Agora: a language learner whose memory is a market

1Project overview

A human brain runs on about 20 watts, barely enough to illuminate a dim lightbulb, while training and hosting frontier large language models demands the output of entire industrial data centers. The gap has identifiable causes: computers shuttle memory to the processor for every operation, activate every parameter for every token, compute with costly precision and learn with an algorithm that needs trillions of examples.

Agora is an experiment in the opposite direction. It asks how far a learner can go when memory and computation are the same structure, updates are purely local and sparse, and nothing is stored unless it was surprising. Instead of borrowing the brain's vocabulary of neurons and synapses, it borrows the vocabulary of markets, for a concrete reason: a market is a well-understood machine for aggregating many partial, competing opinions into a single price, and its accounting is exactly the accounting of prediction.

The system has five working parts.

• Traders hold local statistics about one context and bet on what follows it.
• Settlement pays each trader according to how well it called the word that actually arrived. Wealth becomes memory strength.
• Birth and sleep grow memory where the market was wrong and prune it where it no longer earns its keep.
• An analyst reasons by analogy using role vectors that encode which words appear in which positions around a word.
• A curiosity rule reads next whatever lies just beyond the market's current knowledge, while avoiding pages that look like noise.

Performance is measured honestly as compression: the number of bits the market needs to encode sealed pages it has never read. The whole system, including eight public-domain corpora of about 60,000 words each, runs locally in this page. Section 3 walks through using it.

2Mechanisms

2.1Traders and prices

Text is split into lower-case words and punctuation. A trader is attached to one context: the last one to five words, such as “my good”. It holds counts of the words that have followed that context, a count of its trades n, and a trust value τ. A trader's belief about the next word follows the PPM-D estimator: words it has seen get probability proportional to their counts, and the remaining mass, which grows with the number u of distinct words it has seen, is spread according to public base rates.

The base rate b₀ is a smoothed word frequency, quoted by a market maker who trades at every table. A word never seen before must be spelled out letter by letter, costing about 4.75 bits per letter, so unknown vocabulary is paid for rather than ignored. When a context arrives, every trader whose context matches a suffix of it is active. The price of a candidate word is the stake-weighted average of the maker's quote and the active traders' beliefs:

Here k is the context length, from general (one word) to specific (up to five). A trader's stake is the product of its own trust and that of every more general trader beneath it. That design choice matters. In an early version, each trader held absolute wealth, and general traders, which take part in far more markets, accumulated wealth regardless of skill. Step 7 draws these parent and child relationships as a family tree. Holding trust relative to the parent context means a specialist inherits its parent's reputation and only has to beat the parent where the two overlap, much as context tree weighting weighs contexts in classical compression.

2.2Settlement: betting, updating and compressing are one operation

When the actual word w arrives, the market pays its cost, the number of bits an ideal coder would spend given the price:

Then every active trader is settled. A Kelly bettor that spreads its wealth in proportion to its beliefs multiplies that wealth by β(w) / p(w). That multiplication is exactly Bayes' rule for a mixture of models, and the log of total wealth growth equals the bits saved relative to the market price. Agora applies the rule to trust relative to the parent, tempered by a learning rate η and bounded so that no trader is ever infinitely right or wrong:

After settlement each active trader adds w to its counts. Step 6 in Section 3 replays this process word by word, and step 2 shows it live while the market reads. No error signal travels anywhere else: the only structures touched are those that were active for this word.

2.3Birth from surprise, liquidation in sleep

New traders are created only when the market is caught out. If the cost of a word exceeds a threshold θ (4 bits by default), the market opens one new trader, one word more specific than the deepest active one, seeded with the word that surprised it. Predictable text therefore costs no new memory, which is the minimum-description-length principle in operational form: store only what the current model fails to explain. Deep contexts are grown one level per surprise, so the market deepens exactly where it keeps being wrong.

Every S words (60,000 by default) the market sleeps. Every count is halved, and traders left with no counts, or with trust at the floor, are liquidated. Sleep keeps memory bounded, lets old statistics fade in favour of recent evidence, and removes traders that were born from one-off accidents.

