Softmax temperature influences model representation rank and performance.
problem Understanding and optimizing softmax function's impact on model representations.
method Investigated softmax function's role in deep neural networks, introduced rank deficit bias.
result Softmax temperature affects model representation rank and can improve performance.
Simple method improves deep classifier accuracy under noisy labels.
problem Training deep classifiers with noisy labels.
method Probabilistic approach using temperature parameterized softmax.
result Improves accuracy, log-likelihood and calibration on noisy datasets.
Attention temperature improves robustness of ICL in high-dimensional settings.
problem ICL robustness failure under distribution shift in high dimensions.
method Analyzed a Transformer with approximate softmax attention, derived a closed-form error expression, and showed optimal temperature minimizes error.
result Optimal attention temperature minimizes ICL generalization error under distribution shift.
A new topology design improves zero-shot classification performance in contrastive learning.
problem Improving zero-shot classification performance in contrastive visual-textual alignment.
method Proposed an alternative topology design using multiple class tokens and an oblique manifold with negative inner product.
result Improves zero-shot classification performance by an average of 6.1%.
Revises logistic-softmax likelihood for Bayesian meta-learning in few-shot classification.
problem Inherent uncertainty in logistic-softmax leads to suboptimal performance in meta-learning.
method Redesigns logistic-softmax likelihood with a temperature parameter for better control of prior confidence.
result Achieves well-calibrated uncertainty estimates and comparable/superior performance on benchmark datasets.
New method uses temperature to control sparse MoE convergence rates.
problem Sparse MoE convergence rates are slow due to temperature interactions.
method Proposes a novel activation gate to improve convergence rates.
result Improved convergence rates to polynomial rates via novel gate.
Unified framework for critical scaling of inverse temperature in self-attention.
problem Conflicting inverse-temperature laws for long-context self-attention.
method Counting gaps and defining an upper-tail accumulation scale.
result Critical inverse-temperature scale determined by gap-counting function.
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…
We introduce a temperature into the exponential function and replace the softmax output layer of neural nets by a high temperature generalization. Similarly, the logarithm in the log loss we use for training is replaced by a low temperature logarithm. By tuning the two temperatures we create loss functions that are non…
Improved logistic MoE with sigmoid gate shows better sample efficiency.
problem Improving sample efficiency in logistic MoE models.
method Comprehensive analysis of multinomial logistic MoE with modified sigmoid gate, incorporating temperature parameter and using Euclidean score.
result The sigmoid gate leads to lower sample complexity than softmax gate for both parameter and expert estimation.
A softmax operator applied to a set of values acts somewhat like the maximization function and somewhat like an average. In sequential decision making, softmax is often used in settings where it is necessary to maximize utility but also to hedge against problems that arise from putting all of one's weight behind a sing…
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.
The impact of softmax on the value function itself in reinforcement learning (RL) is often viewed as problematic because it leads to sub-optimal value (or Q) functions and interferes with the contraction properties of the Bellman operator. Surprisingly, despite these concerns, and independent of its effect on explorati…
A new loss function improves neural networks' out-of-distribution detection without side effects.
problem Neural networks struggle with out-of-distribution detection due to SoftMax loss issues.
method Proposes IsoMax loss replacing SoftMax loss, maintaining high entropy and fast inferences.
result Significantly improves neural networks' out-of-distribution detection performance.
This paper introduces 'General Cyclical Training' for neural networks.
problem Improving training efficiency and performance of neural networks.
method Cyclical training phases with varying hyperparameters, batch sizes, loss functions, and data augmentation.
result Cyclical weight decay, softmax temperature, and gradient clipping enhance model accuracy.
