Nikhil Singh

Shayne Longpre, Robert Mahari, Ariel Lee et al. · cambridge, cmu

General-purpose artificial intelligence (AI) systems are built on massive swathes of public web data, assembled into corpora such as C4, RefinedWeb, and Dolma. To our knowledge, we conduct the first, large-scale, longitudinal audit of the consent protocols for the web domains underlying AI training corpora. Our audit of 14,000 web domains provides an expansive view of crawlable web data and how codified data use preferences are changing over time. We observe a proliferation of AI-specific clauses to limit use, acute differences in restrictions on AI developers, as well as general inconsistencies between websites' expressed intentions in their Terms of Service and their robots.txt. We diagnose these as symptoms of ineffective web protocols, not designed to cope with the widespread re-purposing of the internet for AI. Our longitudinal analyses show that in a single year (2023-2024) there has been a rapid crescendo of data restrictions from web sources, rendering ~5%+ of all tokens in C4, or 28%+ of the most actively maintained, critical sources in C4, fully restricted from use. For Terms of Service crawling restrictions, a full 45% of C4 is now restricted. If respected or enforced, these restrictions are rapidly biasing the diversity, freshness, and scaling laws for general-purpose AI systems. We hope to illustrate the emerging crises in data consent, for both developers and creators. The foreclosure of much of the open web will impact not only commercial AI, but also non-commercial AI and academic research.

Sarah J. Zhang, Samuel Florin, Ariel N. Lee et al.

We curate a comprehensive dataset of 4,550 questions and solutions from problem sets, midterm exams, and final exams across all MIT Mathematics and Electrical Engineering and Computer Science (EECS) courses required for obtaining a degree. We evaluate the ability of large language models to fulfill the graduation requirements for any MIT major in Mathematics and EECS. Our results demonstrate that GPT-3.5 successfully solves a third of the entire MIT curriculum, while GPT-4, with prompt engineering, achieves a perfect solve rate on a test set excluding questions based on images. We fine-tune an open-source large language model on this dataset. We employ GPT-4 to automatically grade model responses, providing a detailed performance breakdown by course, question, and answer type. By embedding questions in a low-dimensional space, we explore the relationships between questions, topics, and classes and discover which questions and classes are required for solving other questions and classes through few-shot learning. Our analysis offers valuable insights into course prerequisites and curriculum design, highlighting language models' potential for learning and improving Mathematics and EECS education.

Ayush Maheshwari, Nikhil Singh, Amrith Krishna et al.

Sanskrit is a classical language with about 30 million extant manuscripts fit for digitisation, available in written, printed or scannedimage forms. However, it is still considered to be a low-resource language when it comes to available digital resources. In this work, we release a post-OCR text correction dataset containing around 218,000 sentences, with 1.5 million words, from 30 different books. Texts in Sanskrit are known to be diverse in terms of their linguistic and stylistic usage since Sanskrit was the 'lingua franca' for discourse in the Indian subcontinent for about 3 millennia. Keeping this in mind, we release a multi-domain dataset, from areas as diverse as astronomy, medicine and mathematics, with some of them as old as 18 centuries. Further, we release multiple strong baselines as benchmarks for the task, based on pre-trained Seq2Seq language models. We find that our best-performing model, consisting of byte level tokenization in conjunction with phonetic encoding (Byt5+SLP1), yields a 23% point increase over the OCR output in terms of word and character error rates. Moreover, we perform extensive experiments in evaluating these models on their performance and analyse common causes of mispredictions both at the graphemic and lexical levels. Our code and dataset is publicly available at https://github.com/ayushbits/pe-ocr-sanskrit.

Yanjun Cui, Ali Emami, Temiloluwa Prioleau et al.

