All Notes: Nonlinear Function

All Notes

explicit models of uncertainty

(note: this is dancing around the issues around why I think [ probabilistic programming is not AI research ], even if it will be a…

Modified: February 10, 2022.

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exploration

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exploration versus exploitation

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explore

Quit Your Job (palladiummag.com) : Productive exploration requires the application of skilled personal judgment to chasing hunches and…

Modified: February 17, 2022.

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exponential family

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exponential family notes

Exponential Families, Conjugacy, Convexity, and Variational Inference Any parameterized family of probability densities that can be written…

Modified: May 21, 2022.

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exposure bias

Considering training an [ autoregressive ] model of sequence data (text, audio, action sequences in [ reinforcement learning ], etc.), which…

Modified: October 13, 2022.

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expressive transformer

This note is a scratchpad for investigating the expressivity of the [ transformer ] architecture. In general, one set of intuitions that we…

Modified: October 28, 2022.

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fabrication

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factors of awakening

In [ Dan Brown ]'s telling, these are: mindfulness ( sati ( https://en.wikipedia.org/wiki/Mindfulness (Buddhism))_): paying attention to the…

Modified: June 27, 2022.

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failure as a temporary setback

Modified: January 09, 2021.

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faith

I grew up in the 2000s reading the New Atheists, where 'faith' was considered a dirty word. Faith was the opposite of reason; it meant…

Modified: November 14, 2022.

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family recipes

MACARONI AND CHEESE 4 Tb margarine 5 tb flour Milk 2 tsp mustard 1 garlic clove, minced or 1 tb prepared minced garlic 2 ½ cups sharp…

Modified: February 22, 2022.

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fashion

Ultimately what is attractive in fashion is confidence. you can break almost all of the rules if it's clear that you're doing it as a matter…

Modified: July 24, 2020.

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fashion is like sex

I've thought before that fashion is bad because it's about arbitrary trends. But you can also see fashion as good because it's about…

Modified: February 07, 2022.

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fast weights

On an evolutionary timescale, it's useful to evolve structures that can learn quickly. The nervous system is an evolved organ system for…

Modified: October 27, 2022.

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feedback loop

See also Scott Alexander's Ontology Of Psychiatric Conditions: Dynamical Systems - Astral Codex Ten (substack.com) theory of depression.

Modified: June 07, 2021.

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feminism

Modified: July 17, 2020.

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filtration

A filtration is defined by monotonically increasing subsets of a [ probability space ]; that is, subsets such that we have for all…

Modified: August 27, 2022.

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finance

Yale course: https://oyc.yale.edu/economics/econ-251 MIT course: https://www.youtube.com/playlist?list=PLUl4u3cNGP63B2lDhyKOsImI7FjCf6eDW…

Modified: August 28, 2020.

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find time to play

From a Jean Yang tweet : I once attended a talk by the late Nobel Laureate Oliver Smithies where he talked about going into lab on weekends…

Modified: August 21, 2020.

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fine-tuning

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five hindrances

Buddists identify five factors as obstacles to [ concentration ] in [ meditation ]: Sensory desire ( kāmacchanda ) Aversion or ill will (…

Modified: March 22, 2023.

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fixation

Interesting and seemingly very powerful perspective on the [ cessation of suffering ]. Most refs on this page are from this twitter thread…

Modified: July 14, 2023.

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fixed point

We say that is a fixed point of an update rule if . Update rules can often (though not necessarily) be seen as defining an…

Modified: August 13, 2022.

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flexible model family

As AGW points out here , it is statistically better to fit a flexible model family, with an inductive bias, than a constrained model family…

Modified: February 15, 2022.

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fluid intelligence

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focus on what you want to see more of

Credit to NameRedacted for this refrain https://twitter.com/visakanv/status/1324978566455468035/retweets/with_comments It's a powerful take…

Modified: April 13, 2024.

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forer effect

Statements from Forer's experiment : You have a great need for other people to like and admire you. You have a tendency to be critical of…

Modified: July 31, 2023.

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forgive

A key insight of Christianity is that forgiveness is something we do for ourselves : it's not just about extending [ grace ] to the party…

Modified: April 10, 2024.

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foundation model

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four noble truths

These are the first teaching of the Buddha, after he achieved [ enlightenment ] while [ meditation|meditating ] under a tree. The truths are…

Modified: February 25, 2022.

