Richard G. Baraniuk

Vishwanath Saragadam, Daniel LeJeune, Jasper Tan et al. · cmu

Implicit neural representations (INRs) have recently advanced numerous vision-related areas. INR performance depends strongly on the choice of the nonlinear activation function employed in its multilayer perceptron (MLP) network. A wide range of nonlinearities have been explored, but, unfortunately, current INRs designed to have high accuracy also suffer from poor robustness (to signal noise, parameter variation, etc.). Inspired by harmonic analysis, we develop a new, highly accurate and robust INR that does not exhibit this tradeoff. Wavelet Implicit neural REpresentation (WIRE) uses a continuous complex Gabor wavelet activation function that is well-known to be optimally concentrated in space-frequency and to have excellent biases for representing images. A wide range of experiments (image denoising, image inpainting, super-resolution, computed tomography reconstruction, image overfitting, and novel view synthesis with neural radiance fields) demonstrate that WIRE defines the new state of the art in INR accuracy, training time, and robustness.

Vishwanath Saragadam, Randall Balestriero, Ashok Veeraraghavan et al. · cmu

DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of two vectors), where each low-rank tensor is generated by a deep network (DN) that is trained in a self-supervised manner to minimize the mean-squared approximation error. Our key observation is that the implicit regularization inherent in DNs enables them to capture nonlinear signal structures (e.g., manifolds) that are out of the reach of classical linear methods like the singular value decomposition (SVD) and principal component analysis (PCA). Furthermore, in contrast to the SVD and PCA, whose performance deteriorates when the tensor's entries deviate from additive white Gaussian noise, we demonstrate that the performance of DeepTensor is robust to a wide range of distributions. We validate that DeepTensor is a robust and computationally efficient drop-in replacement for the SVD, PCA, nonnegative matrix factorization (NMF), and similar decompositions by exploring a range of real-world applications, including hyperspectral image denoising, 3D MRI tomography, and image classification. In particular, DeepTensor offers a 6dB signal-to-noise ratio improvement over standard denoising methods for signals corrupted by Poisson noise and learns to decompose 3D tensors 60 times faster than a single DN equipped with 3D convolutions.

Shashank Sonkar, MyCo Le, Xinghe Chen et al.

High-quality conversational datasets are crucial for the successful development of Intelligent Tutoring Systems (ITS) that utilize a Large Language Model (LLM) backend. Synthetic student-teacher dialogues, generated using advanced GPT-4 models, are a common strategy for creating these datasets. However, subjects like physics that entail complex calculations pose a challenge. While GPT-4 presents impressive language processing capabilities, its limitations in fundamental mathematical reasoning curtail its efficacy for such subjects. To tackle this limitation, we introduce in this paper an innovative stateful prompt design. Our design orchestrates a mock conversation where both student and tutorbot roles are simulated by GPT-4. Each student response triggers an internal monologue, or `code soliloquy' in the GPT-tutorbot, which assesses whether its subsequent response would necessitate calculations. If a calculation is deemed necessary, it scripts the relevant Python code and uses the Python output to construct a response to the student. Our approach notably enhances the quality of synthetic conversation datasets, especially for subjects that are calculation-intensive. Our preliminary Subject Matter Expert evaluations reveal that our Higgs model, a fine-tuned LLaMA model, effectively uses Python for computations, which significantly enhances the accuracy and computational reliability of Higgs' responses. Code, models, and datasets is available at https://github.com/luffycodes/Tutorbot-Spock-Phys.

Vishwanath Saragadam, Zheyi Han, Vivek Boominathan et al. · cmu

Foveated imaging provides a better tradeoff between situational awareness (field of view) and resolution and is critical in long-wavelength infrared regimes because of the size, weight, power, and cost of thermal sensors. We demonstrate computational foveated imaging by exploiting the ability of a meta-optical frontend to discriminate between different polarization states and a computational backend to reconstruct the captured image/video. The frontend is a three-element optic: the first element which we call the "foveal" element is a metalens that focuses s-polarized light at a distance of $f_1$ without affecting the p-polarized light; the second element which we call the "perifoveal" element is another metalens that focuses p-polarized light at a distance of $f_2$ without affecting the s-polarized light. The third element is a freely rotating polarizer that dynamically changes the mixing ratios between the two polarization states. Both the foveal element (focal length = 150mm; diameter = 75mm), and the perifoveal element (focal length = 25mm; diameter = 25mm) were fabricated as polarization-sensitive, all-silicon, meta surfaces resulting in a large-aperture, 1:6 foveal expansion, thermal imaging capability. A computational backend then utilizes a deep image prior to separate the resultant multiplexed image or video into a foveated image consisting of a high-resolution center and a lower-resolution large field of view context. We build a first-of-its-kind prototype system and demonstrate 12 frames per second real-time, thermal, foveated image, and video capture in the wild.

Sina Alemohammad, Josue Casco-Rodriguez, Lorenzo Luzi et al.

Seismic advances in generative AI algorithms for imagery, text, and other data types has led to the temptation to use synthetic data to train next-generation models. Repeating this process creates an autophagous (self-consuming) loop whose properties are poorly understood. We conduct a thorough analytical and empirical analysis using state-of-the-art generative image models of three families of autophagous loops that differ in how fixed or fresh real training data is available through the generations of training and in whether the samples from previous generation models have been biased to trade off data quality versus diversity. Our primary conclusion across all scenarios is that without enough fresh real data in each generation of an autophagous loop, future generative models are doomed to have their quality (precision) or diversity (recall) progressively decrease. We term this condition Model Autophagy Disorder (MAD), making analogy to mad cow disease.

Lorenzo Luzi, Paul M Mayer, Josue Casco-Rodriguez et al.

The inference stage of diffusion models can be seen as running a reverse-time diffusion stochastic differential equation, where samples from a Gaussian latent distribution are transformed into samples from a target distribution that usually reside on a low-dimensional manifold, e.g., an image manifold. The intermediate values between the initial latent space and the image manifold can be interpreted as noisy images, with the amount of noise determined by the forward diffusion process noise schedule. We utilize this interpretation to present Boomerang, an approach for local sampling of image manifolds. As implied by its name, Boomerang local sampling involves adding noise to an input image, moving it closer to the latent space, and then mapping it back to the image manifold through a partial reverse diffusion process. Thus, Boomerang generates images on the manifold that are ``similar,'' but nonidentical, to the original input image. We can control the proximity of the generated images to the original by adjusting the amount of noise added. Furthermore, due to the stochastic nature of the reverse diffusion process in Boomerang, the generated images display a certain degree of stochasticity, allowing us to obtain local samples from the manifold without encountering any duplicates. Boomerang offers the flexibility to work seamlessly with any pretrained diffusion model, such as Stable Diffusion, without necessitating any adjustments to the reverse diffusion process. We present three applications for Boomerang. First, we provide a framework for constructing privacy-preserving datasets having controllable degrees of anonymity. Second, we show that using Boomerang for data augmentation increases generalization performance and outperforms state-of-the-art synthetic data augmentation. Lastly, we introduce a perceptual image enhancement framework, which enables resolution enhancement.

