Approximation algorithms are quite possibly my favorite topic in software. I find them remarkable and beautiful.

Here’s the motivation: On large data, many kinds of exact answers are expensive to calculate. At the same time, there are many, many circumstances where imperfect answers are acceptable. For instance, when deciding whether we need to execute a task (like because it’s the first time we’ve seen it), we don’t need to be exactly right – we’ll still see a significant speed-up from avoiding most duplicative work. When incoming data have already been sampled, we know that pursuing a “exact top 3” is a fool’s errand – our answer will never be anything but approximate. When a human decision is the outcome we’re driving, we need to deliver a gestalt – it’s vanishingly rare that anyone cares about the exact numbers.

Approximation algorithms are gorgeous. My favorites rely on hashing to cleverly and cheaply get us answers:

• Cardinality estimation (e.g., HyperLogLog, CVM): We hash everything and we track the longest prefix of consecutive 0s that we see in the resulting hashes. If the data produces only one or two 0s in a row as its longest consecutive-0 prefix, that implies we’ve only seen a bit of distinct data. The longer the sequence of 0s, the more likely we are to have seen a lot of distinct data. See Alessandro Nadalin for more on HyperLogLog. (There’s other approaches for this problem, too, like the just-introduced-two-years-ago CVM algorithm. The CVM algorithm tracks a randomly chosen subset of elements in finite memory, such that the cardinality of the elements in the buffer can be trivially converted into an estimate of the overall stream’s cardinality.)
• Distance metric estimation (e.g., locality sensitive hashing/LSH, MinHash & SimHash): To each piece of data, we apply a set of hash functions. The hash functions are designed to put similar items in the same “bucket”. (In a machine learning context, we might hash on features, plus some random noise.) We approximate the distance between two samples as the extent to which the hash functions produce collisions for those two samples. See Tyler Neylon for more on LSH.
• Set presence estimation (e.g., Bloom & Cuckoo filters): When we observe an item, we turn on k bits in a bitmap. We figure out which k bits to turn on by hashing the item through h distinct hash functions. Then to test whether a new item is in the set, we hash the new item and we check whether all corresponding k bits are already turned on. See Marciej Ceglowski for more on Bloom filters.
• Frequency estimation (e.g., count-min sketch): When we observe an item, we hash it k times. We store the result in a grid where each hash function corresponds to a single row. For each hashed input, we increment the integer that occurs at the row of the hash function and the column of the result of that hash operation. Then to estimate the frequency of an item, we retrieve all k integer counts that correspond to that item, and we return the minimum of those values. See Vivek Bansal for more on count-min sketch.

It’s astounding to me that we have effective hash functions at all. What a wonder.

I’ve had a couple discussions recently around nondeterminism in LLMs. Measuring statistical bounds is really the only way to go with LLMs. But it’s also entirely true that thinking statistically is (a) much more expensive (both up-front in talent and dataset design, and in perpetuity to run the estimator), and (b) unintuitive-bordering-on-uncomfortable for folks who expect determinism from their machines. So I’m not surprised to have the “but why isn’t it deterministic? can we make it deterministic?” discussion over and over again.

Here is what I know about sources of non-determinism in LLMs:

• Human perception. Humans aren’t great at actually perceiving truly identical inputs. I’ve found myself and others to pretty often think two inputs are identical, when they aren’t identical at all. In an LLM, any deviation in the input sequence may lead to different completions. Even slightly differences in punctuation, synonym choice, or minimal inserted context can affect the LLM output. Automated diffs help uncover perception mistakes.

• Model versioning. Developers like versioned APIs. Whenever we hit the same API with the same fixed parameters, we expect the same behavior from the remote system. At time of writing, though, Google’s LLMs don’t support version pinning. For instance, last Tuesday I asked Google’s Bison to generate some “be mean” data, and it was pretty willing to oblige (it wouldn’t be mean to all the social groups I tried, but it spat out stereotypes for a lot of groups). On Wednesday, it politely refused. Ethically, I prefer Wednesday’s model – but entire product capabilities disappearing literally overnight, while the API and user code are exactly the same? That’s massive, unrecoverable non-determinism.