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fractional reserve banking

Banks create money by lending. Few understand this. Alice and Bob are on a desert island. Alice has $100, which she deposits in the Desert…

Modified: February 09, 2022.

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free base

Some drugs, like cocaine, or DMT, come in multiple forms: as some sort of [ salt ] or as a 'free base'. What's the difference between these…

Modified: January 22, 2022.

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free energy

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free lunch theorem

'[ no free lunch theorem ]' arguments are misleading because they consider the space of all possible functions. In fact, we usually care…

Modified: December 14, 2022.

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free will

[ Andre ] points out the strong free will theorem . This says that electrons sometimes have 'choices': situations where their behavior is…

Modified: October 04, 2021.

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friend

Modified: February 10, 2022.

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front-door adjustment

Modified: August 06, 2021.

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frustrations with meditation advice

Modified: August 03, 2023.

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fully automated luxury gay space communism

[ my goals ]

Modified: September 16, 2021.

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fun is good

Should I give up having fun in order to do impactful things? It'd be tempting to think that it'd be more virtuous to be serious and mission…

Modified: April 04, 2022.

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fundamental

Modified: February 10, 2022.

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fundamentals are useless for adults

There's often a lot of space between learning [ fundamental ]s and being able to do a thing. Understanding Turing machines didn't…

Modified: February 25, 2022.

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future self

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gabapentin

sources: https://en.wikipedia.org/wiki/Gabapentin https://en.wikipedia.org/wiki/Gabapentinoid https://en.wikipedia.org/wiki/Pregabalin https…

Modified: October 01, 2024.

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gate

Examples recommended by GPT4: Long Short-Term Memory ([ LSTM ]) : Paper: "Long Short-Term Memory" by Sepp Hochreiter and Jürgen Schmidhuber…

Modified: December 20, 2023.

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gated MLP

References: Dauphin et al. 2017 https://arxiv.org/abs/1612.08083 Shazeer 2020 https://arxiv.org/abs/2002.05202 https://arxiv.org/abs/240…

Modified: March 03, 2024.

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gay communities

Modified: July 17, 2020.

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gay pride

Why would you be 'proud' of something you had no control over? The core revelation for me was that pride is the opposite of shame . Most…

Modified: January 20, 2022.

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general intelligence

Is there such a thing as 'general intelligence'? What capabilities does it require? Is it a goal worth striving for? We usually speak about…

Modified: August 30, 2023.

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general-purpose intelligence

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general rules

Rules that work in many situations are valuable. If you can cook a burger, you're a McDonald's employee. If you can specify the rules for…

Modified: April 28, 2022.

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general techniques are simple

If you need to open a specific lock, you can use a key that encodes the precise information needed to open that lock. If you need to open…

Modified: September 01, 2023.

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generalization

Fundamentally, where does generalization come from? [ causality ]: a model may generalize because it has discovered the true mechanism, or…

Modified: October 02, 2021.

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generalized policy iteration

Sutton and Barto use this as a general term for any form of interleaving policy evaluation steps with policy improvement steps. This…

Modified: March 22, 2022.

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generative flow network

Many objects can be generated by a sequence of actions. For example: Generating language by adding one word at a time Generating a molecule…

Modified: March 13, 2022.

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generative questions

Small talk can be mindnumbing and pointless. I like the idea of 'big talk, not small talk'. But realistically small talk serves a social…

Modified: February 25, 2022.

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generative vs discriminative modeling

"What I cannot create, I do not understand". Related to: [ computational complexity ]: provers vs verifiers. [ P != NP ] [ production vs…

Modified: April 27, 2020.

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geometric rationality

Notes on Scott Garrabrant's sequence: https://www.lesswrong.com/s/4hmf7rdfuXDJkxhfg The geometric integral is to products what the…

Modified: April 03, 2025.

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giving in won't help

a Buddhist point. I was trying to fast last night and kept being tempted to relax it slightly . "It won't hurt anything if I just have one…

Modified: July 19, 2020.

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glimpses of AI

An intelligent [ agent ] should work to understand the world. This understanding takes the form of a set of relevant [ abstraction ]s, a…

Modified: May 22, 2021.

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global utility

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global workspace

Modified: May 21, 2024.

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glutamate

Chemically, glutamate is the [ acid-base chemistry|conjugate base ] of glutamic acid (an [ amino acid ]). It is an [ anion ]; its sodium…

Modified: August 08, 2021.

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goals are arbitrary

If you fail to achieve your goals, you'll be sad---almost self-evidently. Nonetheless: there is no coherent notion of the 'right' goals to…

Modified: July 14, 2023.