Jasper Tan, Daniel LeJeune, Blake Mason et al.

Is overparameterization a privacy liability? In this work, we study the effect that the number of parameters has on a classifier's vulnerability to membership inference attacks. We first demonstrate how the number of parameters of a model can induce a privacy--utility trade-off: increasing the number of parameters generally improves generalization performance at the expense of lower privacy. However, remarkably, we then show that if coupled with proper regularization, increasing the number of parameters of a model can actually simultaneously increase both its privacy and performance, thereby eliminating the privacy--utility trade-off. Theoretically, we demonstrate this curious phenomenon for logistic regression with ridge regularization in a bi-level feature ensemble setting. Pursuant to our theoretical exploration, we develop a novel leave-one-out analysis tool to precisely characterize the vulnerability of a linear classifier to the optimal membership inference attack. We empirically exhibit this "blessing of dimensionality" for neural networks on a variety of tasks using early stopping as the regularizer.

Randall Balestriero, Richard G. Baraniuk

A critically important, ubiquitous, and yet poorly understood ingredient in modern deep networks (DNs) is batch normalization (BN), which centers and normalizes the feature maps. To date, only limited progress has been made understanding why BN boosts DN learning and inference performance; work has focused exclusively on showing that BN smooths a DN's loss landscape. In this paper, we study BN theoretically from the perspective of function approximation; we exploit the fact that most of today's state-of-the-art DNs are continuous piecewise affine (CPA) splines that fit a predictor to the training data via affine mappings defined over a partition of the input space (the so-called "linear regions"). {\em We demonstrate that BN is an unsupervised learning technique that -- independent of the DN's weights or gradient-based learning -- adapts the geometry of a DN's spline partition to match the data.} BN provides a "smart initialization" that boosts the performance of DN learning, because it adapts even a DN initialized with random weights to align its spline partition with the data. We also show that the variation of BN statistics between mini-batches introduces a dropout-like random perturbation to the partition boundaries and hence the decision boundary for classification problems. This per mini-batch perturbation reduces overfitting and improves generalization by increasing the margin between the training samples and the decision boundary.

Rudolf H. Riedi, Randall Balestriero, Richard G. Baraniuk

We develop new theoretical results on matrix perturbation to shed light on the impact of architecture on the performance of a deep network. In particular, we explain analytically what deep learning practitioners have long observed empirically: the parameters of some deep architectures (e.g., residual networks, ResNets, and Dense networks, DenseNets) are easier to optimize than others (e.g., convolutional networks, ConvNets). Building on our earlier work connecting deep networks with continuous piecewise-affine splines, we develop an exact local linear representation of a deep network layer for a family of modern deep networks that includes ConvNets at one end of a spectrum and ResNets, DenseNets, and other networks with skip connections at the other. For regression and classification tasks that optimize the squared-error loss, we show that the optimization loss surface of a modern deep network is piecewise quadratic in the parameters, with local shape governed by the singular values of a matrix that is a function of the local linear representation. We develop new perturbation results for how the singular values of matrices of this sort behave as we add a fraction of the identity and multiply by certain diagonal matrices. A direct application of our perturbation results explains analytically why a network with skip connections (such as a ResNet or DenseNet) is easier to optimize than a ConvNet: thanks to its more stable singular values and smaller condition number, the local loss surface of such a network is less erratic, less eccentric, and features local minima that are more accommodating to gradient-based optimization. Our results also shed new light on the impact of different nonlinear activation functions on a deep network's singular values, regardless of its architecture.

Tan Nguyen, Richard G. Baraniuk, Robert M. Kirby et al.

Transformers have achieved remarkable success in sequence modeling and beyond but suffer from quadratic computational and memory complexities with respect to the length of the input sequence. Leveraging techniques include sparse and linear attention and hashing tricks; efficient transformers have been proposed to reduce the quadratic complexity of transformers but significantly degrade the accuracy. In response, we first interpret the linear attention and residual connections in computing the attention map as gradient descent steps. We then introduce momentum into these components and propose the \emph{momentum transformer}, which utilizes momentum to improve the accuracy of linear transformers while maintaining linear memory and computational complexities. Furthermore, we develop an adaptive strategy to compute the momentum value for our model based on the optimal momentum for quadratic optimization. This adaptive momentum eliminates the need to search for the optimal momentum value and further enhances the performance of the momentum transformer. A range of experiments on both autoregressive and non-autoregressive tasks, including image generation and machine translation, demonstrate that the momentum transformer outperforms popular linear transformers in training efficiency and accuracy.

Sina Alemohammad, Li Chen, Richard G. Baraniuk et al.

Can a language model improve from plain text sampled from itself, with no prompts, no teacher, no verifier, and no reward model? Yes, but only when the synthetic corpus is compatible with the student, a relational property of the source-student pair rather than an intrinsic property of the data. We call this the latent capability resurfacing hypothesis: weak self-training can amplify capabilities already present in the pretrained model, but only under this compatibility condition. We study this in the minimal setting of prompt-free unconditional self-training, where base language models are fine-tuned on text generated from the BOS token alone, with no task specification or external supervision. We report three findings. First, synthetic utility is relational rather than intrinsic: self-generated data is the most effective source, same-lineage transfer outperforms stronger but differently trained sources, and cross-family transfer is substantially weaker. Second, common intrinsic proxies fail: neither benchmark-level semantic similarity nor average per-token likelihood under the student predicts which corpora help. Third, this regime produces a surprising byproduct. In controlled Pythia experiments, capability and verbatim memorization decouple: benchmark utility is preserved or improved while held-out exact-match extraction drops by over 95 percent, with no forget set, privacy objective, or targeted unlearning. Together, these results suggest that prompt-free self-training works by amplifying what the student already knows, not by importing structure from the data. They also reveal a regime in which capability and verbatim memorization can be separated without any explicit unlearning objective.

Yehuda Dar, Lorenzo Luzi, Richard G. Baraniuk

We study the generalization behavior of transfer learning of deep neural networks (DNNs). We adopt the overparameterization perspective -- featuring interpolation of the training data (i.e., approximately zero train error) and the double descent phenomenon -- to explain the delicate effect of the transfer learning setting on generalization performance. We study how the generalization behavior of transfer learning is affected by the dataset size in the source and target tasks, the number of transferred layers that are kept frozen in the target DNN training, and the similarity between the source and target tasks. We show that the test error evolution during the target DNN training has a more significant double descent effect when the target training dataset is sufficiently large. In addition, a larger source training dataset can yield a slower target DNN training. Moreover, we demonstrate that the number of frozen layers can determine whether the transfer learning is effectively underparameterized or overparameterized and, in turn, this may induce a freezing-wise double descent phenomenon that determines the relative success or failure of learning. Also, we show that the double descent phenomenon may make a transfer from a less related source task better than a transfer from a more related source task. We establish our results using image classification experiments with the ResNet, DenseNet and the vision transformer (ViT) architectures.