2.4Role vectors and the analyst

Traders cannot generalise: a context they have never seen gets no help from similar contexts. The analyst supplies that help using hyperdimensional computing. Each word receives a fixed random identity vector of ±1 values in 256 dimensions. Each word also accumulates a role vector: every time word a appears k positions before word w, the identity of a is rotated by −k positions and added to the role of w, and the identity of w, rotated by +k, is added to the role of a.

The rotation ρ binds position into the vector, so “the king” and “king the” leave different traces, and words used in the same positions around the same neighbours end up pointing the same way. Similarity is the cosine between role vectors after the mean vector is removed. Nobody tells the system that “lord” and “liege” are related; the relation appears because they sit in the same slots.

When no trader of length two or more matches the current context, the analyst joins the market. It finds the eight words whose roles most resemble the last word, borrows the beliefs of their one-word traders weighted by similarity, and bets half on that borrowed view and half on base rates. It must earn its influence like everyone else: its stake is a share of each pot it joins, updated by the same Kelly rule and kept between 0.1% and 1,000 times the traders' pot. The floor is the fixed-share method from online learning, and it ensures the analyst can win influence back if the text changes.

2.5Curiosity-driven reading

Before choosing a page, the market tastes the opening 80 words of every unread page and measures its cost in bits per word, without learning anything. Let m be the average taste of the last eight pages it read. It then reads the page whose taste is closest to m + 1: slightly beyond current knowledge, where learning progress is likely. Pure novelty-seeking has a known failure, sometimes called the noisy-TV problem, in which an agent fixates on randomness because randomness is always surprising. Agora guards against it: once three pages have been read, any page tasting more than 4 bits above m is marked as noise and never read. Pages you add yourself skip the queue and are read first.

2.6Evaluation

Before any reading, about one page in five of the chosen corpus is sealed as an exam, chosen by a fixed hash so the split never changes; small corpora get extra sealed pages so the exam is not too short. The first 450 words of each sealed page form the test set. After every page read, the market prices the test set without learning, and the chart reports the average cost from equation (3). As a reference, the same text is compressed with deflate, the algorithm inside zip and gzip, using the browser's built-in compressor. A market that beats deflate has captured regularities in language that a generic byte-pattern compressor misses.

3Usage, step by step

Everything below is live. The controls in the bar stay at the top of the screen while you scroll through the steps.

4Results and limitations

The figures below come from test runs of this implementation. Exact numbers vary slightly between runs, because curiosity can read pages in a different order.

Table 1. Compression of held-out Shakespeare. The browser runs use the built-in library; the Python row uses a larger split of the same source.

Table 2. One pass over each corpus in page order with default settings, scored on sealed pages chosen by the same hash the page uses. Alice's test set is small because the book is short.

Across corpora, the ranking follows intuition. The formulaic Bible compresses best, and Moby-Dick, with its enormous vocabulary, worst among the English texts. The French novel costs most, partly because the market must first spell out many inflected word forms. Three further findings stand out. First, sleep is cheap: it removes about 84% of traders for roughly a tenth of a bit per word, which shows that most surprise-born traders record accidents rather than regularities. Second, the market consistently defunds the analyst. On this amount of text, borrowing opinions from similar words loses money against specialists and base rates, even though the role vectors themselves are clearly meaningful. Analogy should begin to pay only with far more data. Third, refinements to the betting rules improved scores by only about 0.1 bits. The binding constraint is data, not cleverness.

The limitations are real. Agora captures local word statistics, not composition: it produces fluent phrases but no reasoning or coherence beyond a sentence or two. The noise filter can reject a legitimate page early on, when it has too little history to judge what counts as normal. Memory, although bounded by sleep, still grows with vocabulary. And unlike the Python version, this page cannot crawl the web, because hosted pages are not permitted to fetch other sites; it reads the built-in corpora and whatever you add.

5References

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3. Kelly, J. L. (1956). A new interpretation of information rate. Bell System Technical Journal, 35(4).
4. Cover, T. and Thomas, J. (2006). Elements of Information Theory, 2nd ed., chapter 6 on gambling and data compression. Wiley.
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