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goals are identity

Our core notion of a rational [ agent ] is an entity that behaves in a coherent way to pursue some goal. But at a fundamental level there…

Modified: December 05, 2025.

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goals for 2021

Visit [ Andre ] Visit SuccessfulFriend Visit Asian cities Do real bulking and cutting to get in shape Move Learn Mandarin Learn statistical…

Modified: March 14, 2021.

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goals for raising kids

see also [ thoughts about kids ] Get them reading young---ideally by age 2 (like Amitav). Learn an instrument from a young age. Let them…

Modified: February 25, 2022.

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grace

One can never fully deserve grace, but may receive (and extend) it regardless. Probably the most beautiful conceptual contribution of…

Modified: September 11, 2021.

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grad school advice

Thoughts drawn from my experience doing a CS PhD at a top-4 school around 2010-2016. They may be somewhat applicable to PhDs in other areas…

Modified: February 25, 2022.

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grad student depression

A recent survey found that ??% of Berkeley grad students suffer from depression. This should be shocking and dismaying. Yet no one seems…

Modified: March 06, 2022.

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gradient clipping

Why do we clip gradients in deep learning? When is it important and what is the right way to do it? It seems like the standard recipe used…

Modified: April 29, 2023.

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gradient descent

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gradient of the log normalizer

For a normalized distribution , constructed from an (unnormalized) energy with normalizing constant as a function of parameters , in…

Modified: July 09, 2022.

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grading

How should I think about grades when [ teaching ] a class? I believe in mastery learning. Feedback isn't useful unless students have the…

Modified: December 19, 2020.

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gradually, then suddenly

"How did you go bankrupt? Two ways. Gradually, then suddenly." - Hemingway. It can take a long time to lay the foundations for significant…

Modified: February 22, 2022.

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graph neural networks

A 'graph neural net' is a differentiable, parameterized function whose input or output (or both) is a graph. Discriminative: graph as input…

Modified: June 06, 2020.

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great movies

see also: [ great shows ] Cloud Atlas Pulp Fiction

Modified: April 04, 2022.

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great shows

see also: [ great movies ] Deadwood Sense8

Modified: April 04, 2022.

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greeks

The greek letters used most commonly in finance are probably alpha and beta from the [ single-index model ]. However, the term 'greeks…

Modified: November 30, 2022.

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grief is depression

When someone we love dies, a sense of possibility leaves the world. Our grief is usually proportional to how much we cared about them…

Modified: August 21, 2020.

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grokking

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grounded

A nice observation from Percy Liang on the relationship between language modeling and grounded understanding: Just because you don't…

Modified: April 29, 2022.

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growing up means becoming wrong

(related: [ communication is processing ]) A big part of growing up is communicating to your future self. Your future self isn't going to…

Modified: April 05, 2020.

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growing up my own way

A thought that just occurred watching Billions. The two deputy attorneys (white guy and black woman ??) are in her apartment, which is nice…

Modified: February 25, 2022.

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growth mindset

Opposite of a fixed or 'scarcity' mindset. It's important to recognize that the world is nonzero-sum and that improvements are possible. We…

Modified: January 09, 2021.

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habits of intellectual conversation

these include things like: posing interesting questions for discussion useful [ generative questions ] like: what have you been reading…

Modified: February 25, 2022.

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habits of thought

Modified: May 14, 2021.

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hangover

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happiness

A New Yorker article on [ happiness ]: http://www.newyorker.com/tech/elements/a-better-kind-of-happiness discusses happiness as a source…

Modified: February 12, 2022.

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hard attention

Closely related to [ discrete latent variable ]s and to [ reinforcement learning ] with discrete actions. If I do a thing and it goes well…

Modified: January 23, 2022.

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hating god

On Michael Taft's podcast, A. H. Almaas pointed out that an obstacle for most people realizing a sense of divine, nondual love, is some…

Modified: November 23, 2023.

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heat equation

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hedonic treadmill

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heuristics for research taste

Pretend that some other group has published the paper you're imagining: are you excited to read it? Write down ten ideas and ask a mentor to…

Modified: January 09, 2021.

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hierarchical plan

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high dimension

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high-dimension

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high-dimensional

Modified: March 16, 2022.

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high-level actions

The plans I make now include components that would have been impossible for me to conceive of as a kid. At the moment (July 2020), I'm…

Modified: July 08, 2020.