Shashank Sonkar, Naiming Liu, Richard G. Baraniuk

Transformer models trained on massive text corpora have become the de facto models for a wide range of natural language processing tasks. However, learning effective word representations for function words remains challenging. Multimodal learning, which visually grounds transformer models in imagery, can overcome the challenges to some extent; however, there is still much work to be done. In this study, we explore the extent to which visual grounding facilitates the acquisition of function words using stable diffusion models that employ multimodal models for text-to-image generation. Out of seven categories of function words, along with numerous subcategories, we find that stable diffusion models effectively model only a small fraction of function words -- a few pronoun subcategories and relatives. We hope that our findings will stimulate the development of new datasets and approaches that enable multimodal models to learn better representations of function words.

Shashank Sonkar, Zichao Wang, Richard G. Baraniuk

This paper investigates the problem of Named Entity Recognition (NER) for extreme low-resource languages with only a few hundred tagged data samples. NER is a fundamental task in Natural Language Processing (NLP). A critical driver accelerating NER systems' progress is the existence of large-scale language corpora that enable NER systems to achieve outstanding performance in languages such as English and French with abundant training data. However, NER for low-resource languages remains relatively unexplored. In this paper, we introduce Mask Augmented Named Entity Recognition (MANER), a new methodology that leverages the distributional hypothesis of pre-trained masked language models (MLMs) for NER. The <mask> token in pre-trained MLMs encodes valuable semantic contextual information. MANER re-purposes the <mask> token for NER prediction. Specifically, we prepend the <mask> token to every word in a sentence for which we would like to predict the named entity tag. During training, we jointly fine-tune the MLM and a new NER prediction head attached to each <mask> token. We demonstrate that MANER is well-suited for NER in low-resource languages; our experiments show that for 100 languages with as few as 100 training examples, it improves on state-of-the-art methods by up to 48% and by 12% on average on F1 score. We also perform detailed analyses and ablation studies to understand the scenarios that are best-suited to MANER.

T. Mitchell Roddenberry, Vishwanath Saragadam, Maarten V. de Hoop et al.

Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively represent signals in a way that couples spatial and spectral features of the signal that is not obvious in the usual discrete representation, paving the way for continuous signal processing and machine learning approaches that were not previously possible. Although INRs using sinusoidal activation functions have been studied in terms of Fourier theory, recent works have shown the advantage of using wavelets instead of sinusoids as activation functions, due to their ability to simultaneously localize in both frequency and space. In this work, we approach such INRs and demonstrate how they resolve high-frequency features of signals from coarse approximations done in the first layer of the MLP. This leads to multiple prescriptions for the design of INR architectures, including the use of complex wavelets, decoupling of low and band-pass approximations, and initialization schemes based on the singularities of the desired signal.

Tam Nguyen, Tu Anh Nguyen, Sina Alemohammad et al.

Activation steering is a method for controlling Large Language Model (LLM) behavior by intervening in its internal representations to increase the alignment with a specific target feature direction. However, standard interventions, such as vector addition, often cause ``collateral damage", defined as unintended changes in the alignment of activations along other non-target feature directions. This damage occurs because standard methods implicitly assume the isotropy of non-target features. In this work, we provide a mathematical formalization of collateral damage and introduce a principled framework that models steering as a constrained optimization problem. Our method finds a new activation that minimizes the expected squared collateral change weighted by the empirical second-moment matrix of activations. This weighting encodes the nonuniform cost of the perturbation in different feature directions, in contrast to isotropic approaches that penalize changes uniformly in all feature directions. By accounting for the empirical second-moment of activations, our approach achieves more precise control while reducing the degradation of model performance on unrelated tasks.

Naiming Liu, Shashank Sonkar, Zichao Wang et al.

We propose novel evaluations for mathematical reasoning capabilities of Large Language Models (LLMs) based on mathematical misconceptions. Our primary approach is to simulate LLMs as a novice learner and an expert tutor, aiming to identify the incorrect answer to math question resulted from a specific misconception and to recognize the misconception(s) behind an incorrect answer, respectively. Contrary to traditional LLMs-based mathematical evaluations that focus on answering math questions correctly, our approach takes inspirations from principles in educational learning sciences. We explicitly ask LLMs to mimic a novice learner by answering questions in a specific incorrect manner based on incomplete knowledge; and to mimic an expert tutor by identifying misconception(s) corresponding to an incorrect answer to a question. Using simple grade-school math problems, our experiments reveal that, while LLMs can easily answer these questions correctly, they struggle to identify 1) the incorrect answer corresponding to specific incomplete knowledge (misconceptions); 2) the misconceptions that explain particular incorrect answers. Our study indicates new opportunities for enhancing LLMs' math reasoning capabilities, especially on developing robust student simulation and expert tutoring models in the educational applications such as intelligent tutoring systems.

Kushal Vyas, Ahmed Imtiaz Humayun, Aniket Dashpute et al.

Implicit neural representations (INRs) have demonstrated success in a variety of applications, including inverse problems and neural rendering. An INR is typically trained to capture one signal of interest, resulting in learned neural features that are highly attuned to that signal. Assumed to be less generalizable, we explore the aspect of transferability of such learned neural features for fitting similar signals. We introduce a new INR training framework, STRAINER that learns transferrable features for fitting INRs to new signals from a given distribution, faster and with better reconstruction quality. Owing to the sequential layer-wise affine operations in an INR, we propose to learn transferable representations by sharing initial encoder layers across multiple INRs with independent decoder layers. At test time, the learned encoder representations are transferred as initialization for an otherwise randomly initialized INR. We find STRAINER to yield extremely powerful initialization for fitting images from the same domain and allow for $\approx +10dB$ gain in signal quality early on compared to an untrained INR itself. STRAINER also provides a simple way to encode data-driven priors in INRs. We evaluate STRAINER on multiple in-domain and out-of-domain signal fitting tasks and inverse problems and further provide detailed analysis and discussion on the transferability of STRAINER's features. Our demo can be accessed at https://kushalvyas.github.io/strainer.html .

Shashank Sonkar, Kangqi Ni, Sapana Chaudhary et al.

Large Language Models (LLMs), when used in educational settings without pedagogical fine-tuning, often provide immediate answers rather than guiding students through the problem-solving process. This approach falls short of pedagogically best practices and limits their effectiveness as educational tools. We term the objective of training LLMs to emulate effective teaching strategies as `pedagogical alignment.' In this paper, we investigate Learning from Human Preferences (LHP) algorithms to achieve this alignment objective. A key challenge in this process is the scarcity of high-quality preference datasets to guide the alignment. To address this, we propose a novel approach for constructing a large-scale dataset using synthetic data generation techniques, eliminating the need for time-consuming and costly manual annotation. Leveraging this dataset, our experiments with Llama and Mistral models demonstrate that LHP methods outperform standard supervised fine-tuning (SFT), improving pedagogical alignment accuracy by 13.1% and 8.7% respectively. Existing evaluation methods also lack quantitative metrics to adequately measure the pedagogical alignment of LLMs. To address this gap, we propose novel perplexity-based metrics that quantify LLMs' tendency to provide scaffolded guidance versus direct answers, offering a robust measure of pedagogical alignment. Our analysis provides compelling evidence for the superiority of LHP methods over SFT in optimizing LLMs' behavior, underscoring the potential of LHP methods in better aligning LLMs with educational objectives and fostering effective learning experiences. Code and models are available \href{https://github.com/luffycodes/Tutorbot-Spock}{here}.

