Neural networks learn task-specific features, influenced by nonlinearity.
problem Understanding the nature of task-dependent feature learning in neural networks.
method Investigation of fully-connected, wide neural networks using Bayesian framework.
result The nature of internal representations depends on neuronal nonlinearity, leading to analog, redundant, or sparse coding schemes.
Learning with feature evolution studies the scenario where the features of the data streams can evolve, i.e., old features vanish and new features emerge. Its goal is to keep the model always performing well even when the features happen to evolve. To tackle this problem, canonical methods assume that the old features …
Sparse coding is a common approach to learning local features for object recognition. Recently, there has been an increasing interest in learning features from spatio-temporal, binocular, or other multi-observation data, where the goal is to encode the relationship between images rather than the content of a single ima…
A hierarchical model shows how scaling laws emerge from sequential feature recovery.
problem Emergence of scaling laws from feature learning in multi-layer networks.
method Layer-wise spectral algorithm adapted to compositional structure, sequential feature detection.
result Sequential detection of latent features, leading to explicit power-law decay of prediction error.
Paper uses deep Ritz method for solving stationary Schrödinger equation, proving convergence and feature emergence.
problem Solving stationary Schrödinger equation with high-dimensional features.
method Deep Ritz method, gradient descent, single-index model, two-neuron model.
result Gradient descent converges to near-optimal solution, feature emergence observed in two-neuron model.
We identify 'critical windows' in diffusion models where specific features emerge, providing a theoretical framework.
problem Understanding narrow time intervals in diffusion models where specific features emerge.
method Developed a formal framework to study these critical windows, showing provable bounds for certain data types.
result Proved that critical windows can be bounded in terms of measures of separation for data from mixtures of log-concave densities.
Recursive Feature Machines show grokking in modular arithmetic without neural networks.
problem Grokking in modular arithmetic tasks.
method Recursive Feature Machines (RFM) with Average Gradient Outer Product (AGOP).
result RFM and neural networks learn block-circulant features to solve modular arithmetic.
Models predict fire and other emergencies in Edmonton.
problem Accurate prediction of emergency events for timely response.
method Data collection, descriptive analysis, feature selection, and negative binomial regression.
result Models perform well, with acceptable prediction errors for weekly and monthly periods.
Catastrophic events, though rare, do occur and when they occur, they have devastating effects. It is, therefore, of utmost importance to understand the complexity of the underlying dynamics and signatures of catastrophic events, such as market crashes. For deeper understanding, we choose the US and Japanese markets fro…
This paper explores emerging methods for estimating variable importance in machine learning.
problem Estimating the importance of variables in machine learning models.
method Least Absolute Shrinkage and Selection Operator (LASSO), Support Vector Machine (SVM), Predictive Error Function (PERF), Random Forest (RF), Extreme Gradient Boosting (XGBOOST).
result PERF and RF showed the best performance in highly correlated data, while PERF and XGBOOST performed poorly on small data sizes.
Financial market is an example of complex system, which is characterized by a highly intricate organization and the emergence of collective behavior. In this paper, we quantify this emergent dynamics in the financial market by using concepts of network synchronization. We consider networks constructed by the correlatio…
Framework improves ML flood mapping generalization.
problem Improving machine learning models' ability to generalize to new conditions.
method Dimensionless, multi-scale features constrained by the Buckingham Π theorem.
result Model outperformed dimensional features, improving AUC in unmapped areas.
Theory explains how deep nets learn features from data.
problem Understanding how deep neural networks learn features from data.
method Developed a noise-nonlinearity phase diagram and a mechanical theory.
result Links feature learning across layers to generalization.
As an emerging research direction, online streaming feature selection deals with sequentially added dimensions in a feature space while the number of data instances is fixed. Online streaming feature selection provides a new, complementary algorithmic methodology to enrich online feature selection, especially targets t…
Neural networks' feature geometry evolves like discrete Ricci flow.
problem Understanding neural feature representations and their geometric transformations.
method Approximating input manifold with geometric graphs and analyzing their evolution during training.
result Neural feature geometry evolves like discrete Ricci flow, with nonlinear activations playing a crucial role.