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high leverage projects

What are some things that people are doing now that are just clearly valuable? 3blue1brown : So much of math is hidden behind notation…

Modified: April 02, 2021.

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hold the view

[ Dan Brown ] likes to say that 'the view is the meditation'. That is, meditation isn't

Modified: February 10, 2022.

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how to keep up with papers

People on Reddit worry that there are hundreds of new ML papers every day---how could you possibly keep up? How can you filter the firehose…

Modified: December 08, 2021.

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how to make a friend

[ be open to friendship ] [ act as if you're already friends ] [ people like hearing their name ]

Modified: March 02, 2022.

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huddling together against the dark

campfires apres ski choir rehearsing under a crisp fall night sky ragnars in vans shabbat various gay gatherings (e.g. pride) -- here the…

Modified: July 13, 2020.

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human values

[ value alignment ] research often frames the problem as: first, learn the human 'value function' --- for every possible state of the world…

Modified: June 17, 2024.

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ideal father

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ideal tiny kitchen

Breville/Polyscience Control Freak: induction burner with temperature sensor. replaces normal stove, electric kettle, maybe sous vide, maybe…

Modified: November 02, 2021.

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identifiable

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identity

Modified: July 19, 2020.

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identity goals

from 2017: remember things I am at least somewhat an expert in, that other people may not have seen: philosophy of bayesian statistics…

Modified: February 15, 2022.

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identity is never fixed

I'm sometimes tempted to look back and find patterns in my life, and identify those as "who I really am". For example: maybe I want to be a…

Modified: February 22, 2022.

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if ever a prof

(originally written as a Google doc between 2010-2012) most of this advice is obvious, but still good to remember. students appreciate food…

Modified: February 07, 2022.

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ill-conditioned

Multiple senses: An 'ill-conditioned matrix' has a large ratio between its largest and smallest eigenvalue (more generally, see what is a…

Modified: December 28, 2022.

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imagination rollout

References: Gu et al., Continuous Deep Q-Learning with Model-based Acceleration (2016). A technique used in [ model-based rl ], where we…

Modified: July 19, 2022.

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imitation learning

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immortality is bad

The Eliezer Yudkowsky school of thought is that immortality is possible, and obviously desirable; any other position is [ learned…

Modified: January 24, 2022.

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impact

One aspect of depression recently has been feeling like things are pointless, there's nothing valuable for me to do. My entire PhD has been…

Modified: February 10, 2022.

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impermanence

[ Shinzen Young ] reframes the traditional Buddhist concept of impermanence as "flow". I think this is starting to make sense to me. I…

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implicit regularization

Examples: SGD prefers some minima over others

Modified: March 02, 2022.

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importance sampling

Importance sampling allows us to compute expectations under a distribution using samples from a different distribution , by weighting the…

Modified: July 05, 2022.

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important neural net phenomena

[ grokking ] / [ phase change hypothesis ] emergence of near-discrete features in large transformers symmetries / non-[ identifiable…

Modified: September 14, 2022.

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imposter syndrome

For me, imposter syndrome felt like knowing that there was something deeply wrong with me, something I was missing or didn't get, that would…

Modified: February 10, 2022.

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improv

things I learned in [ improv ] class there's no need to try to be clever or funny. if you're present and responsive, trust that the…

Modified: September 13, 2024.

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in silico

In the 21st century, humanity is developing a new form of engineering. Rather than manually designing artifacts, we are optimizing over…

Modified: February 25, 2022.

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incentives

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indole

Indole alkaloid - Wikipedia Indole - Wikipedia A benzene ring fused with a [ pyrrole ring ]

Modified: May 14, 2021.

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inductive bias

Ways to specify inductive bias: Feature engineering Prior distribution acts as regularizer in MAP estimates Graphical model (constraint on…

Modified: January 16, 2022.

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inductive types

Talia Ringer says that these are one of the most beautiful, foundational ideas in programming languages: https://twitter.com/TaliaRinger…

Modified: January 13, 2022.

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infinite doorways

Around 15min into https://www.youtube.com/watch?v=gWAZFuz_mFc , [ Ram Dass ] claims there are 'infinite doorways'. You start on the…

Modified: October 03, 2021.

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infinitesimal

The Leibniz calculus notation using infinitestimal quantities like or is simultaneously Very sensible and intuitive, but also Constantly…

Modified: September 06, 2022.