Shashank Sonkar, Kangqi Ni, Lesa Tran Lu et al.

We introduce a new area of study in the field of educational Natural Language Processing: Automated Long Answer Grading (ALAG). Distinguishing itself from Automated Short Answer Grading (ASAG) and Automated Essay Grading (AEG), ALAG presents unique challenges due to the complexity and multifaceted nature of fact-based long answers. To study ALAG, we introduce RiceChem, a dataset derived from a college chemistry course, featuring real student responses to long-answer questions with an average word count notably higher than typical ASAG datasets. We propose a novel approach to ALAG by formulating it as a rubric entailment problem, employing natural language inference models to verify whether each criterion, represented by a rubric item, is addressed in the student's response. This formulation enables the effective use of MNLI for transfer learning, significantly improving the performance of models on the RiceChem dataset. We demonstrate the importance of rubric-based formulation in ALAG, showcasing its superiority over traditional score-based approaches in capturing the nuances of student responses. We also investigate the performance of models in cold start scenarios, providing valuable insights into the practical deployment considerations in educational settings. Lastly, we benchmark state-of-the-art open-sourced Large Language Models (LLMs) on RiceChem and compare their results to GPT models, highlighting the increased complexity of ALAG compared to ASAG. Despite leveraging the benefits of a rubric-based approach and transfer learning from MNLI, the lower performance of LLMs on RiceChem underscores the significant difficulty posed by the ALAG task. With this work, we offer a fresh perspective on grading long, fact-based answers and introduce a new dataset to stimulate further research in this important area. Code: \url{https://github.com/luffycodes/Automated-Long-Answer-Grading}.

T. Mitchell Roddenberry, Leo Tzou, Ivan Dokmanić et al.

Deep learning methods have proven capable of recovering operators between high-dimensional spaces, such as solution maps of PDEs and similar objects in mathematical physics, from very few training samples. This phenomenon of data-efficiency has been proven for certain classes of elliptic operators with simple geometry, i.e., operators that do not change the domain of the function or propagate singularities. However, scientific machine learning is commonly used for problems that do involve the propagation of singularities in a priori unknown ways, such as waves, advection, and fluid dynamics. In light of this, we expand the learning theory to include double fibration transforms--geometric integral operators that include generalized Radon and geodesic ray transforms. We prove that this class of operators does not suffer from the curse of dimensionality: the error decays superalgebraically, that is, faster than any fixed power of the reciprocal of the number of training samples. Furthermore, we investigate architectures that explicitly encode the geometry of these transforms, demonstrating that an architecture reminiscent of cross-attention based on levelset methods yields a parameterization that is universal, stable, and learns double fibration transforms from very few training examples. Our results contribute to a rapidly-growing line of theoretical work on learning operators for scientific machine learning.

Shashank Sonkar, Naiming Liu, Debshila B. Mallick et al.

In this paper, we introduce "Marking", a novel grading task that enhances automated grading systems by performing an in-depth analysis of student responses and providing students with visual highlights. Unlike traditional systems that provide binary scores, "marking" identifies and categorizes segments of the student response as correct, incorrect, or irrelevant and detects omissions from gold answers. We introduce a new dataset meticulously curated by Subject Matter Experts specifically for this task. We frame "Marking" as an extension of the Natural Language Inference (NLI) task, which is extensively explored in the field of Natural Language Processing. The gold answer and the student response play the roles of premise and hypothesis in NLI, respectively. We subsequently train language models to identify entailment, contradiction, and neutrality from student response, akin to NLI, and with the added dimension of identifying omissions from gold answers. Our experimental setup involves the use of transformer models, specifically BERT and RoBERTa, and an intelligent training step using the e-SNLI dataset. We present extensive baseline results highlighting the complexity of the "Marking" task, which sets a clear trajectory for the upcoming study. Our work not only opens up new avenues for research in AI-powered educational assessment tools, but also provides a valuable benchmark for the AI in education community to engage with and improve upon in the future. The code and dataset can be found at https://github.com/luffycodes/marking.

Sina Alemohammad, Zhangyang Wang, Richard G. Baraniuk

Scaling generative AI models is bottlenecked by the scarcity of high-quality training data. The ease of synthesizing from a generative model suggests using (unverified) synthetic data to augment a limited corpus of real data for the purpose of fine-tuning in the hope of improving performance. Unfortunately, however, the resulting positive feedback loop leads to model autophagy disorder (MAD, aka model collapse) that results in a rapid degradation in sample quality and/or diversity. In this paper, we introduce Neon (for Negative Extrapolation frOm self-traiNing), a new learning method that turns the degradation from self-training into a powerful signal for self-improvement. Given a base model, Neon first fine-tunes it on its own self-synthesized data but then, counterintuitively, reverses its gradient updates to extrapolate away from the degraded weights. We prove that Neon works because typical inference samplers that favor high-probability regions create a predictable anti-alignment between the synthetic and real data population gradients, which negative extrapolation corrects to better align the model with the true data distribution. Neon is remarkably easy to implement via a simple post-hoc merge that requires no new real data, works effectively with as few as 1k synthetic samples, and typically uses less than 1% additional training compute. We demonstrate Neon's universality across a range of architectures (diffusion, flow matching, autoregressive, and inductive moment matching models) and datasets (ImageNet, CIFAR-10, and FFHQ). In particular, on ImageNet 256x256, Neon elevates the xAR-L model to a new state-of-the-art FID of 1.02 with only 0.36% additional training compute. Code is available at https://github.com/VITA-Group/Neon

Josue Casco-Rodriguez, Caleb Kemere, Richard G. Baraniuk

Kalman filters provide a straightforward and interpretable means to estimate hidden or latent variables, and have found numerous applications in control, robotics, signal processing, and machine learning. One such application is neural decoding for neuroprostheses. In 2020, Burkhart et al. thoroughly evaluated their new version of the Kalman filter that leverages Bayes' theorem to improve filter performance for highly non-linear or non-Gaussian observation models. This work provides an open-source Python alternative to the authors' MATLAB algorithm. Specifically, we reproduce their most salient results for neuroscientific contexts and further examine the efficacy of their filter using multiple random seeds and previously unused trials from the authors' dataset. All experiments were performed offline on a single computer.

Shashank Sonkar, Naiming Liu, Debshila Basu Mallick et al.