Power system emergency control is generally regarded as the last safety net for grid security and resiliency. Existing emergency control schemes are usually designed off-line based on either the conceived "worst" case scenario or a few typical operation scenarios. These schemes are facing significant adaptiveness and r…
Study shows 'Ordinal Neural Collapse' in deep OR tasks, revealing simple geometric relationships.
problem Understanding neural collapse in deep Ordinal Regression tasks.
method Combining cumulative link models and Unconstrained Feature Model to investigate neural collapse.
result Demonstrates 'Ordinal Neural Collapse' (ONC) with three key properties.
Price without transaction makes no sense. Trading volume authenticates its corresponding price, so there exist mutual information and correlation between price and trading volume. We are curious about fractal features of this correlation and need to know how structures in different scales translate information. To expl…
Study detects emerging trends in financial news articles about Microsoft.
problem Challenges in identifying trends in long-form financial news articles.
method Topic modeling and term frequency for keyword similarity analysis.
result Demonstrates the influence of the pandemic on Microsoft.
New method compares feature importance and rule extraction for text data interpretability.
problem Unexpected differences in explanations from feature importance and rule extraction methods.
method Proposes a new approach to compare explanations from different methods.
result Different methods can lead to unexpected explanations, even for simple models.
New theory explains when pre-trained models can improve downstream tasks.
problem Lack of theoretical understanding of task similarity for transfer learning.
method Feature-centric viewpoint, theoretical results on transferability phase diagram.
result Transfer learning outperforms training from scratch when target task is well represented in feature space.
We explain how neural networks learn to solve modular addition tasks.
problem How two-layer neural networks learn to solve modular addition tasks.
method Formalized a diversification condition during training, proving it allows the network to approximate the correct logic for modular addition.
result Neural networks can robustly identify the correct sum through phase symmetry and frequency diversification.
New DL approach reveals feature construction in dense samples.
problem Understanding deep learning's effectiveness across diverse applications.
method High-density sample task with 5 unique tokens, 500 exemplars per token.
result Emergence of category structure and feature detectors observed.
At present, object recognition studies are mostly conducted in a closed lab setting with classes in test phase typically in training phase. However, real-world problem is far more challenging because: i) new classes unseen in the training phase can appear when predicting; ii) discriminative features need to evolve when…
Graph convolutional network (GCN) is an emerging neural network approach. It learns new representation of a node by aggregating feature vectors of all neighbors in the aggregation process without considering whether the neighbors or features are useful or not. Recent methods have improved solutions by sampling a fixed …
Neural networks learn discrete tasks on continuous data via emergent geometry.
problem Understanding how neural networks perform discrete computations on continuous data.
method Analysis of Riemannian pullback metric across neural network layers.
result Neural networks learn to discretize continuous inputs and perform logical operations on these discretized variables.
Bayesian theory explains abrupt emergence of copy subcircuit in attention.
problem Understanding the abrupt emergence of the copy subcircuit in attention during training.
method Deriving a closed-form posterior over the attention matrix and reducing it to a low-dimensional order parameter space.
result Derive a phase transition in the amount of training data.
In our model, n traders interact with each other and with a central bank; they are taxed on the money they make, some of which is dissipated away by corruption. A generic feature of our model is that the richest trader always wins by 'consuming' all the others: another is the existence of a threshold wealth, below wh…
Bayesian neural networks explore rare fluctuations for better feature learning.
problem Understanding rare but dominant fluctuations in Bayesian neural networks.
method Large-deviation theory and joint optimization over predictors and internal kernels.
result Posterior rate function optimization reveals data-dependent kernel selection.
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.
A vast amount of textual web streams is influenced by events or phenomena emerging in the real world. The social web forms an excellent modern paradigm, where unstructured user generated content is published on a regular basis and in most occasions is freely distributed. The present Ph.D. Thesis deals with the problem …
A neural network approach for feature selection using mutual information.
problem Feature ranking and selection leading to sub-optimal solutions for class separability.
method Stochastic mutual information gradient estimation for dimensionality reduction.
result The network projects features onto an output space maximizing mutual information with class labels.
