Stanford Online
Stanford Online is the Stanford School of Engineering’s portal for academic and professional education offered by Stanford schools and units, including degree programs, credit-bearing courses, professional certificates, and free open content. It is operated by the Stanford Engineering Center for Global & Online Education.
EKF SLAM Couples Robot Pose and Map Uncertainty
EKF SLAM uses correlations between a robot’s pose and landmark positions so that an observation can refine both the robot’s location and its map. But as landmarks are added, the covariance matrix grows quadratically with the size of the state, making updates more costly. In Stanford professor Marco Pavone’s lecture, unknown landmark correspondences add another risk: a mistaken match can persist in the filter’s later estimates.
Sustainable HCI Must Account for Uncertainty in Sensors and Materials
Kristin Williams, an assistant professor of computer science at Emory University, argues that sustainable computing research must treat uncertainty as a design problem, not just a measurement error. Sensors can misrepresent events, and interfaces shape how people interpret those readings and decide what to do; meanwhile, the technologies used to address environmental problems can add to them. Williams calls for systems that make uncertainty legible where people act, while preserving room for judgment rather than presenting sensor data as definitive.
PPO, GRPO, and Distillation Trade Off Credit Assignment and Training Cost
Stanford adjunct professors Afshine and Shervine Amidi compare three post-training methods by how they provide feedback and what training resources they require. PPO uses a learned value function to estimate token-level advantages; GRPO replaces it with comparisons among sampled answers, applying the same completion-level score across tokens in its common outcome-supervised form. On-policy distillation instead compares the student’s predictions on its own generated text with a teacher’s next-token predictions, providing token-level feedback but requiring a teacher.
Known 3D-to-Image Correspondences Make Camera Calibration Solvable
Camera calibration estimates how a camera maps three-dimensional points to pixels, a mapping that published specifications may not define precisely enough for reconstruction, Stanford professor Marco Pavone argues. Known 3D points and their observed image locations are used to estimate a combined projection matrix, from which the camera’s intrinsic parameters and pose can be recovered. But calibration does not resolve depth from a single image: every point along the ray through a pixel could have produced that projection.
LLM Training Moves From Next-Token Prediction to Preference and Reasoning
Stanford adjunct professors Shervine and Afshine Amidi argue that training an assistant requires more than teaching a language model to predict the next token. In their account, pretraining builds broad language and code capabilities; midtraining, supervised fine-tuning and preference or reinforcement-learning methods then shape what the model answers and how it behaves. A central challenge is matching each stage’s data and feedback to its goal while controlling costs, long-context demands and the risk of losing capabilities learned earlier.
Direct and Indirect Methods Solve Trajectory Optimization in Opposite Orders
Stanford professor Marco Pavone argues that finding a feasible robot trajectory is different from finding one that minimizes time or control effort: the latter is an optimal-control problem. In this lecture, he explains two ways to solve it—derive continuous-time optimality conditions before discretizing, or discretize first and optimize the resulting finite-dimensional problem. He develops the indirect approach through Hamiltonians, costates and endpoint conditions, then shows how a free-final-time trajectory can be formulated for a boundary-value solver.
Low-Dispersion Samples Can Make Randomness Unnecessary in Motion Planning
In Stanford’s 2019 lecture on sampling-based motion planning, Professor Marco Pavone argues that planners can search complex robot configuration spaces without explicitly constructing their full obstacle geometry. Instead, they test sampled configurations and connections for collisions, trading a difficult global representation for local checks. Pavone compares PRM’s reusable roadmap with RRT’s incremental search, explains how dynamics change feasible connections, and presents results showing that well-spread deterministic samples can provide asymptotic guarantees without randomness.
LLM Design Trades Model Capacity Against Compute Per Token
Large language model design is a question of how to spend computation, not simply how many parameters a model has. In Stanford’s CME295 lecture, adjunct professor Afshine Amidi uses training budgets, sparse expert routing and attention mechanisms to show how designers allocate work across a model and its tokens; decoding choices, in turn, shape how the model generates answers. The distinction is between a model’s total capacity and the computation it uses for each token.