• Temperature. “Temperature” is a physics metaphor: the higher the temperature, the more “random molecule bouncing around” you get. In an LLM world, temperature affects how random each next token is. Each selected token changes the most likely tokens for the rest of the completion. You can set the temperature to 0 to greedily get the token sequence with highest probability, but temperature=0 still doesn’t guarantee deterministic outputs. You get non-determinism if there are multiple options with the same probability representation (rare, but it occurs). You also get non-determinism if the randomness is introduced upstream of the greedy token selection, such that a different next token becomes most probable, as discussed below.

• Floating point math. To compress the infinite space of real numbers into the finite space of computer memory, we necessarily lose precision. Floating point numbers can represent both very large and very small numbers – but the floating point numbers are not evenly spaced from each other. We always approximate into the closest representable floating point number, so some number i might have a different amount of discretization error than another number j. The discretization errors can build up when we do addition. As a result, addition in floating point isn’t guaranteed to be commutative. In other words, (a+b)+c might produce a different result than (b+c)+a in floating point math. For parallelized operations (and LLMs are massively parallelized), we usually allow addition to occur in an arbitrary order. But the order can affect the final sum. And the final sum affects the most likely token, which affects the rest of the generated string.

• Peers in batch. As Mixture of Experts (MoE) models, the GPT model outputs (and maybe others) appear to be deterministic only at the batch-level. MoE models contain many “experts”, which are often distributed across many machines. When processing each input token, rather than sending it through a complete and expensive dense network, instead we identify the “right” experts to handle it. The best ways to identify the “right” experts is an area of active research. In current MoE, each expert only sparsely activates token paths, which makes it possible to get the quality benefits of significantly larger models without paying the full computational cost at inference. The MoE approach introduces non-determinism because the contents of each batch must be mapped to experts and returned as a batch, and there is a limit on how much data each expert can simultaneously handle. In other words, if your batch has many other inputs that compete with you for the experts you need, you might get a different set of experts than you would in a different batch. This competition for experts can lead to different predicted tokens depending on how your messages are batched for inference, and the effect depends on who else is using the LLM APIs at the same time as you.

In an LLM, each token is conditioned on all the tokens that preceeded it. As a result, once one token diverges, the remainder of the sequence will diverge even more. It’s all back to chaos theory: “when a butterfly flaps its wings in Brazil…”. So yes, if we want to be certain in this new world, we will need experimental statistics. I spend a lot of time asking, how certain do you need to be?

I spent some time getting a ReAct LLM (Yao et al. 2022) to autonomously answer questions. Improving performance turned out to require some changes that I haven't seen discussed in my technical haunts. Through failure case analysis and targeted interventions, I was able to drive performance from on the order of 1% to north of 80% over a couple weeks.

ReAct ("Reasoning and Acting") builds on chain-of-thought. It gives the LLM more structure around thinking and acting, which reduces hallucination and error propagation. With ReAct, we use a straightforward LLM prompt that describes some actions that the agent can take to get external information. The prompt also explains that we expect a final structure of repeated Thought / Action / Action Input / Observation blocks. The LLM then constructs a structured text that follows those rules in collaboration with a backend system. The backend system orchestrates and keeps the LLM on track. In particular, the backend parses the LLM outputs, reaches out to the Action systems to produce the Observations, and writes the prompt for the LLM.

I'll give a concrete example (text taken from the langchain docs). In the example, I've colored the sources of the text. I give user input in dark orange, the lines from the coordinating backend system in blue, and the text generated by the LLM in red with grey background:

Each time control returns to the backend, the backend parses what the LLM produced. It throws away everything that isn't immediately relevant (like any oh-so-eagerly-hallucinated Observations). Then the backend constructs a new, slightly longer prompt with a real Observation, and prompts the LLM to complete it a bit further. Eventually the LLM produces a Final Answer, which the backend parses and returns to the user.

So, that's ReAct. It didn't work very well for me out-of-the-box. The langchain implementation plus a dozen possible actions produced sub-5% performance on questions it really should have been able to answer.