Continuous glucose monitors (CGMs) used in diabetes care collect rich personal health data that could improve day-to-day self-management. However, current patient platforms only offer static summaries which do not support inquisitive user queries. Large language models (LLMs) could enable free-form inquiries about continuous glucose data, but deploying them over sensitive health records raises privacy and accuracy concerns. In this paper, we present CGM-Agent, a privacy-preserving framework for question answering over personal glucose data. In our design, the LLM serves purely as a reasoning engine that selects analytical functions. All computation occurs locally, and personal health data never leaves the user's device. For evaluation, we construct a benchmark of 4,180 questions combining parameterized question templates with real user queries and ground truth derived from deterministic program execution. Evaluating 6 leading LLMs, we find that top models achieve 94\% value accuracy on synthetic queries and 88\% on ambiguous real-world queries. Errors stem primarily from intent and temporal ambiguity rather than computational failures. Additionally, lightweight models achieve competitive performance in our agent design, suggesting opportunities for low-cost deployment. We release our code and benchmark to support future work on trustworthy health agents.

Rupak Majumdar, Nikhil Singh, Sadegh Soudjani

Safety has been a major concern when deploying deep reinforcement learning algorithms in the real world. A promising direction that ensures that the learned policy does not visit unsafe regions is to learn a \emph{barrier function} along with the policy. A barrier is a function from states to reals that assigns low values to the initial states, high values to the unsafe states, and decreases in expectation on each transition; such a function can be used to bound the probability of reaching unsafe states. Previous attempts learned a barrier function directly from exploration data, but this required either large amounts of data or restrictions on the system dynamics. In this paper, we show how kernel embeddings can be used to learn barrier functions during deep reinforcement learning for stochastic systems with unknown dynamics. Our algorithm, \emph{kernel-based safe exploration (KBSE)}, learns an optimal policy and a barrier simultaneously during exploration. The barriers are computed iteratively, represented as conditional mean embeddings, and provide better probabilistic safety guarantees with more exploration. The exploration algorithm uses the learned barrier functions to identify safety violations. In the case of violation, it intervenes to modify the unsafe action to a safe action, thereby ensuring that the exploration is restricted to actions that bound the probability of reaching unsafe states. We evaluate KBSE on several complex continuous control benchmarks. Experimental results establish our new algorithm to be suitable for synthesizing control policies that are probabilistically safe without degradation in reward accumulation.

Nikhil Singh, Chih-Wei Wu, Iroro Orife et al.

Audiovisual representation learning typically relies on the correspondence between sight and sound. However, there are often multiple audio tracks that can correspond with a visual scene. Consider, for example, different conversations on the same crowded street. The effect of such counterfactual pairs on audiovisual representation learning has not been previously explored. To investigate this, we use dubbed versions of movies and television shows to augment cross-modal contrastive learning. Our approach learns to represent alternate audio tracks, differing only in speech, similarly to the same video. Our results, from a comprehensive set of experiments investigating different training strategies, show this general approach improves performance on a range of downstream auditory and audiovisual tasks, without majorly affecting linguistic task performance overall. These findings highlight the importance of considering speech variation when learning scene-level audiovisual correspondences and suggest that dubbed audio can be a useful augmentation technique for training audiovisual models toward more robust performance on diverse downstream tasks.

Tanav Singh Bajaj, Nikhil Singh, Karan Anand et al.

As large language models are increasingly deployed as interacting agents in high-stakes decisions, the AI safety community assumes that safety properties of individual models will compose into safe multi-agent behavior. This position paper argues that this assumption is fundamentally mistaken. In agentic AI, safety is determined by interaction topology, not model weights. When agents deliberate sequentially or aggregate via parallel voting with a judge, the structure of information flow and decision coupling dominates outcomes. Evidence across model families and scales reveals three persistent topology-driven pathologies: ordering instability, where system behavior depends primarily on agent sequence; information cascades, where early judgments propagate regardless of correctness; and functional collapse, where systems satisfy fairness metrics while abandoning meaningful risk discrimination. Contrary to intuition, scaling to more capable models strengthens these effects by increasing consensus formation and reducing the challenge of initial decisions. These failure modes are invisible to model-centric evaluation and alignment procedures. We argue that agentic AI must be treated as a dynamical system rather than a collection of aligned components. Interaction topology must become a primary target of safety evaluation and regulation, with systems required to demonstrate robustness across architectural variations before deployment.

Xiao Yu, Baolin Peng, Ruize Xu et al.

