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Chess-GPT’s Inner World Mannequin | Adam Karvonen

Chess-GPT’s Inner World Mannequin | Adam Karvonen

2024-01-06 11:49:22

A Chess-GPT Linear Emergent World Illustration

Among the many many latest developments in ML, there have been two I discovered attention-grabbing and wished to dig into additional. The primary was gpt-3.5-turbo-instruct’s capacity to play chess at 1800 ELO. The truth that an LLM might study to play chess effectively from random textual content scraped off the web appeared nearly magical. The second was Kenneth Li’s Emergent World Representations paper. There is a wonderful summary on The Gradient and a follow-up from Neel Nanda. In it, they skilled a 25 million parameter GPT to foretell the subsequent character in an Othello sport. It learns to precisely make strikes in video games unseen in its coaching dataset, and utilizing each non-linear and linear probes it was discovered that the mannequin precisely tracks the state of the board.

Nonetheless, this solely labored for a mannequin skilled on an artificial dataset of video games uniformly sampled from the Othello sport tree. They tried the identical methods on a mannequin skilled utilizing video games performed by people and had poor outcomes. To me, this appeared like a significant caveat to the findings of the paper which can restrict its actual world applicability. We can’t, for instance, generate code by uniformly sampling from a code tree.

So I dug into it. I skilled some fashions on chess video games and used linear probes on the skilled fashions. My outcomes had been very constructive, and answered all of my earlier questions (though after all, extra questions had been generated).

A 50 million parameter GPT skilled on 5 million video games of chess learns to play at ~1300 ELO in at some point on 4 RTX 3090 GPUs. This mannequin is just skilled to foretell the subsequent character in PGN strings (1.e4 e5 2.Nf3 …) and isn’t explicitly given the state of the board or the foundations of chess. Regardless of this, with a view to higher predict the subsequent character, it learns to compute the state of the board at any level of the sport, and learns a various algorithm, together with examine, checkmate, castling, en passant, promotion, pinned items, and so on. As well as, to raised predict the subsequent character it additionally learns to estimate latent variables such because the ELO ranking of the gamers within the sport.

All code, knowledge, and fashions have been open sourced.

My preliminary speculation was that Othello-GPT skilled on human video games carried out poorly because of an absence of information. They solely had 130k human Othello video games, however the artificial mannequin was skilled on 20 million video games. I attempted two completely different approaches to create my datasets: First, I had Stockfish ELO 3200 play 5 million video games as White in opposition to a spread of Stockfish 1300-3200 as Black. Hopefully, this artificial dataset of superhuman chess bot video games would supply larger high quality knowledge than human video games. Second, I grabbed 16 million video games from Lichess’s public chess game database. I skilled separate fashions on particular person datasets and numerous mixes of datasets (extra particulars within the appendix).

Initially, I checked out fine-tuning open supply fashions like LLama 7B or OpenLlama 3B. Nonetheless, I nearly instantly needed to abandon that method to maintain my GPU prices down (I used RTX 3090s from runpod). As a substitute, I began coaching fashions from scratch utilizing Andrej Karpathy’s nanogpt repository. I experimented with 25M and 50M parameter fashions.

A graph of Chess-GPT vs Stockfish

It mainly labored on the primary strive. The 50M parameter mannequin performed at 1300 ELO with 99.8% of its strikes being authorized inside at some point of coaching. I discover it pretty spectacular {that a} mannequin with solely 8 layers can appropriately make a authorized transfer 80 turns right into a sport. I left one coaching for a number of extra days and it reached 1500 ELO. I’m nonetheless investigating dataset mixes and I’m certain there’s room for enchancment.

So, gpt-3.5-turbo-instruct’s efficiency is just not magic. Should you give an LLM a number of million chess video games, it’ll study to play chess. My 50M parameter mannequin is orders of magnitude smaller than any affordable estimate of gpt-3.5’s measurement, and it’s inside 300 ELO of its efficiency. As well as, we lately had affirmation that GPT-4’s coaching dataset included a collection of PGN format chess games from gamers with an ELO over 1800.

