Understanding Reasoning LLMs

Crafting a good (reasoning) model

A recent talk I gave on model training, reasoning, and the next frontier.

Solving a Million-Step LLM Task with Zero Errors

LLMs have achieved remarkable breakthroughs in reasoning, insights, and tool use, but chaining these abilities into extended processes at the scale of those routinely executed by humans,...

Build a Reasoning Model (From Scratch)

"An exceptional deep dive into the next frontier of AI.” —Aman Chadha, Google Build a Reasoning Model (From Scratch) is a practical guide to understanding how modern reasoning-oriented LLMs work by building their core methods step by step. The book tells a clear engineering story: start with a conventional pre-trained LLM, learn how text generation works, build reliable evaluation tools, improve reasoning through inference-time methods, then move into training-based approaches such as reinforcement learning and distillation. The progression is deliberate. Early chapters establish the baseline model and explain text generation, KV caching, and evaluation with math verifiers. The middle chapters show how reasoning can be improved without changing model weights, using chain-of-thought prompting, sampling, self-consistency, response scoring, and self-refinement. Later chapters move to changing the model itself through reinforcement learning with verifiable rewards, GRPO improvements, format rewards, and finally distillation from stronger reasoning models into smaller ones. The book is especially useful because it implements the core methods from scratch rather than treating them as black-box library calls. Readers see how self-consistency, self-refinement, Best-of-N, and training-based methods actually work, including their cost and latency trade-offs. It also discusses common failure modes, including cases where refinement can make answers worse. Difficult concepts such as softmax, temperature, and top-p sampling are clarified with code-linked explanations and diagrams, and visual workflows make pipelines and scoring methods easier to follow. Reading the book feels like following a guided technical build rather than a loose survey of AI topics. Each concept is introduced because the project now needs it. Diagrams, roadmaps, code listings, exercises, and repeated workflow summaries help readers stay oriented through advanced material. This structure reflects Sebastian Raschka’s professional strength: explaining complex machine learning topics by making every detail concrete and showing exactly where each section fits in the larger story. He does not treat mechanisms like evaluation, log-probabilities, KL regularization, or distillation as isolated abstractions; he connects them to the goal of making reasoning models understandable and implementable. Physically and organizationally, the book has eight chapters and seven substantial appendixes. That design keeps the main narrative focused while moving supporting material like references, exercise solutions, model source code, larger models, batching, evaluation alternatives, and chat interfaces into ordered appendixes. The result is a logically flowing book that remains hands-on, navigable, and technically deep without constantly interrupting the central build.

LLMs for theory-building

Can AI do abductive reasoning?

A taxonomy for next-generation reasoning models

Where we've been and where we're going with RLVR.

The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity

Recent generations of frontier language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes…

Optimizing Agentic Workflows using Meta-tools

Agentic AI enables LLM to dynamically reason, plan, and interact with tools to solve complex tasks. However, agentic workflows often require many iterative reasoning steps and tool invocations,...

Activation Oracles: Training and Evaluating LLMs as General-Purpose Activation Explainers

Clément Dumas4, Kit Fraser-Taliente6, Subhash Kantamneni6, Julian Minder3, Euan Ong6, Arnab Sen Sharma5, Daniel Wen1

How to Build an LLM Knowledge Base

A hands-on guide to building a simple LLM knowledge base with raw markdown sources, a compiled wiki, reusable prompts, and an agent that keeps improving the knowledge base over time.

LLM Knowledge Bases

A visual breakdown of Andrej Karpathy's approach to building personal knowledge bases powered by LLMs. Learn the 4-phase pipeline: ingest, compile, query, and maintain - with an interactive architecture diagram.

The Ultimate Guide to Fine-Tuning LLMs from Basics to Breakthroughs: An Exhaustive Review of Technologies, Research, Best Practices, Applied Research Challenges and Opportunities (Version 1.0)

Alignment Is Proven To Be Solvable

That LLMs understand natural language as well as they do should dramatically change our understanding of the problem.

Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs

Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first comprehensive study of the reasoning capabilities of LLMs over explicit discrete probability distributions. Given observations from a probability distribution, we evaluate models on three carefully designed tasks, mode identification, maximum likelihood estimation, and sample generation, by prompting them to provide responses to queries about either the joint distribution or its conditionals. These tasks thus probe a range of probabilistic skills, including frequency analysis, marginalization, and generative behavior. Through comprehensive empirical evaluations, we demonstrate that there exists a clear performance gap between smaller and larger models, with the latter demonstrating stronger inference and surprising capabilities in sample generation. Furthermore, our investigations reveal notable limitations, including sensitivity to variations in the notation utilized to represent probabilistic outcomes and performance degradation of over 60% as context length increases. Together, our results provide a detailed understanding of the probabilistic reasoning abilities of LLMs and identify key directions for future improvement.

Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs

Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first comprehensive study of the reasoning capabilities of LLMs over explicit discrete probability distributions. Given observations from a probability distribution, we evaluate models on three carefully designed tasks, mode identification, maximum likelihood estimation, and sample generation, by prompting them to provide responses to queries about either the joint distribution or its conditionals. These tasks thus probe a range of probabilistic skills, including frequency analysis, marginalization, and generative behavior. Through comprehensive empirical evaluations, we demonstrate that there exists a clear performance gap between smaller and larger models, with the latter demonstrating stronger inference and surprising capabilities in sample generation. Furthermore, our investigations reveal notable limitations, including sensitivity to variations in the notation utilized to represent probabilistic outcomes and performance degradation of over 60% as context length increases. Together, our results provide a detailed understanding of the probabilistic reasoning abilities of LLMs and identify key directions for future improvement.

Operadic consistency: a label-free signal for compositional...

Detecting LLM reasoning failures at inference time without ground-truth labels has motivated a wide range of confidence baselines, including self-consistency, semantic entropy, and P(True), built...