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…
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48 results for “Softmax Operator”
Value function estimation is an important task in reinforcement learning, i.e., prediction. The Boltzmann softmax operator is a natural value estimator and can provide several benefits. However, it does not satisfy the non-expansion property, and its direct use may fail to converge even in value iteration. In this pape…
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…
Softmax is found ineffective for NL block, leading to improved performance.
problem Inefficiency of softmax in NL block for global context modeling.
method Empirical analysis and replacement of softmax with scaling factor.
result Improved performance on various datasets with reduced computational cost.
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.
A new operator based on t-distributions improves NN classifiers' robustness to out-of-distribution samples.
problem NN classifiers assign extreme probabilities to out-of-distribution samples, leading to unreliable predictions.
method Derive a novel operator using t-distributions to model uncertainty more accurately.
result Classifiers using the new operator are more robust to out-of-distribution samples.
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.
Paper proposes Sinkformers for Transformers with doubly stochastic attention.
problem Improving Transformer models' accuracy in vision and natural language processing.
method Using Sinkhorn's algorithm to make attention matrices doubly stochastic instead of SoftMax normalization.
result Sinkformers enhance model accuracy in vision and natural language processing tasks.
Efficient algorithm for evaluating hierarchical classification methods at multiple operating points.
problem Evaluating hierarchical classification methods at multiple operating points.
method Efficient algorithm to produce operating characteristic curves for any method that assigns scores to every class in the hierarchy.
result Top-down classifiers are dominated by a naive flat softmax classifier across the entire operating range.
Permutations and matchings are core building blocks in a variety of latent variable models, as they allow us to align, canonicalize, and sort data. Learning in such models is difficult, however, because exact marginalization over these combinatorial objects is intractable. In response, this paper introduces a collectio…
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 study the tradeoff between computational effort and classification accuracy in a cascade of deep neural networks. During inference, the user sets the acceptable accuracy degradation which then automatically determines confidence thresholds for the intermediate classifiers. As soon as the confidence threshold is met,…
New RFs reduce kernel approximation variance and improve Transformer performance.
problem Efficient approximation of Gaussian and softmax kernels for kernel methods and Transformers.
method Parameterized, positive, non-trigonometric RFs optimized for variance reduction.
result Significant variance reduction in practice, outperforming previous methods.
LARF improves random forests with attention mechanisms and contamination models.
problem Improving accuracy in classification tasks with random forests.
method Introduces a two-level attention mechanism and uses a mixture of contamination models.
result Significantly improved classification performance on various datasets.
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…
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.
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.
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.
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.
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.
Unpacking Softmax: How Temperature Drives Representation Collapse, Compression, and Generalizationcs.LG
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.
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…
Softmax Is Not an Artificial Trick: An Information-Theoretic View of Softmax in Neural Networkscs.LG
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…
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…
Modern neural networks are often augmented with an attention mechanism, which tells the network where to focus within the input. We propose in this paper a new framework for sparse and structured attention, building upon a smoothed max operator. We show that the gradient of this operator defines a mapping from real val…
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…
Quaternion self-attention reduces computational cost and improves performance.
problem Existing quaternion self-attention increases computational cost and diverges attention distributions.
method Proposes a shared-score quaternion self-attention mechanism.
result Reduces score-computation multiplications by 75% and softmax operations from four to one.
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 convergence rate of linear Q-learning iterates to a bounded set.
Unified interpretation of softmax cross-entropy and negative sampling for knowledge graph embedding.
problem Lack of theoretical relationship between softmax cross-entropy and negative sampling loss functions in knowledge graph embedding.
method Used Bregman divergence to provide a unified interpretation of the two loss functions.
result Theoretical findings for fair comparison of softmax cross-entropy and negative sampling are derived.
Introduces gradient decay in Softmax for better generalization.
problem Improving generalization performance in neural networks.
method Gradient decay hyperparameter in Softmax for varying gradient rates based on probability.
result Gradient decay rate affects generalization performance and can be tuned for better optimization.
New L2 regularization improves softmax MAB performance.
problem Improving softmax MAB performance with vanishing regularization.
method L2 regularization with vanishing parameter analyzed and proven convergent.
result Vanishing L2 regularization makes softmax MAB more numerically advantageous.
Gradient flow in softmax models tends to produce low-entropy outputs.
problem Understanding the training dynamics of softmax-based models.
method Analysis of gradient flow dynamics in the value-softmax model.
result Gradient flow drives optimization towards low-entropy solutions.
This note considers softmax parameter estimation when little/no labeled training data is available, but a priori information about the relative geometry of class label log-odds boundaries is available. It is shown that `data-free' softmax model synthesis corresponds to solving a linear system of parameter equations, wh…
Softmax PG methods can take extremely long to converge, even with exact gradients.
problem Softmax policy gradient methods can take an impractically long time to converge in reinforcement learning.
method Softmax policy gradient methods with exact gradient computation.
result Softmax PG methods can take exponential number of iterations to converge, even with optimal initialization.
In recent years, the softmax model and its fast approximations have become the de-facto loss functions for deep neural networks when dealing with multi-class prediction. This loss has been extended to language modeling and recommendation, two fields that fall into the framework of learning from Positive and Unlabeled d…
WEINCE improves contrastive learning by correcting softmax biases.
problem Softmax in InfoNCE can lead to misaligned statistical assumptions in contrastive learning.
method WEINCE uses anchor-wise online batch statistics to blend softmax logits with an endpoint shortfall correction.
result WEINCE yields consistent improvements in frozen-feature evaluation across five vision benchmarks.
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.
Generative Adversarial Networks (GAN) have limitations when the goal is to generate sequences of discrete elements. The reason for this is that samples from a distribution on discrete objects such as the multinomial are not differentiable with respect to the distribution parameters. This problem can be avoided by using…
Improved language models with talking-heads attention.
problem Language model perplexity and quality issues.
method Added linear projections in multi-head attention.
result Better perplexities and quality in language tasks.
New insights into the top-K sparse softmax gating function for deep learning.
problem Understanding the theoretical effects of the top-K sparse softmax gating function on density and parameter estimations.
method Using a Gaussian mixture of experts, novel loss functions, and theoretical analysis.
result The convergence rates of density and parameter estimations are parametric under certain conditions, but slow under over-specified models.