Improved similarity search in embeddings using InfoNCE loss.
problem Improving similarity search in embedding models trained by contrastive learning.
method Introduced a new continuity bound for InfoNCE loss via Gâteaux differentiation, preserving the averaging effect of negative samples.
result Demonstrated that the averaging effect of k negative samples in InfoNCE loss carries over to stabilisation of generalisation error as k grows. Reward augmented maximum likelihood (RAML), a simple and effective learning framework to directly optimize towards the reward function in structured prediction tasks, has led to a number of impressive empirical successes. RAML incorporates task-specific reward by performing maximum-likelihood updates on candidate outpu…
K-Means and RBF networks are shown to be equivalent under certain conditions.
problem Discrete clustering vs. continuous optimization in machine learning.
method Established variational and gradient-based equivalence between K-Means and RBF networks.
result Gradient-based updates of RBF centers recover K-Means centroid update rule.
A new method for uncertainty estimation in neural networks using Gaussian-softmax integration.
problem Quantifying uncertainty in neural network predictions.
method Proposes a single-model approach integrating Gaussian distribution with softmax outputs, using mean-field approximation.
result Competitive performance on uncertainty estimation tasks and outperforms many methods on out-of-distribution detection.
Linear Q-learning converges to a bounded set without divergence.
problem Proving linear Q-learning does not diverge and converges to a bounded set.
method No modifications to the original linear Q-learning algorithm, no Bellman completeness or near-optimality assumptions, only an ε-softmax behavior policy with adaptive temperature.
result First L2 convergence rate of linear Q-learning iterates to a bounded set. DSoftKI scales GP regression with full derivative observations.
problem Efficiently fitting and predicting full derivative observations in Gaussian Processes.
method Extends SoftKI by using local temperature vectors for interpolation, enabling encoding of local directional sensitivity.
result DSoftKI achieves accurate predictions and scales to larger datasets with full derivative observations.
New Transformer architecture prevents rank degeneracy in deep attention models.
problem Rank degeneracy in deep attention models.
method Modified Softmax-based attention model with skip connections, centered at identity, and scaled logits.
result Existence of a stable SDE implies well-behaved covariance structure, preventing rank degeneracy.
TS improves class coverage but reduces CP set size, offering a trade-off.
problem Combining temperature scaling with conformal prediction for deep classifiers.
method Empirical study and mathematical theory of TS's effect on CP.
result TS allows trading prediction set size and conditional coverage.
Softmax is an output activation function for modeling categorical probability distributions in many applications of deep learning. However, a recent study revealed that softmax can be a bottleneck of representational capacity of neural networks in language modeling (the softmax bottleneck). In this paper, we propose an…
We consider the problem of detecting out-of-distribution images in neural networks. We propose ODIN, a simple and effective method that does not require any change to a pre-trained neural network. Our method is based on the observation that using temperature scaling and adding small perturbations to the input can separ…
The computational cost of training with softmax cross entropy loss grows linearly with the number of classes. For the settings where a large number of classes are involved, a common method to speed up training is to sample a subset of classes and utilize an estimate of the loss gradient based on these classes, known as…
Optimizing full likelihoods adapts loss scales and shapes for robust modeling.
problem Rigid loss functions limit model adaptability and robustness.
method Optimize full likelihoods with adjustable parameters.
result Adaptive tuning of loss scales and shapes improves model robustness.
MEMEC improves sample efficiency in reinforcement learning.
problem Lack of sample efficiency in reinforcement learning.
method Proposes MEMEC, a Boltzmann policy with state-dependent temperature for more principled exploration.
result MEMEC outperforms other methods on classic RL environments and Atari games.
Stochastic attention learns to retrieve and generate from memory without training.
problem Learning to retrieve and generate from memory efficiently.
method Langevin dynamics on modern Hopfield energy for stochastic attention.
result Stochastic attention can retrieve and generate from memory without training, matching gold standards.
Paper introduces Balanced Meta-Softmax for better long-tailed visual recognition.
problem Long-tailed distribution mismatch between training and testing data.
method Balanced Meta-Softmax, an unbiased extension of Softmax, using a Meta Sampler.
result Balanced Meta-Softmax outperforms state-of-the-art solutions on visual recognition and instance segmentation.