I additionally checked if it was enjoying distinctive video games not present in its coaching dataset. There are sometimes allegations that LLMs simply memorize such a large swath of the web that they seem to generalize. As a result of I had entry to the coaching dataset, I might simply look at this query. In a random pattern of 100 video games, each sport was distinctive and never discovered within the coaching dataset by the tenth flip (20 complete strikes). This needs to be unsurprising contemplating that there are extra potential video games of chess than atoms within the universe.

Subsequent, I wished to see if my mannequin might precisely observe the state of the board. A fast overview of linear probes: We will take the inner activations of a mannequin because it’s predicting the subsequent token, and practice a linear mannequin to take the mannequin’s activations as inputs and predict board state as output. As a result of a linear probe may be very easy, we will have faith that it displays the mannequin’s inside information relatively than the capability of the probe itself. We will additionally practice a non-linear probe utilizing a small neural community as an alternative of a linear mannequin, however we danger being misled because the non-linear probe picks up noise from the information. As a sanity examine, we additionally probe a randomly initialized mannequin.

Within the unique Othello paper, they discovered that solely non-linear probes might precisely assemble the board state of “this sq. has a black / white / clean piece”. For this goal, the probe is skilled on the mannequin’s activations at each transfer. Nonetheless, Neel Nanda discovered {that a} linear probe can precisely assemble the state of the board of “this sq. has my / their / clean piece”. To do that, the linear probe is just skilled on mannequin activations because it’s predicting the Black XOR White transfer. Neel Nanda speculates that the nonlinear probe merely learns to XOR “I’m enjoying white” and “this sq. has my colour”.

Armed with this information, I skilled some linear probes on my mannequin. And as soon as once more, it mainly labored on my first strive. I additionally discovered that my Chess-GPT makes use of a “my / their” board state, relatively than a “black / white” board state. My guess is that the mannequin learns one “program” to foretell the subsequent transfer given a board state, and reuses the identical “program” for each gamers. The linear probe’s goal was to categorise each sq. into one among 13 lessons (clean, white / black pawn, rook, bishop, knight, king, queen). The linear probe precisely categorized 99.2% of squares over 10,000 video games.

To higher interpret the inner predictions of my mannequin, I created some visible warmth maps. These warmth maps had been derived from the probe outputs, which had been skilled on a one-hot goal to foretell whether or not a chess piece, such the black king, was current on a given sq. (1 if current, 0 if not). The primary warmth map reveals the precise board state for the black king. The second warmth map depicts the probe’s confidence with a clipping restrict utilized to the output values the place any worth above 5 is decreased to five. This clipping makes the probe’s output extra binary, as proven by the white sq. in opposition to the black background. The third warmth map presents the probe’s output with none clipping, revealing a gradient of confidence ranges. It reveals that the mannequin is extraordinarily sure that the black king is just not positioned on the white facet of the chessboard.

3 heatmaps of the linear probe for black king location

We see a really related end result for the placement of the white pawns, though the mannequin is much less assured. This board state comes from the twelfth transfer in a chess sport, and the mannequin is extraordinarily assured that no white pawns are in both facet’s again rank.

3 heatmaps of the linear probe for white pawn location

The mannequin nonetheless is aware of the place the clean squares are, however it’s as soon as once more much less assured on this.

3 heatmaps of the linear probe for blank squares location

For this transfer on this chess sport, the linear probe completely reconstructs the state of the board. The probe’s goal is to categorise every sq. into one among 13 classes, every representing a special chess piece or a clean sq.. To create this graph, we simply take the prediction with the best worth for every sq. because the probe’s output.

2 heatmaps of the linear probe for board state

As a result of Chess-GPT discovered to foretell the subsequent transfer in a aggressive sport, relatively than a sport uniformly sampled from a sport tree, there are attention-grabbing latent variables we will probe for. Particularly, I hypothesized that to raised predict the subsequent character, it could study to estimate the ability stage of the gamers concerned.