Flow Batteries Separate Grid Storage Capacity From Power Output
Stanford professor Yi Cui argues that redox-flow batteries could suit grid storage because they separate energy capacity from power output: tank size determines how much energy the system stores, while the electrode stack determines how much power it delivers. In this course preview, he describes the design’s promise and its main constraints: increasing the concentration of redox molecules in the liquids, keeping them stable through repeated cycling and reducing the cost of membranes that limit crossover between the two sides.
Interview-Based AI Agents Predict Individual Survey Responses More Accurately
Stanford professor Michael Bernstein argues that AI agents built from detailed accounts of real people could help decision-makers test how people might respond to products, policies, or organizational changes before acting. But convincing behavior is not the same as accurate prediction: Bernstein says simulations are more useful for surfacing plausible scenarios and guiding further tests than for settling consequential questions on their own. Their reliability depends on the quality of the information behind the agents and on how well the simulated environment reflects real conditions.
The Transformer Replaced Recurrence With Direct Attention Between Tokens
In the opening lecture of Stanford’s CME295 course on transformers and large language models, adjunct professors Afshine and Shervine Amidi explain how the Transformer offered an alternative to recurrent models. They argue that its use of attention let tokens connect directly across a sequence, rather than relying on a recurrent state to carry information forward one step at a time, and helped put language modelling on a more scalable path.
AI Makes Coding a Core Skill Beyond Engineering
Andrew Ng, the Stanford adjunct professor and founder of DeepLearning.AI, argues that generative AI makes coding more worth learning, not less. He says professionals who can specify what they want a computer to do—and use AI to turn that instruction into custom software—are already gaining a productivity advantage across functions such as marketing and recruiting. In Ng’s view, the scarce skill is not writing code by hand but defining the task, outcome and criteria precisely enough for a computer to execute.
On-Policy Distillation Trains LLMs on Their Own Generated Responses
Stanford adjunct professors Shervine and Afshine Amidi argue that pretraining gives large language models broad text-prediction ability, but not necessarily the capacity to follow instructions, reason reliably, or work in specialized domains. They position fine-tuning, reinforcement learning, preference optimization, verifier-guided training and distillation as post-training methods for shaping that capability, highlighting on-policy distillation because it lets a stronger teacher assess answers the student model generates itself.
Tool Use and Feedback Define the Agentic AI Stack
Stanford adjunct professor Aakanksha Chowdhery and assistant professor Azalia Mirhoseini argue that agentic AI requires more than better prompting: systems must reason, use tools to act in an environment, learn from feedback and improve toward goals. Their graduate-level program frames test-time scaling, tool use and self-improvement as the core components, while stressing that evaluation must account for agents working across longer, multi-step tasks rather than isolated responses.
Grid Storage Choices Turn on Efficiency, Cost, and Geography
Stanford instructors Matthew Kanan and Yi Cui argue that meeting rising electricity demand alongside variable renewable generation requires choosing among storage systems with distinct physical and infrastructure constraints. Kanan says the relevant trade-offs are efficiency, cost and geography: pumped hydro depends on reservoirs and elevation, while underground hydrogen storage converts electricity into fuel that requires a salt cavern and equipment to return it to the grid. Cui adds that AI data-center growth strengthens the case for storage, while AI-based materials prediction could accelerate battery development.
Verification Is the Bottleneck for Self-Improving AI Agents
Stanford’s Aakanksha Chowdhery and Azalia Mirhoseini argue that progress in AI is shifting beyond scaling model training toward using more computation at inference time, selecting among candidate outputs, and feeding verified successes back into training. In the opening lecture of CS329A, they trace how post-training made large language models usable assistants and how reasoning models and agents extend that capability into multi-step work. Their central constraint is verification: self-improvement is most tractable where systems can reliably tell whether an answer or action is correct.
LATS, SPRINT, and SWiRL Target Different Bottlenecks in Agent Reasoning
Stanford’s Azalia Mirhoseini argues that improving multi-step AI agents requires more than extending a chain of thought: agents must plan, act, use feedback and revise their course. In this CS329A lecture, she examines three approaches to that problem—LATS, which searches alternative action paths at inference; SPRINT, which identifies work that can run in parallel; and SWiRL, which trains next-action choices from offline tool-use trajectories. Each shifts the trade-off among accuracy, latency, inference cost and the reliability of feedback.
