The Effect of SGD Batch Size on Autoencoder Learning: Sparsity, Sharpness, and Feature Learning

In this work, we investigate the dynamics of stochastic gradient descent (SGD) when training a single-neuron autoencoder with linear or ReLU activation on orthogonal data. We show that for this non-convex problem, randomly initialized SGD with a constant step size successfully finds a global minimum for any batch size choice. However, the particular global minimum found depends upon the batch size. In the full-batch setting, we show that the solution is dense (i.e., not sparse) and is highly aligned with its initialized direction, showing that relatively little feature learning occurs. On the other hand, for any batch size strictly smaller than the number of samples, SGD finds a global minimum which is sparse and nearly orthogonal to its initialization, showing that the randomness of stochastic gradients induces a qualitatively different type of "feature selection" in this setting. Moreover, if we measure the sharpness of the minimum by the trace of the Hessian, the minima found with full batch gradient descent are flatter than those found with strictly smaller batch sizes, in contrast to previous works which suggest that large batches lead to sharper minima. To prove convergence of SGD with a constant step size, we introduce a powerful tool from the theory of non-homogeneous random walks which may be of independent interest.

Improving Prototypical Part Networks with Reward Reweighing, Reselection, and Retraining

In recent years, work has gone into developing deep interpretable methods for image classification that clearly attributes a model's output to specific features of the data. One such of these methods is the prototypical part network (ProtoPNet), which attempts to classify images based on meaningful parts of the input. While this method results in interpretable classifications, this method often learns to classify from spurious or inconsistent parts of the image. Hoping to remedy this, we take inspiration from the recent developments in Reinforcement Learning with Human Feedback (RLHF) to fine-tune these prototypes. By collecting human annotations of prototypes quality via a 1-5 scale on the CUB-200-2011 dataset, we construct a reward model that learns to identify non-spurious prototypes. In place of a full RL update, we propose the reweighted, reselected, and retrained prototypical part network (R3-ProtoPNet), which adds an additional three steps to the ProtoPNet training loop. The first two steps are reward-based reweighting and reselection, which align prototypes with human feedback. The final step is retraining to realign the model's features with the updated prototypes. We find that R3-ProtoPNet improves the overall consistency and meaningfulness of the prototypes, but lower the test predictive accuracy when used independently. When multiple R3-ProtoPNets are incorporated into an ensemble, we find an increase in test predictive performance while maintaining interpretability.

SkipDecode: Autoregressive Skip Decoding with Batching and Caching for Efficient LLM Inference

Autoregressive large language models (LLMs) have made remarkable progress in various natural language generation tasks. However, they incur high computation cost and latency resulting from the autoregressive token-by-token generation. To address this issue, several approaches have been proposed to reduce computational cost using early-exit strategies. These strategies enable faster text generation using reduced computation without applying the full computation graph to each token. While existing token-level early exit methods show promising results for online inference, they cannot be readily applied for batch inferencing and Key-Value caching. This is because they have to wait until the last token in a batch exits before they can stop computing. This severely limits the practical application of such techniques. In this paper, we propose a simple and effective token-level early exit method, SkipDecode, designed to work seamlessly with batch inferencing and KV caching. It overcomes prior constraints by setting up a singular exit point for every token in a batch at each sequence position. It also guarantees a monotonic decrease in exit points, thereby eliminating the need to recompute KV Caches for preceding tokens. Rather than terminating computation prematurely as in prior works, our approach bypasses lower to middle layers, devoting most of the computational resources to upper layers, allowing later tokens to benefit from the compute expenditure by earlier tokens. Our experimental results show that SkipDecode can obtain 2x to 5x inference speedups with negligible regression across a variety of tasks. This is achieved using OPT models of 1.3 billion and 6.7 billion parameters, all the while being directly compatible with batching and KV caching optimization techniques.

MDI+: A Flexible Random Forest-Based Feature Importance Framework

Mean decrease in impurity (MDI) is a popular feature importance measure for random forests (RFs). We show that the MDI for a feature $X_k$ in each tree in an RF is equivalent to the unnormalized $R^2$ value in a linear regression of the response on the collection of decision stumps that split on $X_k$. We use this interpretation to propose a flexible feature importance framework called MDI+. Specifically, MDI+ generalizes MDI by allowing the analyst to replace the linear regression model and $R^2$ metric with regularized generalized linear models (GLMs) and metrics better suited for the given data structure. Moreover, MDI+ incorporates additional features to mitigate known biases of decision trees against additive or smooth models. We further provide guidance on how practitioners can choose an appropriate GLM and metric based upon the Predictability, Computability, Stability framework for veridical data science. Extensive data-inspired simulations show that MDI+ significantly outperforms popular feature importance measures in identifying signal features. We also apply MDI+ to two real-world case studies on drug response prediction and breast cancer subtype classification. We show that MDI+ extracts well-established predictive genes with significantly greater stability compared to existing feature importance measures. All code and models are released in a full-fledged python package on Github.

