Improved singular value approximation for convolutional layers.
problem Improving accuracy of singular value approximation for linear convolutional layers.
method Developed a new spectral density matrix method for singular value approximation with improved accuracy and reduced computational complexity.
result Obtained moderate improvement in singular value distribution compared to circular approximation.
Linear Transformer Block combines MLP and linear attention for near-optimal ICL in linear regression.
problem Achieving near-optimal in-context learning (ICL) risk for linear regression with a Gaussian prior.
method Combines linear attention and MLP components in a Linear Transformer Block (LTB). Establishes correspondence with one-step gradient descent estimators (GDext−β). result LTB achieves nearly Bayes optimal ICL risk for linear regression with a Gaussian prior.
The paper considers the block sampling method for long-range dependent processes. Our theory generalizes earlier ones by Hall, Jing and Lahiri (1998) on functionals of Gaussian processes and Nordman and Lahiri (2005) on linear processes. In particular, we allow nonlinear transforms of linear processes. Under suitable c…
Proposes σ-PCA to learn identifiable linear transformations without whitening.
problem Cannot identify axes with equal variances in PCA.
method Unified model for linear and nonlinear PCA, introducing a missing piece to eliminate rotational indeterminacy.
result Eliminates subspace rotational indeterminacy in PCA.
SympFormer accelerates attention blocks using inertial dynamics on density spaces.
problem Improving the efficiency of self-attention blocks in Transformers.
method Introduced accelerated attention blocks derived from inertial Nesterov dynamics on density spaces.
result Accelerated attention blocks converge faster than classical blocks while preserving oracle calls.
Improved graph embedding through refined linear transformation and community recovery.
problem Identifying meaningful latent communities in graph data.
method Refined graph encoder embedding via linear transformation, self-training, and latent community recovery.
result Improved vertex embedding and better decision boundaries for vertex classification.
This paper precisely estimates transformer derivatives for explicit learning guarantees.
problem Computing fully-explicit generalization bounds for transformers with precise higher-order derivative estimates.
method Analyzes and estimates all higher-order derivatives of transformers with multiple attention heads and layer normalization.
result Obtains explicit pathwise generalization bounds for transformers learning from non-i.i.d. samples.
The article provides formulas for homological blocks of Seifert fibered homology 3-spheres.
problem Calculating Witten-Reshetikhin-Turaev invariants for Seifert fibered homology 3-spheres.
method Explicit modular transformation formulas of homological blocks.
result New proof of Witten asymptotic conjecture for Seifert fibered homology 3-spheres.
This paper proposes network recasting as a general method for network architecture transformation. The primary goal of this method is to accelerate the inference process through the transformation, but there can be many other practical applications. The method is based on block-wise recasting; it recasts each source bl…
A new decision tree variant improves linear model performance.
problem Improving decision tree performance on non-linear data.
method Extremely random tree with non-linear data transformation and linear observer.
result Outperforms linear models on benchmark dataset.
New ODE-Block handles stateful layers with continuous-in-depth functions using basis functions.
problem Handling stateful layers in ODE-Nets.
method Formulate ODE-Block using continuous-in-depth functions with basis function expansions.
result Enables state-of-the-art performance and reduces memory footprint.
Transformers interpreted as probabilistic Laplacian Eigenmaps steps.
problem Improving transformer performance through probabilistic interpretation.
method Probabilistic Laplacian Eigenmaps model derivation and graph diffusion step.
result Subtracting identity from attention matrix improves transformer performance.
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are disjoint. This differs from junction-trees, where two clusters connected by an edge al…
Transformers can approximate Kalman Filtering in linear systems with small error.
problem Approximating Kalman Filtering using Transformers for linear dynamical systems.
method Two-step reduction: 1) Softmax self-attention block approximates Nadaraya-Watson kernel smoothing, 2) This estimator approximates Kalman Filter.
result Constructs a Transformer that implements the Kalman Filter with small additive error, uniformly bounded in time.
In this paper, we propose several dictionary learning algorithms for sparse representations that also impose specific structures on the learned dictionaries such that they are numerically efficient to use: reduced number of addition/multiplications and even avoiding multiplications altogether. We base our work on facto…
DiffusionBlocks trains neural networks by breaking them into independent blocks, reducing memory usage.
problem Memory bottlenecks in end-to-end neural network training.
method Transforming transformer-based networks into independent trainable blocks via a denoising process.
result Independent block-wise training matches end-to-end training performance while reducing memory requirements.
