The Inference Report

Tokenisation is an integral part of the current NLP pipeline. Current tokenisation algorithms such as BPE and Unigram are greedy algorithms -- they make locally optimal decisions without considering the resulting vocabulary as a whole. We instead formulate tokeniser construction as a linear program and solve it using convex optimisation tools, yielding a new algorithm we call ConvexTok. We find ConvexTok consistently improves intrinsic tokenisation metrics and the bits-per-byte (BpB) achieved by language models; it also improves downstream task performance, but less consistently. Furthermore, ConvexTok allows the user to certify how far their tokeniser is from optimal, with respect to a certain objective, via a lower bound, and we empirically find it to be within 1\% of optimal at common vocabulary sizes.

We propose the Integrable Context-Dependent Demand Network (ICDN), a demand-first neural model for multiproduct retail demand. The model learns log-demand as a smooth, context-conditioned function of log-prices, allowing elasticities to be derived exactly from the learned demand surface. On the Dominick's beer dataset, ICDN improves out-of-sample generalization over a directed log-log benchmark and yields more stable, economically plausible elasticity estimates, especially for weakly identified cross-price effects.

Language models must now generalize out of the box to novel environments and work inside inference-scaling search procedures, such as AlphaEvolve, that select rollouts with a variety of task-specific reward functions. Unfortunately, the standard paradigm of LLM post-training optimizes a pre-specified scalar reward, often leading current LLMs to produce low-entropy response distributions and thus to struggle at displaying the diversity that inference-time search will require. We propose Vector Policy Optimization (VPO), an RL algorithm that explicitly trains policies to anticipate diverse downstream reward functions and to produce diverse solutions. VPO exploits that rewards are often vector-valued in practice, like per-test-case correctness in code generation or, say, multiple different user personas or reward models. VPO is essentially a drop-in replacement for the GRPO advantage estimator, but it trains the LLM to output a set of solutions where individual solutions specialize to different trade-offs in the vector reward space. Across four tasks, VPO matches or beats the strongest scalar RL baselines on test-time search (e.g. pass@k and best@k), with the gap widening as the search budget grows. For evolutionary search, VPO models unlock problems that GRPO models cannot solve at all. As test-time search becomes more standardized, optimizing for diversity may need to become the default post-training objective.

Exploration is a prerequisite for learning useful behaviors in sparse-reward, long-horizon tasks, particularly within 3D environments. Curiosity-driven reinforcement learning addresses this via intrinsic rewards derived from the mismatch between the agent's predictive model of the world and reality. However, translating this intrinsic motivation to complex, photorealistic environments remains difficult, as agents can become trapped in local loops and receive fresh rewards for revisiting forgotten states. In this work, we demonstrate that this failure stems from a lack of spatial persistence and episodic context. We show that effective curiosity requires a model of the world that is persistent and continuously updated, paired with an agent that maintains an episodic trajectory history to navigate toward novel regions. We achieve this using an online 3D reconstruction as a persistent model of the world, while the agent policy is parameterized as a sequence model over RGB observations to maintain episodic context. This design enables effective exploration during training while allowing the agent to navigate using solely RGB frames at deployment. Trained purely via curiosity on HM3D, our agent outperforms RL-based active mapping baselines and generalizes zero-shot to Gibson and AI-generated worlds. Our end-to-end policy enables efficient adaptation to downstream tasks, such as apple picking and image-goal navigation, outperforming from-scratch baselines. Please see video results at https://recuriosity.github.io/.

Robustness, domain adaptation, photometric and occlusion invariance, compositional generalisation, temporal robustness, alignment safety, and classical anisotropic regularisation are usually treated as separate problems with separate method families. This paper argues that much of their shared structure is one statistical problem: estimate the covariance of label-preserving deployment nuisance, then regularise the encoder Jacobian along a matrix whose range covers that covariance (the matching principle). CORAL, adversarial training, IRM, augmentation, metric learning, Jacobian penalties, and alignment-style constraints are different estimators of that object, not independent robustness tricks. In the linear-Gaussian model we prove closed-form optimality (Theorem A), including cube-root water-filling within the matched range; necessity of range coverage for quadratic Jacobian penalties (Theorem G); the same range dichotomy at deep global minima; and two falsification controls (Lemma C; Corollaries E), with seven conditional consistency lemmas (D1-D7) for estimation under standard identifiability assumptions. We introduce the Trajectory Deviation Index (TDI), a label-free probe of embedding sensitivity when task accuracy or Jacobian Frobenius norm is insufficient. Thirteen pre-registered blocks from classical ML through Qwen2.5-7B test the predicted matched, then isotropic, then wrong-W ordering on geometry and deployment drift; twelve pass, and the sole exception (Office-31) is an eigengap failure named before the run. At 7B scale, matched style-PMH improves selective honesty and preserves Style TDI where standard DPO degrades it. The contribution is naming the deployment nuisance covariance, stating what the regulariser must do, and supplying a closed-form falsifiable theory once that object is identified, not universality on every leaderboard.

We propose and analyze a conservative drifting method for one-step generative modeling. The method replaces the original displacement-based drifting velocity by a kernel density estimator (KDE)-gradient velocity, namely the difference of the kernel-smoothed data score and the kernel-smoothed model score. This velocity is a gradient field, addressing the non-conservatism issue identified for general displacement-based drifting fields. We prove continuous-time finite-particle convergence bounds for the conservative method on $\R^d$: a joint-entropy identity yields bounds for the empirical Stein drift, the smoothed Fisher discrepancy of the KDE, and the squared center velocity. The main finite-particle correction is a reciprocal-KDE self-interaction term, and we give deterministic and high-probability local-occupancy conditions under which this term is controlled. We keep the quadrature constants explicit and track their possible bandwidth dependence: the root residual-velocity rate $N^{-1/(d+4)}$ holds under an additional $h$-uniform quadrature regularity condition, while a more general growth condition yields the optimized root rate $N^{-(2-β)/(2(d+4-β))}$, where $0\le β<2$. We also analyze the non-conservative drifting method with Laplace kernel, corresponding to the original displacement-based velocity proposed in~\cite{deng2026drifting}. For this method, a sharp companion kernel decomposes the velocity into a positive scalar preconditioning of a sharp-score mismatch plus a Laplace scale-mismatch residual, producing an analogous finite-particle rate with an unavoidable residual term. Finally, we explain how the continuous-time residual-velocity bounds translate into one-step generation guarantees through the explicit drift size $η$.