arXiv subjects

Leon Chlon

Publications and source records attributed to Leon Chlon.

11 recordsLinked to original sources

arXiv2026

Large Geometry Models Are Priors For Fast Physics Pretraining

Language and vision models became data-efficient by pretraining on plentiful unlabelled data; physical field models have such data, over ten million 3D shapes, but geometry pretraining designs its targets rather than deriving them from the physics. Euler-Lagrange geometry pretraining derives them: for attached flow, a shape enters the flow's Euler-Lagrange equation only through coefficients that distance and normal line (the normal up to sign) fix to first order. Their reconstruction error therefore bounds what a representation loses about any field, and fine-tuning on costly simulations need only assemble the global field. We realise it in AREALS, a masked surface autoencoder whose areal tokens carry position, normal and area, pretrained self-supervised and sign-free on 61,822 raw meshes. Because the operating condition enters only through the far field, sensors can supply it: AREALS completes a hidden field in one forward pass without condition labels. It matches the accuracy of the same architecture trained from scratch with half the simulations on DrivAerML and DrivAerNet++ and about a quarter on WindsorML. On DoubleDelta wings, 20 sensors give $3.9\times$ and $4.0\times$ lower field and force error than GABI, a Bayesian inversion method with a learned prior, and beyond the training angles pretraining halves the error.

cs.LG↗

arXiv2026

Symmetry Breaking Is the Price of Finite Capacity

If rotating a problem never changes its answer, one might expect its best model to be rotation-invariant; we show that this fails, predictably and by an exact amount, when capacity is limited. A symmetry groups a model's directions into blocks of equally strong directions, a symmetric model must use each block whole, and when the budget cuts a block every optimal model breaks the symmetry. For a Gaussian problem with a $k$-unit bilinear predictor, the log-loss price of symmetry is exactly $(U_k-I_k)/(2σ^2)$, the signal of the best $k$ directions minus that of the best whole blocks. Because an attention head compares tokens through a similarity of rank at most its head dimension, whatever computation precedes it, the same price governs heads fitted to a symmetric similarity by squared error, and heads trained this way on three-dimensional directions break symmetry at exactly the predicted head dimensions, with the predicted rotation sensitivity (RMSE 0.004). Under softmax attention, flatter attention restores the predicted symmetric head where tested, while with peaked attention broken heads beat every whole-shell symmetric head at 16 of 20 head dimensions. We give a procedure that separates capacity-driven breaking from other causes.

stat.ML↗

arXiv2026

When Thoughts Become Memory: Unifying In-Context Learning and Fine-Tuning

We are the first to give a certified rule for whether unseen data belong in a pretrained model's context or its weights, built on an exact law for their information value. That value, the code length saved on held-out queries, equals in expectation the bits stored about the query, plus a prior repair, minus a decoding loss, for any model, architecture, dataset and task. The law's ceilings certify the choice from one measurement, and an anytime-valid test makes it from held-out queries, with error controlled whenever it stops. Every certificate the ceilings issue on a trained transformer, TabPFN, an occupancy network and a stereo network is correct. The test picks TabPFN over XGBoost and a trained surrogate over an in-context learner on airfoil pressure, calls the better of GPT-2's cache and fine-tune in 61,948 of 64,000 query streams over 32 comparisons, and errs in at most 3.3% of null streams. The law also diagnoses when learning in context helps and when it does not. Deleting part of a context is held-out validation of that part in any model, and adding parts one at a time traces the learning curve in context: one patch that sees a shape feature cuts an occupancy network's code length there a hundredfold, while eight that miss it nearly double it, and one camera that sees the surface beats four in a stereo network. Ranked by this label-free valuation, a kriging learner's three best support cars beat four drawn at random, and on a yes-or-no claim the valuation recovers a published evidence adjudicator, with AUROC 0.91.

stat.ML↗

arXiv2026

Robot World Models Are Not Invariant to How the Actions Are Written

A robot policy is trained with one of two action parameterizations: absolute joint targets, or deltas relative to the current state. The choice is a live engineering decision in robot learning, and a world model conditioned on actions inherits it silently. We show the inheritance is catastrophic. A latent dynamics model trained on one parameterization and handed the identical commanded trajectory written in the other collapses: retrieval degrades by 2.6-13.4x across three robot datasets and two morphologies, goal-conditioned action selection falls from 53% to 15%, and on PushT the two beliefs about the same future are near-orthogonal (cos = 0.067, worst case -0.377), so the predictor does not degrade gracefully, it answers a different question. This is not a distribution-shift artifact in the usual sense: the two encodings are mutually reconstructible at R^2 = 0.996 given the joint input, so no information is lost, and we give the test that separates a valid re-parameterization from a lossy summary or a sensor swap. The test rejected three of the four axes we proposed. The defect lives in the action channel, which the invariance literature for visual models does not examine: work there concerns crops, jitter and camera pose, while the parameterization of the commands goes unaudited. The repair is averaging over the two encodings, and where it goes matters. Averaging the objective restores task performance by itself; averaging the outputs, safe for probabilities by concavity, is not available for direction-valued prediction, where the normalized mean can score below every member of the orbit. What objective-averaging leaves behind is the tail: worst-case agreement stays at 0.78, a disagreement penalty closes it to 0.995, and over a latent rollout it is the difference between a worst case that erodes and one that holds. On PushT, averaging alone does not repair the axis.