Effective theory for Transformer initialization improves model performance.
problem Improving performance of Transformers at initialization.
method Effective-theory analysis of signal propagation in wide and deep Transformers.
result Particular width scalings of initialization and training hyperparameters.
THieF improves day-ahead electricity price prediction accuracy by reconciling hourly and block forecasts.
problem Improving accuracy in predicting day-ahead electricity prices.
method Temporal hierarchy forecasting (THieF) reconciling hourly and block forecasts.
result THieF significantly improves accuracy (up to 13%) at all levels of prediction.
Paper finds sharpness differences in transformer blocks accelerating LLM training.
problem Understanding and accelerating large language model pre-training.
method Uncovering sharpness disparity across transformer blocks and proposing Blockwise Learning Rate.
result Blockwise Learning Rate strategy accelerates LLM pre-training with lower loss and speedup.
This work analyzes how transformers learn common linear regression tasks.
problem Understanding how in-context learning operates in real-world applications with common task structures.
method Analyzing a linear attention model trained on low-rank regression tasks.
result Statistical fluctuations in finite pre-training data induce an implicit regularization, leading to a sharp phase transition in generalization error.
Investigates the fundamental components of attention mechanisms.
problem Understanding the building blocks of attention in deep learning.
method Classified and studied three key mechanisms: additive, multiplicative output, and synaptic attention.
result Additive activation attention is central in proofs of lower bounds.
In real-world applications, not all instances in multi-view data are fully represented. To deal with incomplete data, Incomplete Multi-view Learning (IML) rises. In this paper, we propose the Joint Embedding Learning and Low-Rank Approximation (JELLA) framework for IML. The JELLA framework approximates the incomplete d…
Training-free looped transformers improve model performance without additional training.
problem Improving model performance without additional training or fine-tuning.
method A lightweight inference-time wrapper loops a contiguous mid-stack block of layers of a frozen checkpoint without additional fine-tuning.
result Our method improves model performance across various model families.
In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by the aid of the Malliavin Calculus, extending the procedure employed by Montero and…
DEN learns diverse tasks to generalize to unseen tasks.
problem Generalization from a diverse set of classification tasks with limited data.
method Three-block architecture: covariate transformation, distribution embedding, and classification.
result DEN outperforms existing methods in various synthetic and real tasks.
Improved hyperparameter optimization using simplified Transformer blocks.
problem Discovering optimal architectures in high-dimensional search spaces with limited exploration budgets.
method Simplified Transformer block for modeling hyper-parameter dependencies, actor-critic style algorithm, ensembling.
result Outperformed most algorithms on NAS-Bench-101 and Random Search in discovering more accurate model architectures.
A new quantization strategy reduces Transformer model size and inference time.
problem Heavy computation load and memory overhead in Transformer models for mobile devices.
method Mixed precision quantization with varying bits per word in embedding blocks.
result 11.8x smaller model size and 3.5x speed up for on-device NMT.
Filters in convolutional networks are typically parameterized in a pixel basis, that does not take prior knowledge about the visual world into account. We investigate the generalized notion of frames designed with image properties in mind, as alternatives to this parametrization. We show that frame-based ResNets and De…
Study isotropy groups for complex orthogonal and skew-symmetric matrices.
problem Understanding isotropy subgroups of orthogonal similarity transformations.
method Analysis of group structure of nonsingular block matrices.
result Group structure of isotropy subgroups related to block Toeplitz matrices.
Transformers learn to solve modular arithmetic tasks by in-context learning and skill composition.
problem Understanding how large language models generalize to unseen tasks in modular arithmetic.
method Pre-training on a set of modular arithmetic tasks and evaluating out-of-distribution performance.
result Transformers require two transformer blocks for out-of-distribution generalization, and deeper models exhibit transient out-of-distribution performance.
In many state-of-the-art compression systems, signal transformation is an integral part of the encoding and decoding process, where transforms provide compact representations for the signals of interest. This paper introduces a class of transforms called graph-based transforms (GBTs) for video compression, and proposes…
New L-functions for 3-manifolds connect to Witten invariants and relate to generalized Bernoulli polynomials.
problem Understanding L-functions for 3-manifolds and their invariants. method Using Mellin transforms and asymptotic techniques, proving entire functions and their values.
result Linear relations between L-function values at negative integers, generalizing known zeta functions. Transformers use a unique Hessian structure that differs from classical networks, affecting optimization.
problem Understanding the unique optimization landscape of Transformers.
method Theoretical Hessian analysis of a single self-attention layer in Transformers.
result Transformers have a highly non-linear Hessian structure, distinguishing them from classical networks.