We present a design framework called Conversational Learning with Analytical Step-by-Step Strategies (CLASS) for building advanced Intelligent Tutoring Systems (ITS) powered by high-performance Large Language Models (LLMs). The CLASS framework empowers ITS with two key capabilities. First, through a carefully curated scaffolding dataset, CLASS equips ITS with essential problem-solving strategies, enabling it to provide tutor-like, step-by-step guidance to students. Second, by using a dynamic conversational dataset, CLASS assists ITS in facilitating natural language interactions, fostering engaging student-tutor conversations. The CLASS framework also provides valuable insights into ITS' internal decision-making process which allows seamless integration of user feedback, thus enabling continuous refinement and improvement. We also present a proof-of-concept ITS, referred to as SPOCK, which is trained using the CLASS framework with a focus on introductory college-level biology content. A carefully constructed protocol was developed for SPOCK's preliminary evaluation, examining aspects such as the factual accuracy and relevance of its responses. Experts in the field of biology offered favorable remarks, particularly highlighting SPOCK's capability to break down questions into manageable subproblems and provide encouraging responses to students. Code and models are available at https://github.com/luffycodes/Tutorbot-Spock.

Tan M. Nguyen, Richard G. Baraniuk, Andrea L. Bertozzi et al.

Designing deep neural networks is an art that often involves an expensive search over candidate architectures. To overcome this for recurrent neural nets (RNNs), we establish a connection between the hidden state dynamics in an RNN and gradient descent (GD). We then integrate momentum into this framework and propose a new family of RNNs, called {\em MomentumRNNs}. We theoretically prove and numerically demonstrate that MomentumRNNs alleviate the vanishing gradient issue in training RNNs. We study the momentum long-short term memory (MomentumLSTM) and verify its advantages in convergence speed and accuracy over its LSTM counterpart across a variety of benchmarks. We also demonstrate that MomentumRNN is applicable to many types of recurrent cells, including those in the state-of-the-art orthogonal RNNs. Finally, we show that other advanced momentum-based optimization methods, such as Adam and Nesterov accelerated gradients with a restart, can be easily incorporated into the MomentumRNN framework for designing new recurrent cells with even better performance. The code is available at https://github.com/minhtannguyen/MomentumRNN.

Haoran You, Chaojian Li, Pengfei Xu et al.

(Frankle & Carbin, 2019) shows that there exist winning tickets (small but critical subnetworks) for dense, randomly initialized networks, that can be trained alone to achieve comparable accuracies to the latter in a similar number of iterations. However, the identification of these winning tickets still requires the costly train-prune-retrain process, limiting their practical benefits. In this paper, we discover for the first time that the winning tickets can be identified at the very early training stage, which we term as early-bird (EB) tickets, via low-cost training schemes (e.g., early stopping and low-precision training) at large learning rates. Our finding of EB tickets is consistent with recently reported observations that the key connectivity patterns of neural networks emerge early. Furthermore, we propose a mask distance metric that can be used to identify EB tickets with low computational overhead, without needing to know the true winning tickets that emerge after the full training. Finally, we leverage the existence of EB tickets and the proposed mask distance to develop efficient training methods, which are achieved by first identifying EB tickets via low-cost schemes, and then continuing to train merely the EB tickets towards the target accuracy. Experiments based on various deep networks and datasets validate: 1) the existence of EB tickets, and the effectiveness of mask distance in efficiently identifying them; and 2) that the proposed efficient training via EB tickets can achieve up to 4.7x energy savings while maintaining comparable or even better accuracy, demonstrating a promising and easily adopted method for tackling cost-prohibitive deep network training. Code available at https://github.com/RICE-EIC/Early-Bird-Tickets.

Christopher A. Metzler, Ali Mousavi, Reinhard Heckel et al.

Learning from unlabeled and noisy data is one of the grand challenges of machine learning. As such, it has seen a flurry of research with new ideas proposed continuously. In this work, we revisit a classical idea: Stein's Unbiased Risk Estimator (SURE). We show that, in the context of image recovery, SURE and its generalizations can be used to train convolutional neural networks (CNNs) for a range of image denoising and recovery problems without any ground truth data. Specifically, our goal is to reconstruct an image $x$ from a noisy linear transformation (measurement) of the image. We consider two scenarios: one where no additional data is available and one where we have measurements of other images that are drawn from the same noisy distribution as $x$, but have no access to the clean images. Such is the case, for instance, in the context of medical imaging, microscopy, and astronomy, where noise-less ground truth data is rarely available. We show that in this situation, SURE can be used to estimate the mean-squared-error loss associated with an estimate of $x$. Using this estimate of the loss, we train networks to perform denoising and compressed sensing recovery. In addition, we also use the SURE framework to partially explain and improve upon an intriguing results presented by Ulyanov et al. in "Deep Image Prior": that a network initialized with random weights and fit to a single noisy image can effectively denoise that image. Public implementations of the networks and methods described in this paper can be found at https://github.com/ricedsp/D-AMP_Toolbox.

Christopher A. Metzler, Philip Schniter, Ashok Veeraraghavan et al.

Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and through scattering media, respectively. Unfortunately, traditional phase retrieval algorithms struggle in the presence of noise. Progress has been made recently on more robust algorithms using signal priors, but at the expense of limiting the range of supported measurement models (e.g., to Gaussian or coded diffraction patterns). In this work we leverage the regularization-by-denoising framework and a convolutional neural network denoiser to create prDeep, a new phase retrieval algorithm that is both robust and broadly applicable. We test and validate prDeep in simulation to demonstrate that it is robust to noise and can handle a variety of system models. A MatConvNet implementation of prDeep is available at https://github.com/ricedsp/prDeep.

Tam Nguyen, César A. Uribe, Tan M. Nguyen et al.

In this work, we address two main shortcomings of transformer architectures: input corruption and rank collapse in their output representation. We unveil self-attention as an autonomous state-space model that inherently promotes smoothness in its solutions, leading to lower-rank outputs and diminished representation capacity. Moreover, the steady-state solution of the model is sensitive to input perturbations. We incorporate a Proportional-Integral-Derivative (PID) closed-loop feedback control system with a reference point into the model to improve robustness and representation capacity. This integration aims to preserve high-frequency details while bolstering model stability, rendering it more noise-resilient. The resulting controlled state-space model is theoretically proven robust and adept at addressing the rank collapse. Motivated by this control framework, we derive a novel class of transformers, PID-controlled Transformer (PIDformer), aimed at improving robustness and mitigating the rank-collapse issue inherent in softmax transformers. We empirically evaluate the model for advantages and robustness against baseline transformers across various practical tasks, including object classification, image segmentation, and language modeling.

