infinite ones.
method We analyze the asymptotics of learned feature kernels for various network architectures.
result The leading finite-width corrections to feature kernels have a universal form.
Study compares atom representations in graph neural networks for molecular properties.
problem Incorrect attribution of results in molecular property prediction due to varying atom features.
method Evaluated multiple atom representations on free energy, solubility, and metabolic stability predictions.
result Different atom representations can lead to varying predictive performance in graph neural networks.
New method finds Lie group representations without explicit groups, enabling new neural network architectures.
problem Building neural networks equivariant to arbitrary Lie groups.
method Algorithm to find Lie group representations from Lie algebra structure constants. Self-contained method for constructing Lie group-equivariant neural networks.
result First object-tracking model equivariant to the Poincaré group.
Proposes an unsupervised graph neural network for entire graph representation.
problem Lack of unsupervised methods for entire graph representation.
method Combines hierarchical graph neural networks and mutual information maximization.
result Improves state-of-the-art performance on multiple graph level tasks.
A measure of neural complexity quantifies how hard it is to access information across neurons.
problem Understanding how mutual information is distributed among neurons in neural networks.
method Partial Information Decomposition (PID) to disentangle contributions of single neurons, multiple neurons, and synergistic effects.
result Representational Complexity measures the difficulty of accessing information across multiple neurons.
New approach uses prior knowledge to improve neural network representations.
problem Difficulty in learning robust internal representations without a large training set.
method Incorporates prior information into a pre-trained reasoning module.
result Improves representation learning in diverse self-supervised learning settings.
RedEx improves neural network optimization with convex optimization guarantees.
problem Difficult optimization of neural networks.
method RedEx architecture using convex optimization with semi-definite constraints.
result RedEx can efficiently learn functions fixed methods cannot.
Consider the problem: given the data pair (x,y) drawn from a population with f∗(x)=E[y∣x=x], specify a neural network model and run gradient flow on the weights over time until reaching any stationarity. How does ft, the function computed by the neural network…
New method for high-fidelity shape representations from raw data.
problem Creating accurate shape representations from raw data.
method A simple loss function encouraging neural network to vanish on input point cloud and have unit norm gradient.
result Our method produces high-fidelity, smooth, and natural zero level set surfaces.
Math theory explains how neural networks learn abstract representations.
problem Understanding how neural networks learn abstract representations.
method Mathematical theory reformulating network optimization into mean field optimization over neural preactivations.
result Abstract representations of latent variables are guaranteed to appear in neural networks trained on tasks that depend on these variables.
In this effort, we derive a formula for the integral representation of a shallow neural network with the ReLU activation function. We assume that the outer weighs admit a finite L1-norm with respect to Lebesgue measure on the sphere. For univariate target functions we further provide a closed-form formula for all po…
Defines metrics to compare neural network representations.
problem Comparing neural network representations across different architectures and tasks.
method Developed a family of metric spaces and modified existing measures to quantify representational dissimilarity.
result Identified relationships between neural representations and anatomical features.
INVERT connects neural representations to human-understandable concepts.
problem Lack of understanding and statistical significance in existing explainability methods.
method Inverse Recognition (INVERT) approach that connects learned representations to human-understandable concepts.
result INVERT provides interpretable metrics and statistical significance for representation alignment.
Introduces TT-NF for more compact neural field representations.
problem Finding more compact and easy-to-fit neural field representations.
method Tensor Train parameterization trained with backpropagation.
result Low-rank compression improves downstream task quality metrics.
Neural networks learn distance-based representations, not just intensity.
problem Understanding how neural networks interpret and learn from internal activations.
method Manipulated ReLU and Absolute Value activations to observe sensitivity to distance and intensity perturbations.
result Neural networks are highly sensitive to small distance-based perturbations, challenging the intensity-based interpretation.
Represents neural networks as solutions to inverse problems in Banach spaces.
problem Understanding the function learned by neural networks.
method Variational framework, representer theorem, polynomial ridge splines.
result Neural networks are solutions to inverse problems in Banach spaces.
This work analyzes how neural networks learn representations in actor-critic algorithms.
problem Theoretical support for neural AC algorithms is limited to linear function approximations.
method Mean-field analysis of a two-timescale learning AC algorithm with overparameterized networks.
result Neural AC finds the globally optimal policy at a sublinear rate in the continuous-time and infinite-width limiting regime.
Comparing different neural network representations and determining how representations evolve over time remain challenging open questions in our understanding of the function of neural networks. Comparing representations in neural networks is fundamentally difficult as the structure of representations varies greatly, e…
Novel tRSA combines geometry and topology for brain and model analysis.
problem Traditional RSA overlooks topological information in neural representations.
method Topological RSA (tRSA) using nonlinear monotonic transforms.
result Robust model comparisons and novel insights into neural computation.
Different neural networks trained on the same dataset often learn similar input-output mappings with very different weights. Is there some correspondence between these neural network solutions? For linear networks, it has been shown that different instances of the same network architecture encode the same representatio…
We consider deep feedforward neural networks with rectified linear units from a signal processing perspective. In this view, such representations mark the transition from using a single (data-driven) linear representation to utilizing a large collection of affine linear representations tailored to particular regions of…
New metric captures individual neuron tuning across neural networks.
problem Need a metric that respects individual neuron tuning across different neural networks.
method Derived a 'soft' permutation-based metric using optimal transport theory.
result Metric avoids counter-intuitive outcomes and captures geometric insights.
Representation costs in data science: Unifying function-space views of parametric methods
problem Analyzing representation costs of parametric data-fitting methods
method Developing a general framework for analyzing representation costs through parameter-space regularizers
result Proving that many natural results hold in this abstract setting, including representer theorems for parametric methods on their native spaces
We propose a metric, Layer Saturation, defined as the proportion of the number of eigenvalues needed to explain 99% of the variance of the latent representations, for analyzing the learned representations of neural network layers. Saturation is based on spectral analysis and can be computed efficiently, making live ana…
Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical correlation analysis (CCA). We show that CCA belongs to a family of statistics for mea…
Deep neural network learns compact representations for driving tasks.
problem Improving autonomous driving through better neural network representations.
method Inspired by human brain's hierarchical structure and predictive nature, the paper proposes a deep learning framework that learns compact representations of driving concepts.
result The paper successfully learns compact representations using as few as 16 neural units for car and lane concepts.
Estimates neural representation dimensionality from small sample sizes.
problem Estimating neural representation dimensionality from limited data.
method Proposed a bias-corrected estimator for participation ratio of eigenvalues.
result The estimator is more accurate with finite samples and noise.
DRIFT uses neural flows to replace distributional regression models.
problem Lack of neural network representations for distributional regression models.
method Inverse flow transformations (DRIFT) for distributional regression.
result Neural representations in DRIFT match classical statistical methods in performance.