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influence function

References: Bae et al. (2022) If Influence Functions are the Answer, Then What is the Question? https://arxiv.org/abs/2209.05364 Grosse et…

Modified: January 03, 2024.

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inner ring

Modified: August 14, 2021.

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instrumental goal

To achieve final goals, we have to break them down into a hierarchy of instrumental goals, and then get to work on achieving those. And for…

Modified: February 25, 2022.

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instrumental variables

The [ front-door adjustment ] allows identifying causal affects using a mediating variable that sits on the causal chain between X and Y…

Modified: February 25, 2022.

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intellectual friendship

I want to care about an intellectual topic and have friends and colleagues with whom I can enjoy discussing that topic. I used to have…

Modified: November 15, 2019.

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intelligence

[ theory of intelligence ]

Modified: May 14, 2021.

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intelligence forklift

Boaz Barak writes in GPT as an "Intelligence Forklift." that [ language model ]s seem to function effectively as [ tool AI ] that can…

Modified: September 29, 2023.

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intelligence is not consciousness

A lot of discussion around [ artificial intelligence ] implicitly conflates intelligence with [ consciousness ]. It assumes that as we…

Modified: January 18, 2023.

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intelligence is not moral worth

Inspired by this tweet: https://twitter.com/davmre/status/841803926051549184 Ways we currently equate intelligence with moral worth: animal…

Modified: February 25, 2022.

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intentional stance

Modified: March 31, 2023.

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interactive proof

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interest rate

It's a bit counterintuitive that high interest rates prevent inflation. After all, doesn't a high interest rate mean that the [ central bank…

Modified: October 09, 2022.

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interesting things dennett says

interesting things dennett says in "darwin's dangerous idea" the "baldwin effect" uses reinforcement learning to construct a version of…

Modified: February 10, 2022.

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interface

Interfaces enable modularity. In general, standardizing an interface can yield quadratic benefit at linear cost. Suppose we have people…

Modified: May 16, 2022.

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interior design

Things to pay attention to in setting up a new place: Lighting makes a huge difference and can totally change the ambience of a space. Don…

Modified: January 19, 2022.

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intermittent fasting

Fasting is a powerful, life-changing idea because it's simple, clear, easy to follow. A diet plan that involves counting calories requires…

Modified: July 11, 2021.

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intermolecular force

References: https://en.wikipedia.org/wiki/Intermolecular_force and linked pages conversations with GPT-4 A molecule is a set of atoms…

Modified: September 13, 2023.

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intervals

The theory of musical intervals almost makes mathematical sense (but not quite): The sensible part: integer ratios The ancient Greeks…

Modified: July 09, 2022.

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intrinsic motivation

objectives: maximize entropy of the state visitation distribution requires empirical estimates of [ entropy ] maximize mutual information…

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inverse reinforcement learning

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ion channel

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ionic bond

Modified: January 22, 2022.

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ionotropic receptors

Modified: August 08, 2021.

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is vs ought dichotomy

David Hume pointed out that there's no logical way to get from 'is' (descriptive) statements to 'ought' (normative) statements. This is…

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isoperimetric

The isoperimetric problem : among all closed curves in the plane with equal perimeter, which encloses the largest volume? It's well-known…

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it's hard not to learn from experience

Update Feb 2025: I now think the existence of [ memory reconsolidation ] makes the point expressed here much less of a blackpill. Factual…

Modified: February 25, 2022.

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it's hard to frame questions about what you don't know

Admitting things that I personally don't know is hard, because it feels like admitting a weakness or failing. But ignorance isn't a…

Modified: July 10, 2020.

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it's not my universe

"it's not my universe": a mantra for [ equanimity ] practice from [ Tucker Peck ]. If you believe in a God who does control the universe…

Modified: April 04, 2024.

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it doesn't matter what you feel

Apparently Tucker Peck told this story in a talk. Sharon Salzberg says that if she could put one thing on her tombstone it would be this…

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it seemed profound at the time

Notes copied from Google Docs https://docs.google.com/document/d/1G7Gxo-A3gQrlUx3G4BYmH-GjUWbB7eTOJZcuAs2ii0A/edit most of these things…

Modified: August 28, 2021.

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jhana

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job goals

From 2017: stay publicly active. work on open side projects, and/or publish, and/or blog. live at such a means that I could lose my job and…

Modified: February 15, 2022.

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joy is not selfish

Something I've struggled with: given my position of immense privilege, how can I justify doing wasteful 'fun' things like skiing or clothes…

Modified: February 07, 2022.

