POTM 2026-02 initialization (#12)

* POTM 2026-02 initialization

* potm riemannian-mean-flow (#15)

* potm riemannian-mean-flow

* rebasing off of potm-2026-02

* editor tweaks

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Co-authored-by: Michael Pearce <michaelp@graphcore.ai>

* potm-2026-02-latmix (#13)

* Template

* Add Latmix review

* Factored Latent Action Models summary (#14)

* Factored Latent Action Models summary

* action world models typo

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Co-authored-by: Michael Pearce <michaelp@graphcore.ai>

* deep-thinking-ratio potm (#16)

* deep-thinking-ratio potm

* editor tweaks

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Co-authored-by: Michael Pearce <michaelp@graphcore.ai>

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Co-authored-by: benoitgaujac <benoit.gaujac@gmail.com>
Co-authored-by: Douglas Orr <douglaso@graphcore.ai>
Co-authored-by: Tom Cashman <tomca@graphcore.ai>
Co-authored-by: hudlass <lukehudlass@gmail.com>

Author: 5 people

pages/posts/potm/2026/02/deep-thinking-tokens/deep-thinking-tokens.md

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+---
+paper_title: "Think Deep, Not Just Long: Measuring LLM Reasoning Effort via Deep-Thinking Tokens"
+paper_authors: "Wei-Lin Chen, et al."
+paper_orgs: "University of Virginia, Google"
+paper_link: "https://arxiv.org/abs/2602.13517"
+tags:  # see https://graphcore-research.github.io/tags/
+- reasoning
+- long-context
+- transformers
+- llms
+potm_order: 1  # editor to decide
+review_authors:
+- lukehg
+---
+
+### The key idea
+
+Reasoning models have demonstrated improved task performance when compared to their non-reasoning counterparts. This is largely attributed to reasoning models breaking down problems and working through them step-by-step, a by-product of which is an increased sequence length. Yet, it is not always clear that a longer sequence length correlates with better task performance. This work examines the presence of _deep-thinking tokens_ (tokens in which internal predictions undergo large changes throughout model layers prior to convergence) within the reasoning trace and the proportion of the trace that consists of these deep-thinking tokens (the _deep-thinking ratio_). The authors find strong correlation between the deep-thinking ratio and task performance, and use this to propose a strategy for test-time scaling.
+
+![Comparing correlations between task performance and token count or deep-thinking ratio](./fig-1.png)
+<center><figcaption>Figure 1.  Comparison of correlations between accuracy and proxies for thinking effort. The plots illustrate the relationship between model performance and two inference-time measures of thinking effort on GPT-OSS-120B-medium across AIME 2024/2025, HMMT 2025, and GPQA-Diamond. (Left) Output token count exhibits a moderate negative correlation (average r = −0.544), suggesting that output length is an unreliable indicator of performance. (Right) In contrast, our proposed deepthinking ratio demonstrates a strong positive correlation with accuracy (average r = 0.828).</figcaption></center>
+
+### Background
+
+Over the last 18 months, numerous works have suggested that increasing the number of reasoning tokens increases task performance (including [DeepSeek-R1](https://arxiv.org/pdf/2501.12948), [OpenAI o1](https://arxiv.org/pdf/2412.16720), [Qwen3](https://arxiv.org/pdf/2505.09388), [Claude 3.7 Sonnet](https://assets.anthropic.com/m/785e231869ea8b3b/original/claude-3-7-sonnet-system-card.pdf), [Claude Opus 4 & Sonnet 4](https://www-cdn.anthropic.com/6d8a8055020700718b0c49369f60816ba2a7c285.pdf)). However, there is growing evidence indicating that raw token count is an unreliable indicator — the authors of this work propose a new measure which is more correlated with model performance.
+
+### Their method
+The authors propose measuring the probability distribution over the vocabulary after each intermediate hidden state, rather than just the final state. For each layer $l=\{1, \cdots L-1\}$ and generation step $t$, the probability distribution $p_{t,l}$ is given by $\mathrm{softmax}(W_U h_{t, l})$ where $h_{t, l}$ is the layer's hidden state and $W_U \in \mathbb{R}^{|V| \times d}$ in the language modeling head to produce logits over the vocabulary. The final layer's probability distribution is given by $p_{t, L}$.
+
+The authors posit that tokens with distributions that stabilise in deeper layers corresponds to needing more extended internal thinking, wheras distributions that stabilise quickly do not benefit from additional thinking. They measure how long a token's distribution takes to stabilise by considering the Jensen-Shannon divergence (JSD) between $p_{t,l}$ and $p_{t, L}$:
+$$
+D_{t, l} := \mathrm{JSD}(p_{t,L} \parallel p_{t, l}) = H\bigg(\frac{p_{t,L} + p_{t,l}}{2}\bigg) - \frac{1}{2}\big(H(p_t, L) + H(p_t, l)\big)
+$$
+where $H(\cdot)$ denotes Shannon entropy.
+
+The depth in which the model has "settled" is defined as 
+
+$$
+c_t = \min\big\{l \in \{ 1, \cdots, L \} \,:\, \bar{D}_{t, l} \leq g \big\}
+$$
+
+where $\bar{D}_{t, l} = \displaystyle\min_{j\leq l}{D}_{t, j}$ defines what a layer has settled at and $g$ is a fixed threshold.
+
+If the settling depth is within later layers (determined by a _depth fraction_ $\rho$), it is considered to be a deep-thinking token. The proportion of these tokens across the overall generated sequence determines the deep-thinking ratio. The authors find that this metric correlates with task performance much more strongly than other metrics such as sequence length (see Table 1 below).
+
+
+![Correlations to task performance with different metrics](./fig-table-1.png)
+<center><figcaption>Table 1. Pearson correlations between task accuracy and different inference-time measures, including length-based and confidence-based baselines, across eight model variants and four reasoning benchmarks.</figcaption></center>
+
+
+### Results
+
+In order to make this observation useful in practice, the authors propose adopting this metric in best-of-$n$ settings, in which a subset of the $n$ responses are sampled and a majority voting is carried out over the sampled responses. By comparing different sampling strategies (including self-consistency over all responses, mean over all responses, sampling by longest sequences, sampling by shortest sequences, sampling by self-certainty, and finally sampling by their deep-thinking ratio, denoted as _think@$n$_), the authors find consistent improvement in task performance over numerous reasoning benchmarks.
+
+![Deep-thinking ratio is a better metric in best-of-n settings for sampling responses](./fig-table-2.png)
+<center><figcaption>Table 2. Comparison of task accuracy and average inference cost (k tokens) under different aggregation methods, across four reasoning benchmarks. The reported cost reductions (Δ%) are shown relative to Cons@n. Think@n achieves the best overall performance while reducing inference cost by approximately 50%. Methods with † adopt a prefix length of 50 to determine early stopping.</figcaption></center>
+
+
+### Takeaways
+
+This work uncovers a new metric for determining how well a model is reasoning. Given the expense associated with long-context lengths, there is great value to the community to find new ways of optimising reasoning traces, and so it will be interesting to see if the ideas explored in this work end up being adopted by those training reasoning models to yield more efficient generation.