cs.RO↗

arXiv2026

Exact Finite Attention Responses From RoPE Derivatives

We derive exact local responses for attention interventions, allowing candidate edits to be scored from a cached baseline and one backward pass. The starting point is the RoPE derivative $\partial_p z(p) = A z(p)$: its integral gives the finite positional displacement, which we carry through the softmax without linearising either rotation or normalisation. The resulting predictions achieve 95.36--96.52% sign accuracy across 92,160 executed positional edits on 768 held-out prompt sets, reducing answer-margin MAE by 73.6--82.5% against the positional Jacobian and by 36.2--50.9% against zero. For simultaneous key and value edits, the same divided-difference calculus isolates the interaction term $C_{KV} = \sum_j (p'_j - p_j)\,\varepsilon_j$, which is omitted by adding separate attributions. Retaining it reduces downstream margin MAE by more than a factor of nine in every setting of a 5,120-intervention sweep across two Qwen sizes, two tasks, and multiple layers; reductions against a quadratic interaction correction are 75.9--98.5%. Exactness concerns the edited attention write; downstream predictions contract that response with a baseline gradient and are evaluated by native execution. The calculus also yields a KL certificate for local approximation error, an exact query-conditioned gradient-step representation whose curvature identifies attention-preserving query directions, and minimum-norm query control. Sparse evaluation supports candidate ranking and cache decisions under explicit local distortion criteria.

stat.ML↗

arXiv2026

RoPE attention is an exact forward-pass gradient step with softmax intact

We derive an exact gradient-step representation of the RoPE-softmax forward pass. For every deterministic RoPE-softmax attention head with arbitrary affine projection weights, we construct a query-dependent effective matrix $ΔM_i$ satisfying $y_i = μ_i + u_i^\top ΔM_i$, where $μ_i$ is the uniform mean of the attended values and $u_i$ is the augmented query input. The construction applies the classical exponential divided difference $ρ= ϕ_1$ to retain the softmax exactly. Its positive coefficients give a unit gradient-step representation on a query-conditioned quadratic objective. The same function connects the RoPE generator to exact positional finite differences. We derive a tokenwise formula for the error of reusing one query's matrix and prove that a nonconstant finite-cache head cannot admit a globally exact affine query readout. Reconstruction checks and frozen-reuse calibration on one pretrained Qwen2.5-0.5B layer verify the representation and quantify the correction required when one query's matrix is reused.

stat.ML↗

arXiv2026

LLMs are Bayesian, In Expectation, Not in Realization

Bayesian accounts of in-context learning face a direct objection: exact posterior predictives for exchangeable data are invariant to task-preserving order, yet transformers change next-token probabilities when the same examples are serialized differently. We show this objection targets a structural invariant rather than the quantity scoring online prediction. For any Bayesian reference, excess prequential code length is exactly cumulative predictive KL. For unordered support sets that must be serialized, the expected regret of a single admissible ordering decomposes into that of the order-averaged predictor plus an order-averaging gain. Exchangeability violations are therefore not binary refutations; they are priced by log loss. We instantiate the theory with KT/Dirichlet finite-alphabet prediction and coarsened Bayesian linear-regression (BLR) predictive distributions. On Qwen2.5-7B/14B, floored candidate distributions at support $256$ have one-step excess code lengths of $0.020/0.011$ bits for Bernoulli and $0.039/0.022$ bits for four-way categorical prediction, with candidate mass above $0.999$; coarsened BLR continuations increasingly match the posterior-predictive digit distribution as support grows. A frequentist plug-in baseline sharpens the reading: the predictive distributions sit closer to the Bayesian posterior predictive than to the maximum-likelihood plug-in, by a margin largest at small support, where the plug-in is degenerate, and vanishing as the references converge. Position interventions and a from-scratch ablation localize order sensitivity to the positional encoding, activation patching tests causal use of decoded sufficient statistics, and permutation mixtures quantify the downstream log-loss cost of arbitrary orderings. Transformers need not realize exchangeable posterior predictives for every serialization to be Bayes-competitive prequential predictors.