Longer Agent Task Horizons Still Fall Short of Dependable Autonomy
Stanford’s Aakanksha Chowdhery argues that longer agent task horizons should not be mistaken for dependable autonomy. Her CS329A lecture distinguishes among benchmarks that measure how long agents can complete tasks at given reliability levels, whether their outputs match professional work, and whether they can synthesize research with verifiable evidence. Across those measures, the central limitation is persistent: agents improve on well-specified tasks but remain unreliable when success requires recovery, organizational context, or judgment about what work needs doing.
Verification, Not Sampling, Limits Test-Time Scaling for AI Agents
Stanford’s Azalia Mirhoseini argues that repeated sampling improves reasoning-model performance only when a system can reliably identify correct candidates—and that verification cannot recover answers the generator never produces. In this CS329A lecture, she examines outcome-based and process-based reward models, rollout-generated labels and verifier ensembles as approaches to the gap between producing a correct solution and selecting it. The central systems question is how to spend a fixed inference budget among generating more candidates, using stronger or more numerous verifiers, and verifying each candidate more deeply.
Train-Time Scaling Makes Verifiable Reasoning More Consistent, Not Necessarily More Capable
Stanford adjunct professor Aakanksha Chowdhery argues that train-time scaling can make reasoning models more reliable by feeding verified outputs back into training, but only when a base model can already produce some useful solutions and sampled answers provide meaningful reward variation. In CS329A, she uses STaR, DeepSeekMath’s group-relative policy optimization and DAPO to show how self-generated rationales, relative rewards and RL stability techniques improve performance on verifiable tasks such as mathematics and code. The unresolved question, she says, is whether these methods expand a model’s problem-solving ability or chiefly make solutions it could already reach more likely to appear.
Test-Time Scaling Depends on Verifying Rare Correct Answers
Stanford computer scientist Azalia Mirhoseini argues that test-time compute can turn an existing language model into a more capable system by generating, revising and evaluating many candidate answers after a query arrives, rather than relying on a single response or additional training. The approach works best where outputs can be reliably verified—through formal checkers, unit tests or comparable signals—and where the value of better results justifies added cost and latency. But she cautions that extra inference cannot substitute for stronger pre-training on the hardest problems, and that weak verification can leave correct answers buried among more plausible wrong ones.
EM and PCA Make Structure Tractable Through Different Assumptions
Stanford computer science professor Chris Ré presents expectation-maximization as a local optimization method for latent-variable models: it alternates between estimating posterior assignments and refitting parameters through a tight ELBO, ensuring that observed-data likelihood does not decrease without guaranteeing a global optimum. He contrasts it with PCA, which compresses centered, appropriately scaled data by projecting it onto covariance eigenvectors that capture the most variation. Ré cautions that PCA’s individual coordinates can be unstable when relevant eigenvalues are close.
Unlabeled Learning Depends on Assumptions About Hidden Structure
Stanford computer scientist Chris Ré argues that unsupervised learning can recover useful structure only by making explicit assumptions about what generated unlabeled data. In CS229’s treatment of k-means and Gaussian mixture models, he presents k-means as a local, least-squares method for compact clusters and GMMs as a probabilistic model of latent Gaussian sources, with EM alternating between estimated memberships and parameter updates to improve likelihood without guaranteeing a global optimum.
Shared Covariance Makes Gaussian Discriminant Analysis a Linear Classifier
Chris Ré presents Gaussian discriminant analysis as a generative alternative to logistic regression: rather than learning \(P(y\mid x)\) directly, it models how features arise within each class and combines those distributions with class prevalence. Under GDA’s shared-covariance assumption, the model’s quadratic terms cancel, producing a linear decision boundary and the same sigmoid-form posterior logistic regression can express. Ré argues that the closed-form efficiency of GDA—and of naive Bayes for text—comes from structural assumptions that can improve data efficiency when plausible but become liabilities when the data-generating story is wrong.