pages/posts/potm/2026/02/deep-thinking-tokens/fig-1.png

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+---
+paper_title: "Factored Latent Action World Models"
+paper_authors: "Zizhao Wang, Chang Shi et al."
+paper_orgs: "University of Texas at Austin, Sony AI"
+paper_link: "https://arxiv.org/abs/2602.16229"
+tags:  # see https://graphcore-research.github.io/tags/
+- video-generation
+- reinforcement-learning
+potm_order: 1  # editor to decide
+review_authors: [ "tomca" ]  # "<alias>"
+---
+
+### The key idea
+
+This paper proposes Factored Latent Action Models (FLAM), a framework for learning controllable world models from action-free videos in environments that contain multiple entities acting independently.
+Instead of representing scene dynamics with a single latent action for the entire scene, FLAM factorizes the state into multiple entities and assigns each entity its own latent action.
+This reduces the complexity of modeling joint actions and improves prediction accuracy and representation quality.
+<!-- When applied with reinforcement learning, FLAM allows for improved policy learning in multi-entity environments. -->
+
+![A multi-entity scenario: a vanilla Latent Action Model encodes the scene change with a single latent action. FLAM decomposes the state into K factors, each with its own latent action.](./fig1.png)
+
+### Background
+
+World models aim to learn environment dynamics so that an agent can predict future observations and plan actions. 
+Recently, latent action models such as [Genie](https://arxiv.org/abs/2402.15391) have allowed world models to be trained from videos without action labels. These models:
+
+* Use an inverse dynamics model to infer a latent action explaining the transition between two frames;
+* Use a forward dynamics model to predict the next frame, given the current frame and an inferred latent action.
+
+This allows controllable dynamics to be learnt from datasets without ground truth action labels, such as unlabelled Internet videos.
+However, prior approaches encode _all_ changes in the scene into a _single_ latent action, which becomes difficult when multiple entities act simultaneously, as the latent action has to represent all combinations of actions. This causes the complexity of the action space to grow exponentially with the number of entities.
+
+### Their method
+
+FLAM addresses this limitation by factorizing the state and action representations. The method is trained in two stages.
+
+![Two training stages of FLAM. (a) A VQ-VAE is pretrained to extract features for latent action model learning. (b) FLAM infers latent actions and makes predictions for each factor independently, with all modules trained jointly to minimze the prediction error.](./fig3.png)
+
+#### 1. Feature extraction
+
+A VQ-VAE encoder converts each video frame into discrete latent features to provide a compact representation for efficient learning. The VQ-VAE is frozen for the next stage.
+
+#### 2. Factorized latent action learning
+
+The scene is decomposed into $K$ slots (factors) using [slot attention](https://arxiv.org/abs/2006.15055), where causal temporal attention encourages slots to bind consistently to the same object. For each slot:
+
+* An inverse dynamics model infers a latent action that explains the change between the current and next slot state. The predicted action is regularized by sampling from a normal distribution, with KL divergence penalizing deviation of the distribution from a unit normal prior.
+* A forward dynamics model predicts the next state of each slot using all the current slot states and the inferred action.
+
+Both dynamics models are implemented using the spatiotemporal attention described in [Genie](https://arxiv.org/abs/2402.15391), with spatial attention to all slots in the current timestep. Finally, predicted slot states are aggregated and can be decoded using the VQ-VAE back into the next video frame.
+
+FLAM is trained end-to-end with
+
+* Prediction loss between predicted and true frame features;
+* KL regularization on latent actions, to prevent trivial copying of the next state.
+
+Unlike prior methods, FLAM learns representation and dynamics simultaneously, encouraging slots to correspond to entities defined by independent actions rather than by visual similarity.
+
+### Results
+
+The results show:
+
+* Improved prediction accuracy: FLAM achieves the best results across metrics such as PSNR, SSIM, LPIPS, and FVD compared to prior latent action models and object-centric baselines.
+* Successful entity factorization: The learned factors correspond closely to individual agents or correlated groups of agents.
+* Robust scaling: Accuracy is stable as the number of slots increases beyond the number of independent entities, and also with an increasing number of entities in the scene.
+* Improved policy learning: Latent actions inferred from video can generate pseudo action labels, to enable sample-efficient behavior cloning.