stat.ML↗

arXiv2026

Predictable Compression Failures: Order Sensitivity and Information Budgeting for Evidence-Grounded Binary Adjudication

Transformers used for evidence-grounded binary adjudication (e.g., support/refute, yes/no, or verifier-backed pass/fail decisions) can be sensitive to the order in which exchangeable evidence is presented, producing dispersion across permutations and unreliable attempted answers under a verifier-relative Bernoulli predicate. We treat evidence order as a nuisance variable and formalize an expectation-realization gap: next-token training can minimize expected conditional description length over orderings while a fixed ordering remains position-sensitive. Our Quantified Martingale Violation (QMV) bound predicts the dispersion induced by adjacent-rank positional sensitivity, with $O(\log n)$ growth in the harmonic regime; our Expectation-level Decompression Law (EDFL) specializes a KL convexity/data-processing bound to Bernoulli predicates, yielding Bits-to-Trust (B2T), Risk-of-Hallucination (RoH), and an Information Sufficiency Ratio (ISR) gate for answer/abstain decisions. On 3,059 grounded items from FEVER, HotpotQA, NQ-Open, PopQA, and Controls, we observe logarithmic dispersion and positive Jensen gains from uniform permutation mixtures. In one pre-specified held-out audit (528 items), the analytically fixed ISR$=1$ gate attains 0.0-0.7% hallucination with 20.6-27.9% abstention (95% CIs), supporting the operating point without claiming universal calibration across all model families or unrestricted generation.

stat.ML↗

arXiv2026

Attention Deficits in Language Models: Causal Explanations for Procedural Hallucinations

Large language models can follow complex procedures yet fail at a seemingly trivial final step: reporting a value they themselves computed moments earlier. We study this phenomenon as \emph{procedural hallucination}: failure to execute a verifiable, prompt-grounded specification even when the correct value is present in context. In long-context binding tasks with a known single-token candidate set, we find that many errors are readout-stage routing failures. Specifically, failures decompose into Stage~2A (gating) errors, where the model does not enter answer mode, and Stage~2B (binding) errors, where it enters answer mode but selects the wrong candidate (often due to recency bias). In the hard regime, Stage~2B accounts for most errors across model families in our tasks (Table~1). On Stage~2B error trials, a linear probe on the final-layer residual stream recovers the correct value far above chance (e.g., 74\% vs.\ 2\% on Qwen2.5-3B; Table~2), indicating that the answer is encoded but not used. We formalize ``present but not used'' via available vs.\ used mutual information and pseudo-prior interventions, yielding output-computable diagnostics and information-budget certificates. Finally, an oracle checkpointing intervention that restates the true binding near the query can nearly eliminate Stage~2B failures at long distance (e.g., Qwen2.5-3B $0/400 \rightarrow 399/400$ at $k = 1024$; Table~8).

stat.ML↗

arXiv2025

Robust Multimodal Learning via Entropy-Gated Contrastive Fusion

Real-world multimodal systems routinely face missing-input scenarios, and in reality, robots lose audio in a factory or a clinical record omits lab tests at inference time. Standard fusion layers either preserve robustness or calibration but never both. We introduce Adaptive Entropy-Gated Contrastive Fusion (AECF), a single light-weight layer that (i) adapts its entropy coefficient per instance, (ii) enforces monotone calibration across all modality subsets, and (iii) drives a curriculum mask directly from training-time entropy. On AV-MNIST and MS-COCO, AECF improves masked-input mAP by +18 pp at a 50% drop rate while reducing ECE by up to 200%, yet adds 1% run-time. All back-bones remain frozen, making AECF an easy drop-in layer for robust, calibrated multimodal inference.

stat.ML↗

arXiv2018

Multitaper Spectral Estimation HDP-HMMs for EEG Sleep Inference

Electroencephalographic (EEG) monitoring of neural activity is widely used for sleep disorder diagnostics and research. The standard of care is to manually classify 30-second epochs of EEG time-domain traces into 5 discrete sleep stages. Unfortunately, this scoring process is subjective and time-consuming, and the defined stages do not capture the heterogeneous landscape of healthy and clinical neural dynamics. This motivates the search for a data-driven and principled way to identify the number and composition of salient, reoccurring brain states present during sleep. To this end, we propose a Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM), combined with wide-sense stationary (WSS) time series spectral estimation to construct a generative model for personalized subject sleep states. In addition, we employ multitaper spectral estimation to further reduce the large variance of the spectral estimates inherent to finite-length EEG measurements. By applying our method to both simulated and human sleep data, we arrive at three main results: 1) a Bayesian nonparametric automated algorithm that recovers general temporal dynamics of sleep, 2) identification of subject-specific "microstates" within canonical sleep stages, and 3) discovery of stage-dependent sub-oscillations with shared spectral signatures across subjects.

stat.ML↗