Shows that the notion of what a derivative is -- NOT what one learns in first year calculus -- that it is the "best" linear approximation to a function.This idea allows us to extend the derivative beyond what one sees in first year calculus; meaning, extending the idea of derivative to higher dimensional functions.In fact, it can be used in an "infinite" dimensional setting to derive equations of motion in physics.

A new geometric proof of the result that for primitive Pythagorean triples:c is oddone of the legs is divisible by 4the other leg is odd.Conjectures that partition the set of primitive Pythagorean hypotenuses into two sets.Conjectures that try to examine the complexity of these two partitioning sets.

Derives recursive computational formulas for EMA and its standard deviation.Derives formulas for computing higher unbiased moments.

The general theme is to show that the differencing and summing oof sequences of numbers are inverse operations in some sense. This is easy to do and helps us understand the continuous analogs of these; namely, differentiation and integration.Goes further and examines difference equations and relates them to the continuous notion of differential equations. Once again, it uses the easier discrete problem to help understand the continuous one.Places supporting concepts to the appendices. These

📓 Number Cookbook: Number Understanding of Language Models and How to Improve ItThis research paper examines the numerical understanding and processing abilities (NUPA) of large language models (LLMs). The authors create a benchmark to test LLMs on four numerical representations (integers, floating-point numbers, fractions, and scientific notation) across 17 tasks grouped into four ability categories. They find that, despite strong problem-solving capabilities, LLMs struggle with basic numerical

🧩 Jigsaw Puzzles: Splitting Harmful Questions to Jailbreak Large Language ModelsThis research paper investigates the vulnerabilities of large language models (LLMs) to "jailbreak" attacks, where malicious users attempt to trick the model into generating harmful content. The authors propose a new attack strategy called Jigsaw Puzzles (JSP) which breaks down harmful questions into harmless fractions and feeds them to the LLM in multiple turns, bypassing the model's built-in safeguards. The paper

“Go West young men”! Era il messaggio per coloro (soprattutto giovani) che volevano realizzare il “sogno americano”, cioè, in sostanza, quello di un’esistenza migliore.Cosa c’entra questo con l’Intelligenza Artificiale ed il Machine Learning? Beh, sicuramente l’AI ed il ML sono una “nuova frontiera”, stimolante, promettente, ma anche piena di rischi. Ma non è tutto qui....

The great theories of economics seem to have great explanatory power, but the actual world is often far too complicated and messy to fully test them out. Professor Ignacio Palacios-Huerta, an economist at the London School of Economics has an answer – sport. In the contained setting of competitive sport, he says, the rules are clear and you know who is doing what. This means, with some analysis, you can see vibrant illustrations of well-known economic theories playing out before your eyes. Ignacio

🤝 Multi-expert Prompting with LLMsThe research paper presents Multi-expert Prompting, a novel method for improving the reliability, safety, and usefulness of Large Language Models (LLMs). Multi-expert Prompting simulates multiple experts within an LLM, collecting their answers to an instruction and aggregating them into a final response. This process leverages the Nominal Group Technique, a human-designed decision-making framework, to ensure a balanced and comprehensive output, surpassing the

Continued

They dive in even deeper

🔎 Investigating the Role of Prompting and External Tools in Hallucination Rates of Large Language ModelsThis paper examines the effectiveness of different prompting techniques and frameworks for mitigating hallucinations in large language models (LLMs). The authors investigate how these techniques, including Chain-of-Thought, Self-Consistency, and Multiagent Debate, can improve reasoning capabilities and reduce factual inconsistencies. They also explore the impact of LLM agents, which are AI

Podcast sobre área y perímetro

Podcast acerca de area y perimetro

🌀 Mind Your Step (by Step): Chain-of-Thought can Reduce Performance on Tasks where Thinking Makes Humans WorseThis research paper examines how chain-of-thought (CoT) prompting—encouraging models to reason step-by-step—affects large language and multimodal model performance across tasks. While CoT generally boosts performance, the authors find it significantly hampers model accuracy in three specific contexts: implicit statistical learning, facial recognition, and classifying data with exceptions

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❓Measuring short-form factuality in large language modelsThis document introduces SimpleQA, a new benchmark for evaluating the factuality of large language models. The benchmark consists of over 4,000 short, fact-seeking questions designed to be challenging for advanced models, with a focus on ensuring a single, indisputable answer. The authors argue that SimpleQA is a valuable tool for assessing whether models "know what they know", meaning their ability to correctly answer questions with high

Tradotto in italiano come “apprendimento automatico”, il machine learning è uno dei concetti più importanti e rivoluzionari dell’era moderna digitale. Questo campo dell’intelligenza artificiale ha la capacità di far imparare le macchine senza che esse siano programmate e lo fa attraverso algoritmi sofisticati. A differenza della programmazione tradizionale, il machine learning si concentra appunto sullo sviluppo di algoritmi che saranno in grado poi di analizzare dei dati, prendere delle decisioni

On the campaign trail for the US presidency, former president Donald Trump has been saying that the US is becoming a more dangerous than Venezuela.He also claims that the crime data for the US that the FBI collects is missing the most violent cities. Is he right? Tim Harford investigates, with the help of Bastian Herre from Our World in Data and Jay Albanese from Virginia Commonwealth University.Presenter: Tim Harford Producer: Bethan Ashmead Latham Series producer: Tom Colls Production