Quantum dilogarithm function proven from a linear difference equation.
problem Proving Faddeev's quantum dilogarithm from a linear difference equation.
method Proved Faddeev's quantum dilogarithm using Borel summation of a formal power series solution of a linear difference equation.
result Borel summation of a formal power series solution produces Faddeev's quantum dilogarithm.
WavPool improves deep neural networks with wavelet-based pooling.
problem Improving efficiency and performance of deep neural networks.
method Introducing WavPool, a wavelet-transform-based pooling layer.
result WavPool outperforms existing network architectures by 10% on CIFAR-10.
Transformers can implement reinforcement learning algorithms from data without updates.
problem Training reinforcement learning algorithms from data without parameter updates.
method Design a teacher-mimicking training procedure for transformers to implement policy-improvement methods.
result Gradient flow converges to an optimal parameter manifold corresponding to the desired RL update.
For each n>0 there is a one complex parameter family of homeomorphisms of the circle consisting of linear fractional transformations `conjugated by z→zn'. We show that these families are free of relations, which determines the structure of `the group of homeomorphisms of finite type'. We also discuss a numbe…
Paper analyzes why deeper layers of ViTs perform worse on out-of-distribution tasks.
problem Performance degradation of intermediate layers in ViTs under distribution shift.
method Extensive linear probing experiments across various benchmarks and fine-grained analysis of transformer modules.
result Probing feedforward network activations yields best performance under significant distribution shift.
CoDA Nets improve interpretability in neural networks.
problem Improving interpretability in neural networks.
method Dynamic Alignment Units (DAUs) for input-dependent linear transformations.
result CoDA Nets achieve on par results with ResNet and VGG models on complex datasets.
HaKAN uses Hahn-KAN blocks to forecast multivariate time series.
problem Long-term time series forecasting challenges with high complexity and spectral bias.
method HaKAN integrates channel independence, patching, and a stack of Hahn-KAN blocks with residual connections. It uses Hahn polynomial-based learnable activation functions.
result HaKAN consistently outperforms state-of-the-art methods on various forecasting benchmarks.
We show LLMs can be locally linear, enabling better control of activations.
problem Suboptimal control of LLM activations during generation.
method Model LLM inference as a linear dynamical system, compute feedback controllers using Jacobians, and adapt classical control theory.
result Robust, fine-grained control of LLM activations across models and tasks.
PLN-Nets with two linear layers and parallel LN achieve universal approximation.
problem Limitations of standard neural network architectures in universal approximation.
method Introduced PLN-Nets combining two linear layers with parallel LN.
result PLN-Nets achieve universal approximation, while standard LN has limited power.
We propose unitary group convolutions (UGConvs), a building block for CNNs which compose a group convolution with unitary transforms in feature space to learn a richer set of representations than group convolution alone. UGConvs generalize two disparate ideas in CNN architecture, channel shuffling (i.e. ShuffleNet) and…
Conservation laws, heirarchies, scattering theory and Bäcklund transformations are known to be the building blocks of integrable partial differential equations. We identify these as facets of a theory of Poisson group actions, and apply the theory to the ZS-AKNS nxn heirarchy (which includes the non-linear Schrödinger …
This letter presents a novel Block Bayesian Hypothesis Testing Algorithm (Block-BHTA) for reconstructing block sparse signals with unknown block structures. The Block-BHTA comprises the detection and recovery of the supports, and the estimation of the amplitudes of the block sparse signal. The support detection and rec…
In many video coding systems, separable transforms (such as two-dimensional DCT-2) have been used to code block residual signals obtained after prediction. This paper proposes a parametric approach to build graph-based separable transforms (GBSTs) for video coding. Specifically, a GBST is derived from a pair of line gr…
PARD generates graphs efficiently and invariantly to node ordering.
problem Graph generation sensitivity to node ordering.
method Integrates autoregressive and diffusion models with a partial order for nodes and edges.
result PARD achieves state-of-the-art performance on molecular and non-molecular datasets.
Unified framework for solving linear systems with improved convergence rates.
problem Efficiently solving linear systems with randomized batch-sampling methods.
method Developed a unified randomized batch-sampling Kaczmarz framework with concentration inequalities for analysis.
result Derived new expected linear convergence rate bounds that are tighter and more reflective of empirical behavior.