Initially, I skilled the probe on a regression job, the place its job is to foretell the ELO of the White participant. It might do that by coaching on the inner activations of the mannequin between strikes 25 and 35, as it could be extraordinarily troublesome to foretell participant ability early within the sport. Nonetheless, nearly all of the video games within the Lichess dataset are between 1550 ELO and 1930 ELO, which is a comparatively slender band. The linear probe skilled on Chess-GPT had a mean error of 150 ELO, which appeared good at first look. Nonetheless, a linear probe skilled on a randomly initialized mannequin had a mean error of 215 ELO. The slender window of ELO in most video games made it troublesome to discern the mannequin’s stage of data. Distinguishing between a 1700 and 1900 ELO participant simply looks as if a really troublesome job.

So, I then skilled the probe on a classification job, the place it needed to determine gamers under an ELO of 1550 or above an ELO of 2050. On this case, the probe carried out a lot better. A probe skilled on a randomly initialized mannequin appropriately categorized 66% of gamers, whereas a probe skilled on Chess-GPT appropriately categorized 89% of gamers.

To an extent, that is unsurprising. This jogs my memory of the OpenAI’s 2017 Sentiment Neuron paper. In it, they skilled an LSTM to foretell the subsequent character in Amazon critiques. Once they skilled a linear probe on the mannequin’s internals utilizing simply 232 labeled examples, it grew to become a state-of-the-art sentiment classifier. OpenAI wrote then that “We imagine the phenomenon is just not particular to our mannequin, however is as an alternative a normal property of sure massive neural networks which can be skilled to foretell the subsequent step or dimension of their inputs”. With this context, it’s nearly an anticipated end result.

The proof right here can be stronger if I additionally carried out causal interventions on the mannequin utilizing these probes. For instance, I might intervene to alter the mannequin’s inside illustration of the board state, and see if it makes authorized strikes underneath the brand new state of the board. Or, I might intervene on the mannequin’s illustration of participant ability and see if it performs higher or worse. Sadly, I simply ran out of time. This was a Christmas break mission, and it’s time to get again to work.

Nonetheless, I nonetheless contemplate the findings to be robust. Linear probes have a restricted capability, and are an accepted technique of benchmarking what a mannequin has discovered. I adopted normal finest practices of coaching the probes on a coaching set, and testing them on a separate check set. The board state particularly is a really concrete job to probe in opposition to. Probing for ability stage does have a risk that the mannequin is studying some characteristic that’s largely correlated with ability, however 89% is an efficient end result for the troublesome job of discerning the ELO of gamers in a chess sport after 25 strikes.

As Neel Nanda mentioned, there are lots of benefits to deciphering fashions skilled on slender, constrained duties comparable to Othello or Chess. It’s troublesome to interpret what a big LLM like Llama is modeling internally when predicting tokens in an unconstrained area like poetry. There was profitable interpretation of straightforward fashions skilled on toy duties like sorting an inventory. Fashions skilled on video games present an excellent intermediate step that’s each tractable and attention-grabbing.

My instant thought is to search for some kind of inside tree search. Once I play chess, I carry out a kind of tree search, the place I first contemplate a spread of strikes, then contemplate my opponent’s responses to those strikes. Does Chess-GPT carry out an analogous inside calculation when predicting the subsequent character? Contemplating that it’s higher than I’m, it appears believable.

Different potential instructions:

  • Carry out causal interventions on the mannequin utilizing these linear probes.
  • Examine why the mannequin generally fails to make a authorized transfer or mannequin the true state of the board.
  • How does the mannequin compute the state of the board, or the placement of a particular piece?
  • I fine-tuned GPT-2 on a 50 / 50 mixture of OpenWebText and chess video games, and it discovered to play chess and continued to output believable wanting textual content. Perhaps there’s one thing attention-grabbing to take a look at there?

If enthusiastic about dialogue or collaboration, be happy to contact me through e-mail. There may be additionally this Twitter thead for public dialogue functions.

Appendix

Each Neel Nanda and I skilled our probes to foretell “my piece / their piece” as an alternative of “white piece / black piece”. To foretell “white piece / black piece”, you simply have to coach the linear probe on the mannequin’s activations at each transfer. To foretell “my piece / their piece”, it’s a must to practice the linear probe on the mannequin’s activations at each white XOR black transfer.