Paper introduces hierarchical softmax for global hierarchical classification tasks.
problem Improving classification accuracy in tasks with class hierarchies.
method Global hierarchical neural networks using hierarchical softmax.
result Hierarchical softmax outperforms regular softmax in multiple datasets.
Typically, Softmax is used in the final layer of a neural network to get a probability distribution for output classes. But the main problem with Softmax is that it is computationally expensive for large scale data sets with large number of possible outputs. To approximate class probability efficiently on such large sc…
Binary testing for softmax models requires many samples, similar to leverage score models.
problem Binary hypothesis testing for softmax models and leverage score models.
method Analyzing sample complexity and drawing analogies between models.
result Sample complexity is asymptotically \(O(ε^{-2})\), where \(ε\) is the distance between model parameters.
Sparse attention model reduces long-context inference time with exponential accuracy guarantees.
problem Efficiently processing long-context queries in large language models.
method Formalizes attention as a projection onto key vectors, analyzes entropic relaxation, and introduces Vashista Sparse Attention.
result Sparse attention concentrates on a constant-size active face, leading to exponential decay of inactive tokens' mass and linear scaling of active face error.
The paper investigates polynomial alternatives to softmax in transformer models.
problem The effectiveness of softmax attention in transformers is questioned.
method The authors explore polynomial activations as alternatives to softmax, focusing on their ability to regularize the attention matrix.
result Certain polynomials can serve as effective substitutes for softmax in transformer applications, achieving strong performance.
Softmax is a standard final layer used in Neural Nets (NNs) to summarize information encoded in the trained NN and return a prediction. However, Softmax leverages only a subset of the class-specific structure encoded in the trained model and ignores potentially valuable information: During training, models encode an ar…
Cross-entropy loss together with softmax is arguably one of the most common used supervision components in convolutional neural networks (CNNs). Despite its simplicity, popularity and excellent performance, the component does not explicitly encourage discriminative learning of features. In this paper, we propose a gene…
Despite great popularity of applying softmax to map the non-normalised outputs of a neural network to a probability distribution over predicting classes, this normalised exponential transformation still seems to be artificial. A theoretic framework that incorporates softmax as an intrinsic component is still lacking. I…
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.
Computations for the softmax function are significantly expensive when the number of output classes is large. In this paper, we present a novel softmax inference speedup method, Doubly Sparse Softmax (DS-Softmax), that leverages sparse mixture of sparse experts to efficiently retrieve top-k classes. Different from most…
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.
In a multi-class classification problem, it is standard to model the output of a neural network as a categorical distribution conditioned on the inputs. The output must therefore be positive and sum to one, which is traditionally enforced by a softmax. This probabilistic mapping allows to use the maximum likelihood pri…
Recent neural network and language models rely on softmax distributions with an extremely large number of categories. Since calculating the softmax normalizing constant in this context is prohibitively expensive, there is a growing literature of efficiently computable but biased estimates of the softmax. In this paper …
Transformers use ReLUs to approximate softmax efficiently.
problem Analyzing resource usage in softmax transformer models.
method Translating ReLU approximation results to softmax attention mechanisms.
result Economic resource bounds for softmax attention mechanisms.
Solves challenges in estimating parameters of softmax gating Gaussian mixture models.
problem Identifiability issues and complex interactions in Gaussian mixture of experts.
method Proposes novel Voronoi loss functions and establishes convergence rates of MLE.
result Connects convergence rate of MLE to a solvability problem of polynomial equations.
Speaker Recognition is a challenging task with essential applications such as authentication, automation, and security. The SincNet is a new deep learning based model which has produced promising results to tackle the mentioned task. To train deep learning systems, the loss function is essential to the network performa…
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.
FEM improves attention mechanisms by applying value-driven log-linear tilts.
problem Standard attention mechanisms read via convex average, limiting channel-wise selection.
method Free Energy Mixer (FEM) applies a value-driven, per-channel log-linear tilt to a fast prior over indices.
result FEM outperforms strong baselines on NLP, vision, and time-series tasks.