Shashank Sonkar, Naiming Liu, Richard G. Baraniuk

The pursuit of personalized education has led to the integration of Large Language Models (LLMs) in developing intelligent tutoring systems. To better understand and adapt to individual student needs, including their misconceptions, LLMs need to be trained on extensive datasets of student-tutor dialogues. Our research uncovers a fundamental challenge in this approach: the ``Student Data Paradox.'' This paradox emerges when LLMs, trained on student data to understand learner behavior, inadvertently compromise their own factual knowledge and reasoning abilities. We investigate this paradox by training state-of-the-art language models on student-tutor dialogue datasets and evaluating their performance across multiple benchmarks. These benchmarks assess various aspects of language model capabilities, including reasoning, truthfulness, and common sense understanding. Our findings reveal significant declines in the models' performance across these diverse benchmarks, indicating a broad impact on their capabilities when trained to model student behavior. Our research makes two primary contributions: (1) empirical demonstration of the Student Data Paradox through quantitative analysis of model performance, and (2) introduction of ``hallucination tokens'' as a mitigation strategy. These tokens, while improving performance, highlight the persistent challenge of balancing accurate student behavior modeling with maintaining the LLM's integrity as an educational tool. This study emphasizes the need for innovative solutions to reconcile the conflicting goals of faithfully understanding diverse student cognition while preserving the model's ability to provide accurate information and guidance.

Shashank Sonkar, Xinghe Chen, Naiming Liu et al.

Accurately modeling student cognition is crucial for developing effective AI-driven educational technologies. A key challenge is creating realistic student models that satisfy two essential properties: (1) accurately replicating specific misconceptions, and (2) correctly solving problems where these misconceptions are not applicable. This dual requirement reflects the complex nature of student understanding, where misconceptions coexist with correct knowledge. This paper investigates whether Large Language Models (LLMs) can be instruction-tuned to meet this dual requirement and effectively simulate student thinking in algebra. We introduce MalAlgoPy, a novel Python library that generates datasets reflecting authentic student solution patterns through a graph-based representation of algebraic problem-solving. Utilizing MalAlgoPy, we define and examine Cognitive Student Models (CSMs) - LLMs instruction tuned to faithfully emulate realistic student behavior. Our findings reveal that LLMs trained on misconception examples can efficiently learn to replicate errors. However, the training diminishes the model's ability to solve problems correctly, particularly for problem types where the misconceptions are not applicable, thus failing to satisfy second property of CSMs. We demonstrate that by carefully calibrating the ratio of correct to misconception examples in the training data - sometimes as low as 0.25 - it is possible to develop CSMs that satisfy both properties. Our insights enhance our understanding of AI-based student models and pave the way for effective adaptive learning systems.

Tam Nguyen, Ngoc N. Tran, Khai Nguyen et al.

Sparse Mixture of Experts (SMoE) has emerged as a key to achieving unprecedented scalability in deep learning. By activating only a small subset of parameters per sample, SMoE achieves an exponential increase in parameter counts while maintaining a constant computational overhead. However, SMoE models are susceptible to routing fluctuations--changes in the routing of a given input to its target expert--at the late stage of model training, leading to model non-robustness. In this work, we unveil the limitation of SMoE through the perspective of the probabilistic graphical model (PGM). Through this PGM framework, we highlight the independence in the expert-selection of tokens, which exposes the model to routing fluctuation and non-robustness. Alleviating this independence, we propose the novel Similarity-Aware (S)MoE, which considers interactions between tokens during expert selection. We then derive a new PGM underlying an (S)MoE-Attention block, going beyond just a single (S)MoE layer. Leveraging the token similarities captured by the attention matrix, we propose the innovative Attention-Aware (S)MoE, which employs the attention matrix to guide the routing of tokens to appropriate experts in (S)MoE. We theoretically prove that Similarity/Attention-Aware routing help reduce the entropy of expert selection, resulting in more stable token routing mechanisms. We empirically validate our models on various tasks and domains, showing significant improvements in reducing routing fluctuations, enhancing accuracy, and increasing model robustness over the baseline MoE-Transformer with token routing via softmax gating.

Hossein Babaei, Mel White, Sina Alemohammad et al.

State-Space Models (SSMs) have re-emerged as a powerful tool for online function approximation, and as the backbone of machine learning models for long-range dependent data. However, to date, only a few polynomial bases have been explored for this purpose, and the state-of-the-art implementations were built upon the best of a few limited options. In this paper, we present a generalized method for building an SSM with any frame or basis, rather than being restricted to polynomials. This framework encompasses the approach known as HiPPO, but also permits an infinite diversity of other possible "species" within the SSM architecture. We dub this approach SaFARi: SSMs for Frame-Agnostic Representation.

Shashank Sonkar, Richard G. Baraniuk

We introduce Many-Shot Regurgitation (MSR) prompting, a new black-box membership inference attack framework for examining verbatim content reproduction in large language models (LLMs). MSR prompting involves dividing the input text into multiple segments and creating a single prompt that includes a series of faux conversation rounds between a user and a language model to elicit verbatim regurgitation. We apply MSR prompting to diverse text sources, including Wikipedia articles and open educational resources (OER) textbooks, which provide high-quality, factual content and are continuously updated over time. For each source, we curate two dataset types: one that LLMs were likely exposed to during training ($D_{\rm pre}$) and another consisting of documents published after the models' training cutoff dates ($D_{\rm post}$). To quantify the occurrence of verbatim matches, we employ the Longest Common Substring algorithm and count the frequency of matches at different length thresholds. We then use statistical measures such as Cliff's delta, Kolmogorov-Smirnov (KS) distance, and Kruskal-Wallis H test to determine whether the distribution of verbatim matches differs significantly between $D_{\rm pre}$ and $D_{\rm post}$. Our findings reveal a striking difference in the distribution of verbatim matches between $D_{\rm pre}$ and $D_{\rm post}$, with the frequency of verbatim reproduction being significantly higher when LLMs (e.g. GPT models and LLaMAs) are prompted with text from datasets they were likely trained on. For instance, when using GPT-3.5 on Wikipedia articles, we observe a substantial effect size (Cliff's delta $= -0.984$) and a large KS distance ($0.875$) between the distributions of $D_{\rm pre}$ and $D_{\rm post}$. Our results provide compelling evidence that LLMs are more prone to reproducing verbatim content when the input text is likely sourced from their training data.

Naiming Liu, Shashank Sonkar, Richard G. Baraniuk

Large Language Models (LLMs) have demonstrated remarkable capabilities in various educational tasks, yet their alignment with human learning patterns, particularly in predicting which incorrect options students are most likely to select in multiple-choice questions (MCQs), remains underexplored. Our work investigates the relationship between LLM generation likelihood and student response distributions in MCQs with a specific focus on distractor selections. We collect a comprehensive dataset of MCQs with real-world student response distributions to explore two fundamental research questions: (1). RQ1 - Do the distractors that students more frequently select correspond to those that LLMs assign higher generation likelihood to? (2). RQ2 - When an LLM selects a incorrect choice, does it choose the same distractor that most students pick? Our experiments reveals moderate correlations between LLM-assigned probabilities and student selection patterns for distractors in MCQs. Additionally, when LLMs make mistakes, they are more likley to select the same incorrect answers that commonly mislead students, which is a pattern consistent across both small and large language models. Our work provides empirical evidence that despite LLMs' strong performance on generating educational content, there remains a gap between LLM's underlying reasoning process and human cognitive processes in identifying confusing distractors. Our findings also have significant implications for educational assessment development. The smaller language models could be efficiently utilized for automated distractor generation as they demonstrate similar patterns in identifying confusing answer choices as larger language models. This observed alignment between LLMs and student misconception patterns opens new opportunities for generating high-quality distractors that complement traditional human-designed distractors.

