Anish Lakkapragada

Anish Lakkapragada, Essam Sleiman, Saimourya Surabhi et al.

Multi-Task Learning (MTL) is a growing subject of interest in deep learning, due to its ability to train models more efficiently on multiple tasks compared to using a group of conventional single-task models. However, MTL can be impractical as certain tasks can dominate training and hurt performance in others, thus making some tasks perform better in a single-task model compared to a multi-task one. Such problems are broadly classified as negative transfer, and many prior approaches in the literature have been made to mitigate these issues. One such current approach to alleviate negative transfer is to weight each of the losses so that they are on the same scale. Whereas current loss balancing approaches rely on either optimization or complex numerical analysis, none directly scale the losses based on their observed magnitudes. We propose multiple techniques for loss balancing based on scaling by the exponential moving average and benchmark them against current best-performing methods on three established datasets. On these datasets, they achieve comparable, if not higher, performance compared to current best-performing methods.

Anish Lakkapragada

We introduce Exponential Family Discriminant Analysis (EFDA), a unified generative framework that extends classical Linear Discriminant Analysis (LDA) beyond the Gaussian setting to any member of the exponential family. Under the assumption that each class-conditional density belongs to a common exponential family, EFDA derives closed-form maximum-likelihood estimators for all natural parameters and yields a decision rule that is linear in the sufficient statistic, recovering LDA as a special case and capturing nonlinear decision boundaries in the original feature space. We prove that EFDA is asymptotically calibrated and statistically efficient under correct specification, and we generalise it to $K \geq 2$ classes and multivariate data. Through extensive simulation across five exponential-family distributions (Weibull, Gamma, Exponential, Poisson, Negative Binomial), EFDA matches the classification accuracy of LDA, QDA, and logistic regression while reducing Expected Calibration Error (ECE) by $2$-$6\times$, a gap that is structural: it persists for all $n$ and across all class-imbalance levels, because misspecified models remain asymptotically miscalibrated. We further prove and empirically confirm that EFDA's log-odds estimator approaches the Cramér-Rao bound under correct specification, and is the only estimator in our comparison whose mean squared error converges to zero. Complete derivations are provided for nine distributions. Finally, we formally verify all four theoretical propositions in Lean 4, using Aristotle (Harmonic) and OpenGauss (Math, Inc.) as proof generators, with all outputs independently machine-checked by AXLE (Axiom).

Anish Lakkapragada

Classical statistical inference and learning theory often fail to explain the success of modern neural networks. A key reason is that these models are non-identifiable (singular), violating core assumptions behind PAC bounds and asymptotic normality. Singular learning theory (SLT), a physics-inspired framework grounded in algebraic geometry, has gained popularity for its ability to close this theory-practice gap. In this paper, we empirically study SLT in toy settings relevant to interpretability and phase transitions. First, we understand the SLT free energy $\mathcal{F}_n$ by testing an Arrhenius-style rate hypothesis using both a grokking modulo-arithmetic model and Anthropic's Toy Models of Superposition. Second, we understand the local learning coefficient $λ_α$ by measuring how it scales with problem difficulty across several controlled network families (polynomial regressors, low-rank linear networks, and low-rank autoencoders). Our experiments recover known scaling laws while others yield meaningful deviations from theoretical expectations. Overall, our paper illustrates the many merits of SLT for understanding neural network phase transitions, and poses open research questions for the field.

Anish Lakkapragada, Amol Khanna, Edward Raff et al.

As machine learning becomes increasingly prevalent in impactful decisions, recognizing when inference data is outside the model's expected input distribution is paramount for giving context to predictions. Out-of-distribution (OOD) detection methods have been created for this task. Such methods can be split into representation-based or logit-based methods from whether they respectively utilize the model's embeddings or predictions for OOD detection. In contrast to most papers which solely focus on one such group, we address both. We employ dimensionality reduction on feature embeddings in representation-based methods for both time speedups and improved performance. Additionally, we propose DICE-COL, a modification of the popular logit-based method Directed Sparsification (DICE) that resolves an unnoticed flaw. We demonstrate the effectiveness of our methods on the OpenOODv1.5 benchmark framework, where they significantly improve performance and set state-of-the-art results.

Anish Lakkapragada

Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for these activation functions is that without them, neural networks only can model a line. However, a novel explanation we propose in this paper for the impracticality of neural networks without activation functions, or linear neural networks, is that they actually reduce both training and testing performance. Having more parameters makes LNNs harder to optimize, and thus they require more training iterations than linear regression to even potentially converge to the optimal solution. We prove this hypothesis through an analysis of the optimization of an LNN and rigorous testing comparing the performance between both LNNs and linear regression on synthethic, noisy datasets.

Anish Lakkapragada, Aaron Kline, Onur Cezmi Mutlu et al.

A formal autism diagnosis can be an inefficient and lengthy process. Families may wait months or longer before receiving a diagnosis for their child despite evidence that earlier intervention leads to better treatment outcomes. Digital technologies which detect the presence of behaviors related to autism can scale access to pediatric diagnoses. This work aims to demonstrate the feasibility of deep learning technologies for detecting hand flapping from unstructured home videos as a first step towards validating whether models and digital technologies can be leveraged to aid with autism diagnoses. We used the Self-Stimulatory Behavior Dataset (SSBD), which contains 75 videos of hand flapping, head banging, and spinning exhibited by children. From all the hand flapping videos, we extracted 100 positive and control videos of hand flapping, each between 2 to 5 seconds in duration. Utilizing both landmark-driven-approaches and MobileNet V2's pretrained convolutional layers, our highest performing model achieved a testing F1 score of 84% (90% precision and 80% recall) when evaluating with 5-fold cross validation 100 times. This work provides the first step towards developing precise deep learning methods for activity detection of autism-related behaviors.