The paper proves neural networks with ReLU and softmax can approximate any function.
problem Approximating functions and class labels in neural networks.
method Extended universal approximator theory to neural networks with ReLU and softmax.
result Neural networks with ReLU and softmax can approximate any function and class labels.
This research explores using kernels in the softmax layer for better contextual word classification.
problem Improving contextual word classification accuracy.
method Replacing the inner product in the softmax layer with various kernel functions and comparing their performance.
result Different kernel settings yield varying performance in contextual word classification tasks.
Softmax attention approximates complex functions and subsumes many known universal approximators.
problem Universal approximation of continuous sequence-to-sequence functions.
method Interpolation-based analysis of attention's internal mechanism, showing its ability to approximate ReLU functions.
result Softmax attention is a universal approximator for continuous sequence-to-sequence functions.
Paper speeds up neural language model inference by 20x for top-k word prediction.
problem Slow inference speed of neural language models on mobile devices.
method Introduced a screening model using Gumbel softmax to approximate softmax layer.
result Achieved 20.4x speedup with 98.9% precision@1 and 99.3% precision@5 for German to English translation.
New CNN approach reduces overconfidence in object classification predictions.
problem Overconfident predictions from deep models, especially SoftMax layer.
method Introduces CNN probabilistic approach using Logit layer for Bayesian inference.
result Proposed approach shows promising performance compared to SoftMax.
WEST compresses word embeddings and softmax layers for memory efficiency.
problem Memory constraints in large vocabulary models.
method WEST encodes words with sequences of sub-units, improving compression without performance loss.
result WEST achieves significant compression without sacrificing performance.
Unified framework for studying softmax attention under large prompts.
problem Challenges in theoretical analysis of softmax attention.
method Measure-based framework for finite and infinite prompts.
result Softmax attention converges to linear attention in the large-prompt regime.
Proposes learnable monotonic functions to improve softmax's limitations.
problem Softmax's limited representational capacity in large output vocabularies.
method Learn parametric monotonic functions on logits.
result Improves quality metrics over traditional Linear-Softmax in language models.
Hierarchical Softmax approximates class probabilities for large datasets efficiently.
problem Computational inefficiency of Softmax for large-scale classification tasks.
method Used Hierarchical Softmax to approximate class probabilities efficiently.
result Hierarchical Softmax performance degrades as the number of classes increases.
Softmax policy gradient achieves global optimality in wide neural networks with entropy regularization.
problem Optimizing softmax policies with neural networks in the mean-field regime.
method Modeling neural networks as Wasserstein gradient flows and proving global optimality of fixed points.
result Global optimality of softmax policy gradient in wide single hidden layer neural networks with entropy regularization.
A new loss function speeds up sequence-to-sequence models for continuous outputs.
problem Slow and memory-intensive softmax layer limits vocabulary size and translation quality.
method Proposes a probabilistic loss and continuous embedding layer training/inference procedure.
result Models achieve up to 2.5x speed-up in training time with similar translation quality.
Improved classifier accuracy by using more of the class-specific structure in trained models.
problem Softmax ignores valuable information encoded in the full array of class response distributions.
method Developed a hybrid classifier (Softmax-Pooling Hybrid, SPH) that uses Softmax on high-scoring samples and a log-likelihood method on low-scoring samples. result Reduces test set error by 6% to 23% using the exact same trained model.
Introduces RPL for improved class prediction and uncertainty assessment.
problem Softmax's limitations in calculating class probabilities and handling uncertainty.
method Develops a new prediction layer (RPL) based on the open-world assumption.
result RPL provides more meaningful class prediction probabilities and handles uncertainty better.
New method adds uncertainty estimation to softmax outputs.
problem Uncertainty estimation in neural networks.
method Extend softmax layer with an additional constant input.
result Performs comparably to more computationally expensive methods.
A method to automatically choose feature dimensions in linear attention for better approximation quality.
problem Choosing the feature dimension in linear attention to balance quality and efficiency.
method Statistical degrees of freedom for determining feature dimension, layer-wise training strategy.
result Our method achieves smaller approximation error compared to fixed dimensions and improves model performance.
Transformers learn to perform logistic regression in-context.
problem Understanding how transformers learn to perform specific tasks in-context.
method Constructed multi-layer transformers that perform in-context logistic regression through normalized gradient descent.
result Transformers can be trained to perform in-context logistic regression effectively.