Large language models (LLMs) have achieved strong performance in language-centric tasks. However, in agentic settings, LLMs often struggle to anticipate action consequences and adapt to environment dynamics, highlighting the need for world-modeling capabilities in LLM-based agents. We propose Reinforcement World Model Learning (RWML), a self-supervised method that learns action-conditioned world models for LLM-based agents on textual states using sim-to-real gap rewards. Our method aligns simulated next states produced by the model with realized next states observed from the environment, encouraging consistency between internal world simulations and actual environment dynamics in a pre-trained embedding space. Unlike next-state token prediction, which prioritizes token-level fidelity (i.e., reproducing exact wording) over semantic equivalence and can lead to model collapse, our method provides a more robust training signal and is empirically less susceptible to reward hacking than LLM-as-a-judge. We evaluate our method on ALFWorld and $τ^2$ Bench and observe significant gains over the base model, despite being entirely self-supervised. When combined with task-success rewards, our method outperforms direct task-success reward RL by 6.9 and 5.7 points on ALFWorld and $τ^2$ Bench respectively, while matching the performance of expert-data training.

Manuel Cherep, Pranav M R, Pattie Maes et al.

The web is littered with images, once created for human consumption and now increasingly interpreted by agents using vision-language models (VLMs). These agents make visual decisions at scale, deciding what to click, recommend, or buy. Yet, we know little about the structure of their visual preferences. We introduce a framework for studying this by placing VLMs in controlled image-based choice tasks and systematically perturbing their inputs. Our key idea is to treat the agent's decision function as a latent visual utility that can be inferred through revealed preference: choices between systematically edited images. Starting from common images, such as product photos, we propose methods for visual prompt optimization, adapting text optimization methods to iteratively propose and apply visually plausible modifications using an image generation model (such as in composition, lighting, or background). We then evaluate which edits increase selection probability. Through large-scale experiments on frontier VLMs, we demonstrate that optimized edits significantly shift choice probabilities in head-to-head comparisons. We develop an automatic interpretability pipeline to explain these preferences, identifying consistent visual themes that drive selection. We argue that this approach offers a practical and efficient way to surface visual vulnerabilities, safety concerns that might otherwise be discovered implicitly in the wild, supporting more proactive auditing and governance of image-based AI agents.

Anjali Sharma, Priya Banerjee, Nikhil Singh

This study presents a weakly supervised method for identifying faults in infrared images of substation equipment. It utilizes the Faster RCNN model for equipment identification, enhancing detection accuracy through modifications to the model's network structure and parameters. The method is exemplified through the analysis of infrared images captured by inspection robots at substations. Performance is validated against manually marked results, demonstrating that the proposed algorithm significantly enhances the accuracy of fault identification across various equipment types.

Nikhil Singh

This paper describes the system description for the HinglishEval challenge at INLG 2022. The goal of this task was to investigate the factors influencing the quality of the code-mixed text generation system. The task was divided into two subtasks, quality rating prediction and annotators disagreement prediction of the synthetic Hinglish dataset. We attempted to solve these tasks using sentence-level embeddings, which are obtained from mean pooling the contextualized word embeddings for all input tokens in our text. We experimented with various classifiers on top of the embeddings produced for respective tasks. Our best-performing system ranked 1st on subtask B and 3rd on subtask A.

Jiangnan Fang, Cheng-Tse Liu, Jieun Kim et al.

In this work, we propose a Multi-LLM summarization framework, and investigate two different multi-LLM strategies including centralized and decentralized. Our multi-LLM summarization framework has two fundamentally important steps at each round of conversation: generation and evaluation. These steps are different depending on whether our multi-LLM decentralized summarization is used or centralized. In both our multi-LLM decentralized and centralized strategies, we have k different LLMs that generate diverse summaries of the text. However, during evaluation, our multi-LLM centralized summarization approach leverages a single LLM to evaluate the summaries and select the best one whereas k LLMs are used for decentralized multi-LLM summarization. Overall, we find that our multi-LLM summarization approaches significantly outperform the baselines that leverage only a single LLM by up to 3x. These results indicate the effectiveness of multi-LLM approaches for summarization.