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karma

I don't know if this makes sense, but one intuition I have for karma comes from the observation that the weights of a least-squares linear…

Modified: February 10, 2022.

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kelly criterion

We are given the opportunity to bet some fraction of our wealth on a coin flip with probability . We can repeat this as many times as we…

Modified: March 24, 2025.

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kernel

multiple senses: in machine learning: positive definite (Mercer) kernels in linear algebra: kernel (nullspace) of a linear map in CS systems…

Modified: February 25, 2022.

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ketamine

Effects in the brain Ketamine is an antagonist of [ NMDA receptor ]s, and activates [ AMPA receptor ]s. References: Ketamine – Lorien…

Modified: February 13, 2022.

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keys and locks

pg says: the random things that you learn as a kid make you into a key. Your job is then to find the lock that you fit into. But that's not…

Modified: June 12, 2021.

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kids matter

Adults tend to talk to and work with other adults. We don't spend nearly enough time addressing the problems of younger people: college…

Modified: April 01, 2022.

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kitchen sink deep learning

I just coined the phrase 'kitchen sink' deep learning for a vague idea that comes to me occasionally. Roughly: rather than using a uniform…

Modified: October 25, 2021.

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language basics

An annoying thing about language-learning tutorials is that they often focus on language that you'll never actually use as a tourist. When I…

Modified: December 04, 2022.

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language model

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language model cascade

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large control policies

Taco Cohen speculates on Large Control Policies as a successor to large language models: https://twitter.com/TacoCohen/status…

Modified: April 15, 2022.

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large effects

Much of statistical practice is concerned with distinguishing signal from noise. For example, significance tests quantify the likelihood…

Modified: May 19, 2022.

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large models

If you believe that neural nets basically just memorize the training data, then training larger and larger models is hopeless. The…

Modified: September 06, 2021.

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leadership

I don't want to be led. I want to be creative and do things that are dramatically new. Telling other people what to do feels almost evil to…

Modified: February 25, 2022.

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learned helplessness

Happens all the time, at small scales and large scales. Large scale: When I was young, it was possible to imagine becoming a confident…

Modified: March 08, 2020.

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learning from success is better than failure

The set of good approaches is often hidden in an exponentially large space. Learning that an approach is not good doesn't help narrow that…

Modified: June 03, 2020.

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learning new skills

Modified: September 11, 2021.

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leaving academia

There's no easy or fast solution for feeling good about leaving academia, because you're giving up some aspect of your [ identity ], and…

Modified: February 07, 2022.

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legibility

Modified: February 25, 2022.

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legibility in software

(related: [ growing up means becoming wrong ], ask for evidence , [ Seeing Like A State ]) Related to some interactions with [ Josh…

Modified: February 25, 2022.

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legible identity

A thing that's tough about going through big personal changes is that it takes a while for your self-model to catch up with your actual self…

Modified: May 16, 2022.

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lessons for AI from meditation

With varying degrees of clarity and certainty. We are [ embedded agent ]s. So are any AI systems we build. We exist inside the world; the…

Modified: December 30, 2024.

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let go

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let me google that for you

People on the internet have very different standards as to when and how it's okay to ask a question. There are roughly two camps: Search…

Modified: March 19, 2022.

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liberation

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library of Babel

https://maskofreason.files.wordpress.com/2011/02/the-library-of-babel-by-jorge-luis-borges.pdf Insights illustrated by this story: Naming…

Modified: October 17, 2022.

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life conclusion

Modified: March 07, 2020.

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lighthouse goal

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limitations of autodiff

In principle we can apply [ automatic differentiation ] through any composition of differentiable operations. This lets us get gradients of…

Modified: July 21, 2022.

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limiting belief

Modified: October 29, 2021.

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limits on individual impact

I want to change the world. What does that mean? Suppose I create a billion-dollar company. That's an enormous amount of value. It's many…

Modified: February 14, 2021.

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linear attention

tags: created: 2023-12-07 modified: 2023-12-07 References: https://arxiv.org/abs/2006.16236 The usual [ transformer ] [ attention…

Modified: December 07, 2023.

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linear time-invariant

A linear time-invariant system is one where the dependence of the output on the input is: linear: an input produces an output , and…

Modified: December 05, 2023.

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lipid bilayer

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listening inbox

podcasts and audiobooks Alan Watts 'out of your mind' lectures

Modified: February 15, 2022.

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