Josue Casco-Rodriguez, Nanda H. Krishna, Richard G. Baraniuk

Biological neural networks (like the hippocampus) can internally generate "replay" resembling stimulus-driven activity. Recent computational models of replay use noisy recurrent neural networks (RNNs) trained to path-integrate. Replay in these networks has been described as Langevin sampling, but new modifiers of noisy RNN replay have surpassed this description. We re-examine noisy RNN replay as sampling to understand or improve it in three ways: (1) Under simple assumptions, we prove that the gradients replay activity should follow are time-varying and difficult to estimate, but readily motivate the use of hidden state leakage in RNNs for replay. (2) We confirm that hidden state adaptation (negative feedback) encourages exploration in replay, but show that it incurs non-Markov sampling that also slows replay. (3) We propose the first model of temporally compressed replay in noisy path-integrating RNNs through hidden state momentum, connect it to underdamped Langevin sampling, and show that, together with adaptation, it counters slowness while maintaining exploration. We verify our findings via path-integration of 2D triangular and T-maze paths and of high-dimensional paths of synthetic rat place cell activity.

Hossein Babaei, Mel White, Richard G. Baraniuk

State Space Models (SSMs) have emerged as powerful components for sequence modeling, enabling efficient handling of long-range dependencies via linear recurrence and convolutional computation. However, their effectiveness depends heavily on the choice and initialization of the state matrix. In this work, we build on the SaFARi framework and existing WaLRUS SSMs to introduce a new variant, W4S4 (WaLRUS for S4), a new class of SSMs constructed from redundant wavelet frames. WaLRUS admits a stable diagonalization and supports fast kernel computation without requiring low-rank approximations, making it both theoretically grounded and computationally efficient. We show that WaLRUS retains information over long horizons significantly better than HiPPO-based SSMs, both in isolation and when integrated into deep architectures such as S4. Our experiments demonstrate consistent improvements across delay reconstruction tasks, classification benchmarks, and long-range sequence modeling, confirming that high-quality, structured initialization enabled by wavelet-based state dynamic offers substantial advantages over existing alternatives. WaLRUS provides a scalable and versatile foundation for the next generation of deep SSM-based models.

Hossein Babaei, Mel White, Sina Alemohammad et al.

State-Space Models (SSMs) have proven to be powerful tools for modeling long-range dependencies in sequential data. While the recent method known as HiPPO has demonstrated strong performance, and formed the basis for machine learning models S4 and Mamba, it remains limited by its reliance on closed-form solutions for a few specific, well-behaved bases. The SaFARi framework generalized this approach, enabling the construction of SSMs from arbitrary frames, including non-orthogonal and redundant ones, thus allowing an infinite diversity of possible "species" within the SSM family. In this paper, we introduce WaLRUS (Wavelets for Long-range Representation Using SSMs), a new implementation of SaFARi built from Daubechies wavelets.

Shashank Sonkar, Naiming Liu, Xinghe Chen et al.

As artificial intelligence systems become increasingly prevalent in education, a fundamental challenge emerges: how can we verify if an AI truly understands how students think and reason? Traditional evaluation methods like measuring learning gains require lengthy studies confounded by numerous variables. We present a novel evaluation framework based on a two-phase Turing-like test. In Phase 1, students provide open-ended responses to questions, revealing natural misconceptions. In Phase 2, both AI and human experts, conditioned on each student's specific mistakes, generate distractors for new related questions. By analyzing whether students select AI-generated distractors at rates similar to human expert-generated ones, we can validate if the AI models student cognition. We prove this evaluation must be conditioned on individual responses - unconditioned approaches merely target common misconceptions. Through rigorous statistical sampling theory, we establish precise requirements for high-confidence validation. Our research positions conditioned distractor generation as a probe into an AI system's fundamental ability to model student thinking - a capability that enables adapting tutoring, feedback, and assessments to each student's specific needs.

Gabriel Díaz Ramos, Toros Arikan, Richard G. Baraniuk

The Obstacle Avoiding Rectilinear Steiner Minimum Tree (OARSMT) problem, which seeks the shortest interconnection of a given number of terminals in a rectilinear plane while avoiding obstacles, is a critical task in integrated circuit design, network optimization, and robot path planning. Since OARSMT is NP-hard, exact algorithms scale poorly with the number of terminals, leading practical solvers to sacrifice accuracy for large problems. We propose MazeNet, a deep learning-based method that learns to solve the OARSMT from data. MazeNet reframes OARSMT as a maze-solving task that can be addressed with a recurrent convolutional neural network (RCNN). A key hallmark of MazeNet is its scalability: we only need to train the RCNN blocks on mazes with a small number of terminals; larger mazes can be solved by replicating the same pre-trained blocks to create a larger network. Across a wide range of experiments, MazeNet achieves perfect OARSMT-solving accuracy, significantly reduces runtime compared to classical exact algorithms, and can handle more terminals than state-of-the-art approximate algorithms.

Tan M. Nguyen, Tam Nguyen, Nhat Ho et al.

Self-attention is key to the remarkable success of transformers in sequence modeling tasks including many applications in natural language processing and computer vision. Like neural network layers, these attention mechanisms are often developed by heuristics and experience. To provide a principled framework for constructing attention layers in transformers, we show that the self-attention corresponds to the support vector expansion derived from a support vector regression problem, whose primal formulation has the form of a neural network layer. Using our framework, we derive popular attention layers used in practice and propose two new attentions: 1) the Batch Normalized Attention (Attention-BN) derived from the batch normalization layer and 2) the Attention with Scaled Head (Attention-SH) derived from using less training data to fit the SVR model. We empirically demonstrate the advantages of the Attention-BN and Attention-SH in reducing head redundancy, increasing the model's accuracy, and improving the model's efficiency in a variety of practical applications including image and time-series classification.

Paul Mayer, Lorenzo Luzi, Ali Siahkoohi et al.

Generative models unfairly penalize data belonging to minority classes, suffer from model autophagy disorder (MADness), and learn biased estimates of the underlying distribution parameters. Our theoretical and empirical results show that training generative models with intentionally designed hypernetworks leads to models that 1) are more fair when generating datapoints belonging to minority classes 2) are more stable in a self-consumed (i.e., MAD) setting, and 3) learn parameters that are less statistically biased. To further mitigate unfairness, MADness, and bias, we introduce a regularization term that penalizes discrepancies between a generative model's estimated weights when trained on real data versus its own synthetic data. To facilitate training existing deep generative models within our framework, we offer a scalable implementation of hypernetworks that automatically generates a hypernetwork architecture for any given generative model.