Nikhil Singh, Manuel Cherep, Pattie Maes · mit

The fidelity with which neural networks can now generate content such as music presents a scientific opportunity: these systems appear to have learned implicit theories of such content's structure through statistical learning alone. This offers a potentially new lens on theories of human-generated media. When internal representations align with traditional constructs (e.g. chord progressions in music), they show how such categories can emerge from statistical regularities; when they diverge, they expose limits of existing frameworks and patterns we may have overlooked but that nonetheless carry explanatory power. In this paper, focusing on music generators, we introduce a method for discovering interpretable concepts using sparse autoencoders (SAEs), extracting interpretable features from the residual stream of a transformer model. We make this approach scalable and evaluable using automated labeling and validation pipelines. Our results reveal both familiar musical concepts and coherent but uncodified patterns lacking clear counterparts in theory or language. As an extension, we show such concepts can be used to steer model generations. Beyond improving model transparency, our work provides an empirical tool for uncovering organizing principles that have eluded traditional methods of analysis and synthesis.

Manuel Cherep, Chengtian Ma, Abigail Xu et al.

Environments built for people are increasingly operated by a new class of economic actors: LLM-powered software agents making decisions on our behalf. These decisions range from our purchases to travel plans to medical treatment selection. Current evaluations of these agents largely focus on task competence, but we argue for a deeper assessment: how these agents choose when faced with realistic decisions. We introduce ABxLab, a framework for systematically probing agentic choice through controlled manipulations of option attributes and persuasive cues. We apply this to a realistic web-based shopping environment, where we vary prices, ratings, and psychological nudges, all of which are factors long known to shape human choice. We find that agent decisions shift predictably and substantially in response, revealing that agents are strongly biased choosers even without being subject to the cognitive constraints that shape human biases. This susceptibility reveals both risk and opportunity: risk, because agentic consumers may inherit and amplify human biases; opportunity, because consumer choice provides a powerful testbed for a behavioral science of AI agents, just as it has for the study of human behavior. We release our framework as an open benchmark for rigorous, scalable evaluation of agent decision-making.

Shayne Longpre, Nikhil Singh, Manuel Cherep et al. · mit

Progress in AI is driven largely by the scale and quality of training data. Despite this, there is a deficit of empirical analysis examining the attributes of well-established datasets beyond text. In this work we conduct the largest and first-of-its-kind longitudinal audit across modalities--popular text, speech, and video datasets--from their detailed sourcing trends and use restrictions to their geographical and linguistic representation. Our manual analysis covers nearly 4000 public datasets between 1990-2024, spanning 608 languages, 798 sources, 659 organizations, and 67 countries. We find that multimodal machine learning applications have overwhelmingly turned to web-crawled, synthetic, and social media platforms, such as YouTube, for their training sets, eclipsing all other sources since 2019. Secondly, tracing the chain of dataset derivations we find that while less than 33% of datasets are restrictively licensed, over 80% of the source content in widely-used text, speech, and video datasets, carry non-commercial restrictions. Finally, counter to the rising number of languages and geographies represented in public AI training datasets, our audit demonstrates measures of relative geographical and multilingual representation have failed to significantly improve their coverage since 2013. We believe the breadth of our audit enables us to empirically examine trends in data sourcing, restrictions, and Western-centricity at an ecosystem-level, and that visibility into these questions are essential to progress in responsible AI. As a contribution to ongoing improvements in dataset transparency and responsible use, we release our entire multimodal audit, allowing practitioners to trace data provenance across text, speech, and video.

Manuel Cherep, Nikhil Singh

Learning robust audio representations currently demands extensive datasets of real-world sound recordings. By applying artificial transformations to these recordings, models can learn to recognize similarities despite subtle variations through techniques like contrastive learning. However, these transformations are only approximations of the true diversity found in real-world sounds, which are generated by complex interactions of physical processes, from vocal cord vibrations to the resonance of musical instruments. We propose a solution to both the data scale and transformation limitations, leveraging synthetic audio. By randomly perturbing the parameters of a sound synthesizer, we generate audio doppelgängers-synthetic positive pairs with causally manipulated variations in timbre, pitch, and temporal envelopes. These variations, difficult to achieve through augmentations of existing audio, provide a rich source of contrastive information. Despite the shift to randomly generated synthetic data, our method produces strong representations, outperforming real data on several standard audio classification tasks. Notably, our approach is lightweight, requires no data storage, and has only a single hyperparameter, which we extensively analyze. We offer this method as a complement to existing strategies for contrastive learning in audio, using synthesized sounds to reduce the data burden on practitioners.