An Investigation into the Effects of Pre-training Data Distributions for Pathology Report Classification

Pre-trained transformer models have demonstrated success across many natural language processing (NLP) tasks. In applying these models to the clinical domain, a prevailing assumption is that pre-training language models from scratch on large-scale biomedical data results in substantial improvements. We test this assumption with 4 pathology classification tasks on a corpus of 2907 prostate cancer pathology reports. We evaluate 5 transformer pre-trained models that are the same size but differ in pre-training corpora. Specifically, we analyze 3 categories of models: 1)General-domain: BERT and Turing Natural Language Representation (TNLR) models, which use general corpora for pre-training, 2)Mixed-domain: BioBERT which is obtained from BERT by including PubMed abstracts in pre-training and Clinical BioBERT which additionally includes MIMIC-III clinical notes and 3)Domain-specific: PubMedBERT which is pre-trained from scratch on PubMed abstracts. We find the mixed-domain and domain-specific models exhibit faster feature disambiguation during fine-tuning. However, the domain-specific model, PubMedBERT, can overfit to minority classes when presented with class imbalance, a common scenario in pathology report data. At the same time, the mixed-domain models are more resistant to overfitting. Our findings indicate that the use of general natural language and domain-specific corpora in pre-training serve complementary purposes for pathology report classification. The first enables resistance to overfitting when fine-tuning on an imbalanced dataset while the second allows for more accurate modelling of the fine-tuning domain. An expert evaluation is also conducted to reveal common outlier modes of each model. Our results could inform better fine-tuning practices in the clinical domain, to possibly leverage the benefits of mixed-domain models for imbalanced downstream datasets.

Explaining black box text modules in natural language with language models

Large language models (LLMs) have demonstrated remarkable prediction performance for a growing array of tasks. However, their rapid proliferation and increasing opaqueness have created a growing need for interpretability. Here, we ask whether we can automatically obtain natural language explanations for black box text modules. A "text module" is any function that maps text to a scalar continuous value, such as a submodule within an LLM or a fitted model of a brain region. "Black box" indicates that we only have access to the module's inputs/outputs. We introduce Summarize and Score (SASC), a method that takes in a text module and returns a natural language explanation of the module's selectivity along with a score for how reliable the explanation is. We study SASC in 3 contexts. First, we evaluate SASC on synthetic modules and find that it often recovers ground truth explanations. Second, we use SASC to explain modules found within a pre-trained BERT model, enabling inspection of the model's internals. Finally, we show that SASC can generate explanations for the response of individual fMRI voxels to language stimuli, with potential applications to fine-grained brain mapping. All code for using SASC and reproducing results is made available on Github.

Bridging Discrete and Backpropagation: Straight-Through and Beyond

Backpropagation, the cornerstone of deep learning, is limited to computing gradients solely for continuous variables. This limitation hinders various research on problems involving discrete latent variables. To address this issue, we propose a novel approach for approximating the gradient of parameters involved in generating discrete latent variables. First, we examine the widely used Straight-Through (ST) heuristic and demonstrate that it works as a first-order approximation of the gradient. Guided by our findings, we propose a novel method called ReinMax, which integrates Heun's Method, a second-order numerical method for solving ODEs, to approximate the gradient. Our method achieves second-order accuracy without requiring Hessian or other second-order derivatives. We conduct experiments on structured output prediction and unsupervised generative modeling tasks. Our results show that \ours brings consistent improvements over the state of the art, including ST and Straight-Through Gumbel-Softmax. Implementations are released at https://github.com/microsoft/ReinMax.

A Mixing Time Lower Bound for a Simplified Version of BART

Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression algorithm. The posterior is a distribution over sums of decision trees, and predictions are made by averaging approximate samples from the posterior. The combination of strong predictive performance and the ability to provide uncertainty measures has led BART to be commonly used in the social sciences, biostatistics, and causal inference. BART uses Markov Chain Monte Carlo (MCMC) to obtain approximate posterior samples over a parameterized space of sums of trees, but it has often been observed that the chains are slow to mix. In this paper, we provide the first lower bound on the mixing time for a simplified version of BART in which we reduce the sum to a single tree and use a subset of the possible moves for the MCMC proposal distribution. Our lower bound for the mixing time grows exponentially with the number of data points. Inspired by this new connection between the mixing time and the number of data points, we perform rigorous simulations on BART. We show qualitatively that BART's mixing time increases with the number of data points. The slow mixing time of the simplified BART suggests a large variation between different runs of the simplified BART algorithm and a similar large variation is known for BART in the literature. This large variation could result in a lack of stability in the models, predictions, and posterior intervals obtained from the BART MCMC samples. Our lower bound and simulations suggest increasing the number of chains with the number of data points.

SOFFLFM: Super-resolution optical fluctuation Fourier light-field microscopy

Fourier light-field microscopy (FLFM) uses a micro-lens array (MLA) to segment the Fourier Plane of the microscopic objective lens to generate multiple two-dimensional perspective views, thereby reconstructing the three-dimensional(3D) structure of the sample using 3D deconvolution calculation without scanning. However, the resolution of FLFM is still limited by diffraction, and furthermore, dependent on the aperture division. In order to improve its resolution, a Super-resolution optical fluctuation Fourier light field microscopy (SOFFLFM) was proposed here, in which the Sofi method with ability of super-resolution was introduced into FLFM. SOFFLFM uses higher-order cumulants statistical analysis on an image sequence collected by FLFM, and then carries out 3D deconvolution calculation to reconstruct the 3D structure of the sample. Theoretical basis of SOFFLFM on improving resolution was explained and then verified with simulations. Simulation results demonstrated that SOFFLFM improved lateral and axial resolution by more than sqrt(2) and 2 times in the 2nd and 4th order accumulations, compared with that of FLFM.

Learning Using Privileged Information for Zero-Shot Action Recognition

Zero-Shot Action Recognition (ZSAR) aims to recognize video actions that have never been seen during training. Most existing methods assume a shared semantic space between seen and unseen actions and intend to directly learn a mapping from a visual space to the semantic space. This approach has been challenged by the semantic gap between the visual space and semantic space. This paper presents a novel method that uses object semantics as privileged information to narrow the semantic gap and, hence, effectively, assist the learning. In particular, a simple hallucination network is proposed to implicitly extract object semantics during testing without explicitly extracting objects and a cross-attention module is developed to augment visual feature with the object semantics. Experiments on the Olympic Sports, HMDB51 and UCF101 datasets have shown that the proposed method outperforms the state-of-the-art methods by a large margin.