See Also

In Othello-GPT, the mannequin had a vocabulary of 60 tokens, comparable to the 60 authorized squares the place a chunk could possibly be positioned. So, Neel Nanda simply probed at each even character for a white “my piece / their piece” probe, and at each odd character for a black “my piece / their piece” probe. In my case, the enter to Chess-GPT was a string like “1.e4 e5 2.Nf3 …”.

So, I skilled the white “my piece / their piece” probe on the mannequin’s activations on the index of each “.” because it’s predicting the subsequent character. For instance, the probe can be skilled on “1.” and “1.e4 e5 2.” as inputs. For a black “my piece / their piece” probe, I skilled it on the index of each even “ “ character. I skilled a linear probe on the “white piece / black piece” goal, and it obtained a classification accuracy of 86%.

Neel Nanda excluded the primary 5 and final 5 strikes of the sport when coaching his probes. I discovered that my linear probes accuracy didn’t change when skilled on all strikes or all however the first 5 strikes.

The LLMs had been character stage fashions relatively than utilizing byte-pair encoding and tokenization. From manually inspecting gpt-3.5 tokenization, it appears to be like like a regular tokenizer has barely over 1 character per token for a PGN string, excluding areas. As my mannequin had a vocabulary of simply 32 tokens, I used to be capable of scale back my mannequin measurement by 25 million parameters in comparison with utilizing a regular tokenizer with a vocabulary of fifty,257 tokens. Throughout coaching, I ensured that each batch started with “;1.”, a delimiter token adopted by a brand new sport. I did strive coaching a mannequin by randomly sampling blocks that often started in the midst of a sport, though its 1024 context size meant that it often additionally obtained the start of a sport in a while. The mannequin nonetheless discovered to play chess. I might be curious what kind of heuristics that mannequin discovered to deduce the board state when receiving an enter that begins in the midst of a chess sport.

All code, fashions, and datasets are open supply.
To coach, check, or visualize linear probes on the LLMs, please go to: https://github.com/adamkarvonen/chess_llm_interpretability

To play the nanoGPT mannequin in opposition to Stockfish, please go to: https://github.com/adamkarvonen/chess_gpt_eval/tree/local_llama

To coach a Chess-GPT from scratch, please go to: https://github.com/adamkarvonen/nanoGPT

All pretrained fashions can be found right here: https://huggingface.co/adamkarvonen/chess_llms

All datasets can be found right here: https://huggingface.co/datasets/adamkarvonen/chess_games

Wandb coaching loss curves and mannequin configs will be seen right here: https://api.wandb.ai/links/adam-karvonen/u783xspb

Mannequin Title Probe Layer Goal ELO Classification Accuracy Board State Classification Accuracy Authorized Transfer Charge
Randomly Initialized 8 layer mannequin 5 65.8% 70.8% 0%
Randomly Initialized 16 layer mannequin 12 66.5% 70.6% 0%
8 Layer Mannequin skilled on Lichess Video games 7 88.0% 98.0% 99.6%
16 Layer Mannequin skilled on Lichess Video games 12 89.2% 98.6% 99.8%
16 Layer Mannequin skilled on Stockfish Video games 12 N/A 99.2% 99.7%

There are some caveats for the next graph: Sadly, I by chance deleted a part of the logs for the 16 layer Stockfish mannequin, however I imagine it was skilled on round 120 billion enter characters. All different fashions had been skilled for a complete of 60 billion enter characters. The fashions had been skilled for a number of epochs – the datasets ranged in measurement from 4 – 7 billion characters. The labels stand for the dataset from hugging face that the mannequin was skilled on in addition to the variety of layers within the mannequin. On this graph, for 1 sport a win counts as 1 level, a draw as 0.5, and a loss as 0. We lose some info in comparison with a stacked bar chart, however I felt it could be too crowded.

A line chart comparing various LLM's win rates against Stockfish

A bar chart of accuracy per layer for ELO

A bar chart of accuracy per layer for board state classification



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