Feature-based time series representations have attracted substantial attention in a wide range of time series analysis methods. Recently, the use of time series features for forecast model averaging has been an emerging research focus in the forecasting community. Nonetheless, most of the existing approaches depend on …
A minimal model of a market of myopic non-cooperative agents who trade bilaterally with random bids reproduces qualitative features of short-term electric power markets, such as those in California and New England. Each agent knows its own budget and preferences but not those of any other agent. The near-equilibrium pr…
There has been an increasing interest in the area of emergent communication between agents which learn to play referential signalling games with realistic images. In this work, we consider the signalling game setting of Havrylov and Titov and investigate the effect of the feature extractor's weights and of the task bei…
The thresholded feature has recently emerged as an extremely efficient, yet rough empirical approximation, of the time-consuming sparse coding inference process. Such an approximation has not yet been rigorously examined, and standard dictionaries often lead to non-optimal performance when used for computing thresholde…
MACQ method explains deep learning models by analyzing feature contributions across prediction levels.
problem Explaining deep learning model predictions.
method Global gradient-based, model-agnostic approach focusing on marginal attribution.
result MACQ separates feature contributions from interaction effects and visualizes 3-way relationships.
A RL framework selects features to balance bias and accuracy dynamically.
problem Bias in automated feature selection when predictors are correlated.
method Multi-component reward function with policy gradient for dynamic regularization and bias mitigation.
result Model balances fairness and accuracy during training.
We explore a simple lattice field model intended to describe statistical properties of high frequency financial markets. The model is relevant in the cross-disciplinary area of econophysics. Its signature feature is the emergence of a self-organized critical state. This implies scale invariance of the model, without tu…
A new GNN module learns geometric scattering features for better graph classification and feature exploration.
problem Learning long-range graph relations and extracting meaningful features from graphs.
method Proposes a learnable geometric scattering (LEGS) module in graph neural networks (GNNs), incorporating wavelet filters.
result LEGS-based GNNs outperform existing methods in graph classification and feature extraction tasks.
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…
Contrastive learning struggles with class collapse and feature suppression, revealing bias towards simpler solutions.
problem Contrastive learning struggles with class collapse and feature suppression, especially in supervised and unsupervised settings.
method Unified theoretical framework to determine which features are learnt by CL, revealing bias towards simpler solutions.
result Bias towards simpler solutions is a key factor in class collapse and feature suppression.
NeurT-FDR controls FDR by incorporating feature hierarchy.
problem Controlling FDR in complex, large-scale hypothesis testing problems.
method NeurT-FDR uses a neural network to parametrize test-level covariates and a regression framework to adjust feature hierarchy.
result NeurT-FDR makes substantially more discoveries than competitive baselines.
Investigates spectral properties of neural networks, showing invariance under certain conditions.
problem Understanding the spectral evolution and invariance in linear-width neural networks.
method Empirical and theoretical analysis of spectra of weight matrices in high-dimensional settings.
result Spectra of weight matrices are invariant under certain training conditions, with implications for feature learning.
Gradient Starvation causes neural networks to focus on a subset of features, leading to imbalance.
problem Neural networks focusing on only a subset of features despite having access to more.
method Using Dynamical Systems theory, identified properties of learning dynamics leading to feature imbalance.
result Gradient descent can lead to feature imbalance in over-parameterized networks.
DNNs generalize object recognition in novel orientations via neurons tuned to common features.
problem Understanding how DNNs generalize to objects in novel orientations.
method Training DNNs with familiar objects from multiple viewpoints and analyzing neuron responses.
result DNNs disseminate orientation-invariance from familiar objects to recognize objects in novel orientations.
Paper identifies how neural networks learn features.
problem Understanding how neural networks automatically select features.
method Deep Neural Feature Ansatz, implementing average gradient outer product.
result Recursive Feature Machines achieve state-of-the-art performance.
Cross-GCN models cross features in GCN for better performance.
problem GCN's lack of cross feature modeling limits its effectiveness.
method Introduces Cross-feature Graph Convolution (Cross-GCN) to model cross features explicitly.
result Explicit cross feature modeling improves GCN's performance on tasks requiring cross features.