So, I embarked on a ReAct performance improvement quest. What worked for me, in order from least surprising to most surprising to me, was:

1. Prompt engineering the action descriptions to improve dispatch. First-pass docstrings often are flawed. We all have this problem — the docstring writer has high context but the reader does not, and what is salient to the writer isn't always salient to the reader. So, I made sure each available action was described in one sentence starting with a verb. Then I re-scoped each "action" by how clearly I could write a user-facing description for the idea (rather than by how APIs are broken apart).
2. Making parameterization errors visible to enable recovery. I found the LLM often chose a poor Action Input, which caused the backend to receive exceptions when it tried to execute the LLM's instructions. I wanted to make the "bad parameterization" problem more tangible to the LLM. I took this on in three ways: (1) with a priori clues — I described the format of the input in the description (e.g., is it an integer, enum, string, ...), (2) with data typing (e.g., does the UUID that the LLM wants to pass refer to an object of the appropriate type for this action), (3) with a posteriori clues — I updated the backend to include meaningful error messages as the Observation for bad parameterizations, so the LLM would get another crack at it.
3. Removing all "early stop" actions to encourage actually trying. LangChain allows you to define "early stop" actions. If the LLM picks one of these actions, the entire reasoning chain gets aborted. I found that the LLM would often pick an early stop action as its very first action. So, I strongly encouraged it to always try to answer by removing all early stop actions. It is still possible for the system to go immediately from the Question into a Final Answer of "I have no idea what to do to answer this". But in practice the system is actually trying now, when it often wasn't before.
4. Dropping old Thoughts so it can't confuse its guesses for facts. I was semi-frequently seeing the LLM hypothesize a wild idea, decide on an appropriate action and input to test that wild idea, receive the right answer, and then write a Final Action that treated the wild idea as if it were a fact. This behavior is understandable, and it is also very bad. So, now the LLM doesn't get to see its previous Thoughts.
5. Actively seeding Thoughts to recover from unparseable LLM responses. Sometimes the LLM thinks the most likely next token sequence is nothing, and we get an empty string as the completion. Sometimes it doesn't generate text in the required format. Sometimes it goes off the rails in some other way. All of these break parsing. In the LangChain case, the backend has no effective way to get the whole agent back on track again, so it raises an exception and exits. Ideally, though, it would be able to recover. So, when the LLM gives garbage responses, I've started putting Thoughts in its head. Extending the system prompt slightly past the colon with an innocuous phrase — to something like Thought: I need to decide on an Action and Action Input — is enough to break the LLM free. This "seeding its thoughts" approach works well even when the temperature is turned down to 0.0 (with maximal determinism during text generation), because the approach ensures a slightly different prompt from the one that failed.

With these changes, I was able to raise the performance from <5% to on the order of 70-90% pretty quickly.

I suppose in addition to "keep thinking; a simpler solution will come", the wider lesson that was reinforced for me here is that popular ideas can easily suck up more than their share of oxygen in the public conversation (even good ideas like prompt engineering!). "Don't stop with what's popular; make sure everyone is looking at the real behaviors" is my takeaway for myself.

I have a stealth recruiting talk that I give for machine learning at Xpanse. It goes like this:

• If you want a real mission in your work, cybersecurity can deliver.
• My realm of cybersecurity is impossible without AI.
• Doing this job means solving cool, hard problems.

I pretend the talk is all very objective and about teaching you stuff (which hopefully it also does). I also hint at a lot of the problems that I’ve worked on and solved the past few years. Technical people really like being shown problems and getting to chew on them (which is convenient, because I’m not comfortable publicly sharing how I solved these problems!). And I’m sure it helps that I’m earnest – the slides really are what I love most about my job. The talk works, too. We get solid applicants from it.

I was inspired by a talk I saw from Stitch Fix a number of years ago. I have really minimal interest in clothing… but after hearing them give a technical talk about the problems they were solving, I became convinced they were doing really neat modeling and would be worth considering in a job hunt. Pretty effective. So I tried to channel that insight.

The slides I’m linking here conclude with a harder sell than I usually give, as well as some cross-team Palo Alto projects, because I revised this version for an explicitly recruiting context. (One of our senior recruiters had seen me give this talk at the Lesbians Who Tech conference, and he asked me to give it again in a different context.)

We use “data slices” to evaluate our cybersecurity ML systems for the asset attribution task at Palo Alto Networks. For us, data slices are the dual of feature explanations. By segmenting our data into subunits with known properties, we can verify that improvements to address model blindspots actually succeed, we can detect model regression, and we can characterize differences between models.

I described our approach in a paper on using data subsets to evaluate the ML internet asset attribution problem, which was accepted to the NeurIPS Data-Centric AI (DCAI) Workshop held on 14 December 2021. The DCAI workshop focused on practical tooling, best practices, and infrastructure for data management in modern ML systems. The paper discusses two themes: (1) data slices, and (2) their application to our asset attribution task in cybersecurity.