Softmax confidence misrepresents uncertainty in neural networks.
problem Neural networks fail to increase uncertainty on out-of-distribution data.
method Investigates two implicit biases in softmax confidence.
result Softmax confidence correlates with epistemic uncertainty due to decision boundary structure and deep network filtering.
Softmax and k-means clustering are mathematically linked, improving neural network robustness.
problem Improving neural network robustness against adversarial attacks.
method Formally proving the connection between softmax and k-means, proposing Centroid Based Tailoring.
result The proposed Gauss network is less susceptible to one-pixel attacks.
Metric learning aims at learning a distance which is consistent with the semantic meaning of the samples. The problem is generally solved by learning an embedding for each sample such that the embeddings of samples of the same category are compact while the embeddings of samples of different categories are spread-out i…
Adaptively sparse Transformers improve interpretability and diversity in NLP.
problem Standard Transformers use dense attention, limiting interpretability and diversity.
method Introduces adaptively sparse Transformers using α-entmax for context-dependent sparsity. result Improves interpretability and diversity in NLP tasks without sacrificing accuracy.
A new neural network layer integrates graph learning into classification tasks.
problem Lack of relational information in standard deep learning architectures for label predictions.
method Derives backpropagation equations for a differentiable graph learning layer.
result Smooth label transitions, improved generalization, and robustness to adversarial attacks.
Improved SincNet for better speaker recognition.
problem Speaker recognition challenges and the need for better deep learning models.
method Proposes AM-SincNet, a SincNet-based model with an improved AM-Softmax layer.
result Improved speaker recognition performance, achieving a 40% Frame Error Rate reduction.
ZeroS improves Transformers by adding negative weights, matching or beating softmax attention.
problem Limited performance of linear attention methods, especially in long context sequences.
method Proposes Zero-Sum Linear Attention (ZeroS) that removes the zero-order term and reweights zero-sum softmax residuals.
result ZeroS matches or exceeds standard softmax attention across various benchmarks, theoretically expanding representable functions.
Lower bounds set for infinite-precision transformers.
problem Understanding limitations of infinite-precision transformers.
method Used VC dimension technique to prove lower bounds.
result First lower bounds for two tasks: function composition and SUM2. Model compression is essential for serving large deep neural nets on devices with limited resources or applications that require real-time responses. As a case study, a state-of-the-art neural language model usually consists of one or more recurrent layers sandwiched between an embedding layer used for representing inp…
Gradient flow on softmax attention minimizes nuclear norm of weight matrices.
problem Classification with separate key and query weight matrices.
method Gradient flow on exponential loss, separability assumption, reparameterization, approximate KKT conditions.
result Gradient flow implicitly minimizes nuclear norm of weight matrices, contrasting with Frobenius norm minimization.
Density-Softmax improves uncertainty estimation and robustness without sampling, reducing model size and latency.
problem Sampling-based uncertainty estimation methods suffer from large model size and high latency.
method Combines a Lipschitz-constrained feature extractor with the softmax layer to create a sampling-free deterministic framework.
result Density-Softmax reduces over-confidence under distribution shifts and achieves competitive results in uncertainty and robustness.
Gradient descent converges geometrically to optimal self-attention parameters.
problem Training softmax self-attention layers for linear regression.
method Structure-aware gradient descent with preconditioner and regularizer.
result Gradient descent converges geometrically to global minima.
Transformers can emulate various algorithms by prompting, proving universality.
problem How to emulate algorithms using fixed-weight Transformers.
method Two modes of in-context algorithm emulation: task-specific and prompt-programmable. Constructing prompts that encode algorithm parameters into token representations.
result Fixed-weight Transformers can emulate a broad class of algorithms via prompts.
Proposes a new method to improve multiclass probability calibration.
problem Uncalibrated class probabilities in multiclass classifiers leading to over-confidence.
method Dirichlet calibration method applicable to any model class, derived from Dirichlet distributions.
result Improved probabilistic predictions across various datasets and classifiers.
Investigates optimal parameter allocation in Transformers for efficiency and expressivity.
problem Balancing expressivity and efficiency in Transformer model parameters.
method Mathematical analysis and theoretical characterization of attention heads and head dimensions.
result Later layers can operate more efficiently with reduced parameters due to saturation of softmax activations.