Manuel Cherep, Nikhil Singh, Jessica Shand

Neural audio synthesis methods now allow specifying ideas in natural language. However, these methods produce results that cannot be easily tweaked, as they are based on large latent spaces and up to billions of uninterpretable parameters. We propose a text-to-audio generation method that leverages a virtual modular sound synthesizer with only 78 parameters. Synthesizers have long been used by skilled sound designers for media like music and film due to their flexibility and intuitive controls. Our method, CTAG, iteratively updates a synthesizer's parameters to produce high-quality audio renderings of text prompts that can be easily inspected and tweaked. Sounds produced this way are also more abstract, capturing essential conceptual features over fine-grained acoustic details, akin to how simple sketches can vividly convey visual concepts. Our results show how CTAG produces sounds that are distinctive, perceived as artistic, and yet similarly identifiable to recent neural audio synthesis models, positioning it as a valuable and complementary tool.

Matthew Groh, Aruna Sankaranarayanan, Nikhil Singh et al.

Recent advances in technology for hyper-realistic visual and audio effects provoke the concern that deepfake videos of political speeches will soon be indistinguishable from authentic video recordings. The conventional wisdom in communication theory predicts people will fall for fake news more often when the same version of a story is presented as a video versus text. We conduct 5 pre-registered randomized experiments with 2,215 participants to evaluate how accurately humans distinguish real political speeches from fabrications across base rates of misinformation, audio sources, question framings, and media modalities. We find base rates of misinformation minimally influence discernment and deepfakes with audio produced by the state-of-the-art text-to-speech algorithms are harder to discern than the same deepfakes with voice actor audio. Moreover across all experiments, we find audio and visual information enables more accurate discernment than text alone: human discernment relies more on how something is said, the audio-visual cues, than what is said, the speech content.

Iddo Drori, Sarah Zhang, Reece Shuttleworth et al.

We demonstrate that a neural network pre-trained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates new questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a new dataset of questions from MIT's largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia University's Computational Linear Algebra. We solve questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pre-trained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8% to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work is the first to automatically solve university-level mathematics course questions at a human level and the first work to explain and generate university-level mathematics course questions at scale, a milestone for higher education.

Leonard Tang, Elizabeth Ke, Nikhil Singh et al.

We solve university level probability and statistics questions by program synthesis using OpenAI's Codex, a Transformer trained on text and fine-tuned on code. We transform course problems from MIT's 18.05 Introduction to Probability and Statistics and Harvard's STAT110 Probability into programming tasks. We then execute the generated code to get a solution. Since these course questions are grounded in probability, we often aim to have Codex generate probabilistic programs that simulate a large number of probabilistic dependencies to compute its solution. Our approach requires prompt engineering to transform the question from its original form to an explicit, tractable form that results in a correct program and solution. To estimate the amount of work needed to translate an original question into its tractable form, we measure the similarity between original and transformed questions. Our work is the first to introduce a new dataset of university-level probability and statistics problems and solve these problems in a scalable fashion using the program synthesis capabilities of large language models.

Kyle Lennon, Katharina Fransen, Alexander O'Brien et al.

Although LEGO sets have entertained generations of children and adults, the challenge of designing customized builds matching the complexity of real-world or imagined scenes remains too great for the average enthusiast. In order to make this feat possible, we implement a system that generates a LEGO brick model from 2D images. We design a novel solution to this problem that uses an octree-structured autoencoder trained on 3D voxelized models to obtain a feasible latent representation for model reconstruction, and a separate network trained to predict this latent representation from 2D images. LEGO models are obtained by algorithmic conversion of the 3D voxelized model to bricks. We demonstrate first-of-its-kind conversion of photographs to 3D LEGO models. An octree architecture enables the flexibility to produce multiple resolutions to best fit a user's creative vision or design needs. In order to demonstrate the broad applicability of our system, we generate step-by-step building instructions and animations for LEGO models of objects and human faces. Finally, we test these automatically generated LEGO sets by constructing physical builds using real LEGO bricks.