Shashank Sonkar, Richard G. Baraniuk

We explore whether Large Language Models (LLMs) are capable of logical reasoning with distorted facts, which we call Deduction under Perturbed Evidence (DUPE). DUPE presents a unique challenge to LLMs since they typically rely on their parameters, which encode mostly accurate information, to reason and make inferences. However, in DUPE, LLMs must reason over manipulated or falsified evidence present in their prompts, which can result in false conclusions that are valid only under the manipulated evidence. Our goal with DUPE is to determine whether LLMs can arrive at these false conclusions and identify whether the dominant factor influencing the deduction process is the encoded data in the parameters or the manipulated evidence in the prompts. To evaluate the DUPE capabilities of LLMs, we create a DUPEd version of the StrategyQA dataset, where facts are manipulated to reverse the answer to the question. Our findings show that even the most advanced GPT models struggle to reason on manipulated facts - showcasing poor DUPE skills - with accuracy dropping by 45% compared to the original dataset. We also investigate prompt settings inspired from student simulation models, which mitigate the accuracy drop to some extent. Our findings have practical implications for understanding the performance of LLMs in real-world applications such as student simulation models that involve reasoning over inaccurate information.

Shashank Sonkar, Richard G. Baraniuk

This paper investigates the key role of Feed-Forward Networks (FFNs) in transformer models by utilizing the Parallel Attention and Feed-Forward Net Design (PAF) architecture, and comparing it to their Series Attention and Feed-Forward Net Design (SAF) counterparts. Central to the effectiveness of PAF are two main assumptions regarding the FFN block and the attention block within a layer: 1) the primary function of the FFN block is to maintain isotropy among token embeddings and prevent their degeneration, and 2) the residual norm computed in the attention block is substantially smaller than the input token embedding norm. To empirically validate these assumptions, we train PAF variants of two large language models (RoBERTa-large and bert-large-uncased). Our results demonstrate that both assumptions hold true in the PAF design. This study contributes to a deeper understanding of the roles and interactions between FFNs and self-attention mechanisms in transformer architectures.

CJ Barberan, Sina Alemohammad, Naiming Liu et al.

Recurrent Neural Networks (RNNs) are important tools for processing sequential data such as time-series or video. Interpretability is defined as the ability to be understood by a person and is different from explainability, which is the ability to be explained in a mathematical formulation. A key interpretability issue with RNNs is that it is not clear how each hidden state per time step contributes to the decision-making process in a quantitative manner. We propose NeuroView-RNN as a family of new RNN architectures that explains how all the time steps are used for the decision-making process. Each member of the family is derived from a standard RNN architecture by concatenation of the hidden steps into a global linear classifier. The global linear classifier has all the hidden states as the input, so the weights of the classifier have a linear mapping to the hidden states. Hence, from the weights, NeuroView-RNN can quantify how important each time step is to a particular decision. As a bonus, NeuroView-RNN also offers higher accuracy in many cases compared to the RNNs and their variants. We showcase the benefits of NeuroView-RNN by evaluating on a multitude of diverse time-series datasets.

Naiming Liu, Zichao Wang, Richard G. Baraniuk et al.

In education applications, knowledge tracing refers to the problem of estimating students' time-varying concept/skill mastery level from their past responses to questions and predicting their future performance. One key limitation of most existing knowledge tracing methods is that they treat student responses to questions as binary-valued, i.e., whether they are correct or incorrect. Response correctness analysis/prediction ignores important information on student knowledge contained in the exact content of the responses, especially for open-ended questions. In this paper, we conduct the first exploration into open-ended knowledge tracing (OKT) by studying the new task of predicting students' exact open-ended responses to questions. Our work is grounded in the domain of computer science education with programming questions. We develop an initial solution to the OKT problem, a student knowledge-guided code generation approach, that combines program synthesis methods using language models with student knowledge tracing methods. We also conduct a series of quantitative and qualitative experiments on a real-world student code dataset to validate OKT and demonstrate its promise in educational applications.

Vishwanath Saragadam, Jasper Tan, Guha Balakrishnan et al.

We introduce a new neural signal model designed for efficient high-resolution representation of large-scale signals. The key innovation in our multiscale implicit neural representation (MINER) is an internal representation via a Laplacian pyramid, which provides a sparse multiscale decomposition of the signal that captures orthogonal parts of the signal across scales. We leverage the advantages of the Laplacian pyramid by representing small disjoint patches of the pyramid at each scale with a small MLP. This enables the capacity of the network to adaptively increase from coarse to fine scales, and only represent parts of the signal with strong signal energy. The parameters of each MLP are optimized from coarse-to-fine scale which results in faster approximations at coarser scales, thereby ultimately an extremely fast training process. We apply MINER to a range of large-scale signal representation tasks, including gigapixel images and very large point clouds, and demonstrate that it requires fewer than 25% of the parameters, 33% of the memory footprint, and 10% of the computation time of competing techniques such as ACORN to reach the same representation accuracy.

Jasper Tan, Blake Mason, Hamid Javadi et al.

A surprising phenomenon in modern machine learning is the ability of a highly overparameterized model to generalize well (small error on the test data) even when it is trained to memorize the training data (zero error on the training data). This has led to an arms race towards increasingly overparameterized models (c.f., deep learning). In this paper, we study an underexplored hidden cost of overparameterization: the fact that overparameterized models may be more vulnerable to privacy attacks, in particular the membership inference attack that predicts the (potentially sensitive) examples used to train a model. We significantly extend the relatively few empirical results on this problem by theoretically proving for an overparameterized linear regression model in the Gaussian data setting that membership inference vulnerability increases with the number of parameters. Moreover, a range of empirical studies indicates that more complex, nonlinear models exhibit the same behavior. Finally, we extend our analysis towards ridge-regularized linear regression and show in the Gaussian data setting that increased regularization also increases membership inference vulnerability in the overparameterized regime.

Tam Nguyen, Tan M. Nguyen, Dung D. Le et al.

Multi-head attention is a driving force behind state-of-the-art transformers, which achieve remarkable performance across a variety of natural language processing (NLP) and computer vision tasks. It has been observed that for many applications, those attention heads learn redundant embedding, and most of them can be removed without degrading the performance of the model. Inspired by this observation, we propose Transformer with a Mixture of Gaussian Keys (Transformer-MGK), a novel transformer architecture that replaces redundant heads in transformers with a mixture of keys at each head. These mixtures of keys follow a Gaussian mixture model and allow each attention head to focus on different parts of the input sequence efficiently. Compared to its conventional transformer counterpart, Transformer-MGK accelerates training and inference, has fewer parameters, and requires fewer FLOPs to compute while achieving comparable or better accuracy across tasks. Transformer-MGK can also be easily extended to use with linear attention. We empirically demonstrate the advantage of Transformer-MGK in a range of practical applications, including language modeling and tasks that involve very long sequences. On the Wikitext-103 and Long Range Arena benchmark, Transformer-MGKs with 4 heads attain comparable or better performance to the baseline transformers with 8 heads.