Gated Recurrent Unit (GRU) is a recently-developed variation of the long short-term memory (LSTM) unit, both of which are types of recurrent neural network (RNN). Through empirical evidence, both models have been proven to be effective in a wide variety of machine learning tasks such as natural language processing (Wen…
Unified framework for sequence models using test-time regression.
problem Designing efficient sequence models with associative memory.
method Formalizing associative recall as regression over input tokens, deriving various sequence models.
result Clarifies the effectiveness of query-key normalization in softmax attention and offers new generalizations.
The paper analyzes convergence rates of softmax gating in MoE models.
problem The effectiveness and scalability of machine learning models using MoE.
method Convergence analysis of parameter and expert estimation under MoE with softmax gating and its variants.
result Theoretical results show polynomially many data points are needed for strong identifiability conditions, while exponential points are required for linear experts.
Study quantifies how LLMs capture higher-order statistical structure using cumulant expansion.
problem Understanding how LLMs internalize statistical structure during next-token prediction.
method Cumulant-expansion framework treating softmax entropy as perturbation around center distribution.
result Cumulants reveal distinct signatures for mathematical vs. general text prompts, quantifying feature-learning dynamics.
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.
Recently, fully-connected and convolutional neural networks have been trained to achieve state-of-the-art performance on a wide variety of tasks such as speech recognition, image classification, natural language processing, and bioinformatics. For classification tasks, most of these "deep learning" models employ the so…
Transformers handle long documents better with hierarchical segmentation and recurrent layers.
problem Applying BERT to long documents like call transcripts.
method Hierarchical segmentation, recurrent layers, and softmax activation.
result Significant improvement in customer call satisfaction prediction and topic classification tasks.
We replace the output layer of deep neural nets, typically the softmax function, by a novel interpolating function. And we propose end-to-end training and testing algorithms for this new architecture. Compared to classical neural nets with softmax function as output activation, the surrogate with interpolating function…
Paper studies Transformer learning theory for Euclidean and Riemannian domains.
problem Understanding and optimizing Transformer networks for regression tasks.
method Constructive approximation framework using softmax partition of unity and attention mechanism.
result Transformer can achieve uniform ε-approximation error with minimal parameters.
A new method for optimizing regression problems with ReLU units converges.
problem Optimizing regression problems involving ReLU units in large language models.
method Introduced a greedy algorithm based on approximate Newton method, proving convergence in terms of the distance to optimal solution.
result The method converges in the sense of the distance to optimal solution under certain assumptions.
This work is about recognizing human activities occurring in videos at distinct semantic levels, including individual actions, interactions, and group activities. The recognition is realized using a two-level hierarchy of Long Short-Term Memory (LSTM) networks, forming a feed-forward deep architecture, which can be tra…
This study analyzes why attention layers in neural networks can cause signal loss and proposes a solution.
problem Pathological behavior of attention layers in neural networks, leading to signal loss.
method Spectral analysis using Random Matrix Theory to identify and mitigate rank collapse in width.
result A novel solution to mitigate rank collapse in width by removing outlier eigenvalues.
New insights into CE dynamics reveal how Hadamard initialization simplifies softmax.
problem Understanding the dynamics of cross-entropy training loss in deep learning.
method Analyzing a two-layer linear neural network with standard-basis vectors as inputs.
result Gradient flow on cross-entropy converges to neural collapse geometry, proving global convergence.
In this paper we propose a synergistic melting of neural networks and decision trees (DT) we call neural decision trees (NDT). NDT is an architecture a la decision tree where each splitting node is an independent multilayer perceptron allowing oblique decision functions or arbritrary nonlinear decision function if more…
A network architecture improves classification performance on various datasets.
problem Improving classification performance on diverse datasets.
method Divide fully connected layer into three levels, learn existing layers, cluster similar classes, reclassify using clustering masks.
result Achieved state-of-the-art performance with an error rate of 11.56% on Cifar-100.
Transformers learn to cluster Gaussian mixtures as well as the EM algorithm.
problem Learning guarantees of Transformers in multi-class clustering of Gaussian mixtures.
method Developed a theory connecting Transformer's Softmax Attention layers to the EM algorithm's workflow.
result Transformers achieve minimax optimal rate for clustering Gaussian mixtures with sufficient training samples and initialization.
New method for differentially private optimization with general Lipschitz conditions.
problem Differentially private optimization under general Lipschitz conditions.
method Generalized Lipschitz condition for per-sample gradients, tuning clip norm based on minimum per-sample Lipschitz constant.
result Efficacy of the recommended clip norm tuning method verified on 8 datasets.