Sunny Tran, Pranav Krishna, Ishan Pakuwal et al.

Can a machine learn Machine Learning? This work trains a machine learning model to solve machine learning problems from a University undergraduate level course. We generate a new training set of questions and answers consisting of course exercises, homework, and quiz questions from MIT's 6.036 Introduction to Machine Learning course and train a machine learning model to answer these questions. Our system demonstrates an overall accuracy of 96% for open-response questions and 97% for multiple-choice questions, compared with MIT students' average of 93%, achieving grade A performance in the course, all in real-time. Questions cover all 12 topics taught in the course, excluding coding questions or questions with images. Topics include: (i) basic machine learning principles; (ii) perceptrons; (iii) feature extraction and selection; (iv) logistic regression; (v) regression; (vi) neural networks; (vii) advanced neural networks; (viii) convolutional neural networks; (ix) recurrent neural networks; (x) state machines and MDPs; (xi) reinforcement learning; and (xii) decision trees. Our system uses Transformer models within an encoder-decoder architecture with graph and tree representations. An important aspect of our approach is a data-augmentation scheme for generating new example problems. We also train a machine learning model to generate problem hints. Thus, our system automatically generates new questions across topics, answers both open-response questions and multiple-choice questions, classifies problems, and generates problem hints, pushing the envelope of AI for STEM education.

Nikhil Singh, Brandon Kates, Jeff Mentch et al.

This work improves the quality of automated machine learning (AutoML) systems by using dataset and function descriptions while significantly decreasing computation time from minutes to milliseconds by using a zero-shot approach. Given a new dataset and a well-defined machine learning task, humans begin by reading a description of the dataset and documentation for the algorithms to be used. This work is the first to use these textual descriptions, which we call privileged information, for AutoML. We use a pre-trained Transformer model to process the privileged text and demonstrate that using this information improves AutoML performance. Thus, our approach leverages the progress of unsupervised representation learning in natural language processing to provide a significant boost to AutoML. We demonstrate that using only textual descriptions of the data and functions achieves reasonable classification performance, and adding textual descriptions to data meta-features improves classification across tabular datasets. To achieve zero-shot AutoML we train a graph neural network with these description embeddings and the data meta-features. Each node represents a training dataset, which we use to predict the best machine learning pipeline for a new test dataset in a zero-shot fashion. Our zero-shot approach rapidly predicts a high-quality pipeline for a supervised learning task and dataset. In contrast, most AutoML systems require tens or hundreds of pipeline evaluations. We show that zero-shot AutoML reduces running and prediction times from minutes to milliseconds, consistently across datasets. By speeding up AutoML by orders of magnitude this work demonstrates real-time AutoML.

Nikhil Singh, Jeff Mentch, Jerry Ng et al.

Measuring the acoustic characteristics of a space is often done by capturing its impulse response (IR), a representation of how a full-range stimulus sound excites it. This work generates an IR from a single image, which can then be applied to other signals using convolution, simulating the reverberant characteristics of the space shown in the image. Recording these IRs is both time-intensive and expensive, and often infeasible for inaccessible locations. We use an end-to-end neural network architecture to generate plausible audio impulse responses from single images of acoustic environments. We evaluate our method both by comparisons to ground truth data and by human expert evaluation. We demonstrate our approach by generating plausible impulse responses from diverse settings and formats including well known places, musical halls, rooms in paintings, images from animations and computer games, synthetic environments generated from text, panoramic images, and video conference backgrounds.

Yi Hong, Nikhil Singh, Roland Kwitt et al.

We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. As customary in the literature, we start from the energy minimization formulation of linear least-squares in Euclidean spaces and generalize this concept to general nonflat Riemannian manifolds, following an optimal-control point of view. We then specialize this idea to the Grassmann manifold and demonstrate that it yields a simple, extensible and easy-to-implement solution to the parametric regression problem. In fact, it allows us to extend the basic geodesic model to (1) a time-warped variant and (2) cubic splines. We demonstrate the utility of the proposed solution on different vision problems, such as shape regression as a function of age, traffic-speed estimation and crowd-counting from surveillance video clips. Most notably, these problems can be conveniently solved within the same framework without any specifically-tailored steps along the processing pipeline.