May 2026· arXiv.org· Vol abs/2605.31163· 0 citations· 45 references
MathematicsComputer Science
TL;DR
Distilling Bayesian Layers into a pretrained 340M Gated DeltaNet improves RULER long-context retrieval over a matched-compute control, and improves robustness beyond the training regime in controlled collision studies, learned associative recall, and the Zoology MQAR benchmark.
Abstract
We introduce the \emph{design-model framework}: a way to derive efficient recurrent sequence maps from explicit assumptions about memory. A design model writes evidence into memory by exact Bayesian filtering; a query- dependent readout produces a predictive distribution whose mean is the layer output. In our linear-Gaussian instantiation, the \emph{Bayesian Layer} propagates both a mean and a covariance: the covariance tracks uncertainty over stored associations, steering writes toward uncertain directions, attenuating gains as evidence accumulates, and preserving confident memories. The same framework unifies several sub-quadratic recurrences: linear attention, GLA, and Mamba-2/SSD are exact filters under a latent-input design model, whereas DeltaNet and related Delta-rule models are covariance-reset reductions of the Bayesian Layer's design model. Restoring covariance propagation yields closed-form predictions for retrieval dynamics, which we verify empirically, and improves robustness beyond the training regime in controlled collision studies, learned associative recall, and the Zoology MQAR benchmark. Training from scratch on WikiText-103 under matched state budgets lowers perplexity on associative-recall hits. Distilling Bayesian Layers into a pretrained 340M Gated DeltaNet improves RULER long-context retrieval over a matched-compute control, at a 2.5--2.7\% held-out perplexity cost.
It is proposed that a model's uncertainty about a token is reflected not only in the breadth of its output distribution but also in whether a confident prediction is \emph{fragile} under perturbation of its attention pathways, a training-free estimator that masks attention heads and measures the BALD mutual information among the resulting subnetworks.
Minsoo Kim, Sungyoung Ji, Kisung Moon et al.· 0 citations
World models built on the RSSM architecture, such as DreamerV3, keep a recurrent hidden state $h_t$ trained only to reduce prediction error. We show this state also tracks its own confusion, hiding in plain sight: nearly orthogonal to $h_t$'s directions of greatest variance, invisible to any variance-based method. It is functionally distinct from ensemble disagreement, which flags new inputs, and reconstruction error, which flags bad predictions right now. On a test holding prediction error fixed while confusion varies, a linear probe on $h_t$ finds the signal (AUROC 0.72, 5 runs), while an ensemble baseline scores below chance. A discounted count of recent high-error steps explains 80% of the probe's output ($R^2=0.80$). We confirm the signal is causally used, not merely present, by editing $h_t$ directly and watching behaviour change, including a check using real values from other trajectories instead of synthetic edits. Its geometry and closed form generalize across three control tasks; the decisive dissociation test itself holds cleanly on only one, and its practical use, deciding when to check reality instead of trusting imagination, generalizes to only two of the three tasks.
In artificial and biological neural networks, concepts are often encoded as consistent linear directions in representation space. In deep learning, this idea is known as the linear representation hypothesis and underpins many interpretability and control methods based on linear probes, from concept detection to activation steering. Yet while prior work has studied whether such directions should exist $\textit{after}$ training, the dynamics of how they emerge $\textit{during}$ training remain poorly understood. Here, we develop a framework to study the alignment of concept directions during training - a process we call"abstraction". In a minimal linear network setting, we obtain exact solutions for the full trajectory of abstraction. These solutions reveal key analytic principles governing abstraction: (i) data and target geometry jointly determine abstraction at the end-of-learning, (ii) abstraction improves with network depth, and (iii) initialization scale controls the maximum abstraction reached during training. Extending our theory to nonlinear networks, we analyze how the choice of nonlinearity affects abstraction dynamics: erf networks approximate the linear theory, while abstraction in ReLU networks depends less on target geometry and more on input geometry. Across both, we prove a striking attenuation law: both nonlinearities weaken abstraction in activations relative to preactivations. We find evidence for this law in open models (DINOv3, Gemma 4) and apply our theory to improve linear probe generalization in LLMs. Together, our results provide a dynamical theory of abstraction with implications for interpretability and control.
William Yang, Andrew M. Saxe, Peter E. Latham· 0 citations
Large language model (LLM) agents increasingly operate over long interaction histories, where effective reasoning requires identifying and exploiting task-relevant evidence distributed across past observations and actions. However, useful information encoded in previously computed representations is often underutilized during subsequent generation. We propose \textbf{TransMem}, a lightweight inference-time parametric memory module that transforms sparse historical hidden states from a frozen LLM backbone into reusable memory representations. TransMem uses a lightweight gating network to dynamically apply the latent intervention to the current hidden states, without repeatedly encoding the preceding context. To learn transferable memory utilization rather than task-specific knowledge, we introduce evidence-conditioned self-distillation. A memory-augmented student processes the full context and matches the predictive distribution of an evidence-only teacher that shares the same frozen backbone. Experiments on LoCoMo, HotpotQA, and MemoryAgentBench demonstrate consistent improvements across different model architectures and scales. TransMem yields gains of 11.58--29.25 $F_1$ on LoCoMo and 10.20--13.03 $F_1$ on HotpotQA, while improving the average MemoryAgentBench accuracy from 29.54\% to 40.00\%. These results establish sparse historical hidden states as an effective and efficient memory substrate for long-context LLM agents. Our code is available at https://github.com/Haodong-Lei-Ray/TransMem.
Haodong Lei, Junming Liu, Yirong Chen et al.· 0 citations
This framework separates temporal alignment, plasticity, forgetting, and bounded rehearsal in recurrent sequence models, together with numerically stable positive-decay renormalization, to remain competitive in language modeling and improve length extrapolation on variable-digit addition.
Yi-Fan Zhang, Steve Ta, Jasper Zhang et al.· 0 citations
Stochastic-process models are, as a rule, far easier to simulate than to condition. Non-linear observations, non-Gaussian likelihoods, black-box information, and global constraints all induce intractable conditional laws, requiring bespoke, model-specific constructions. We introduce LatentFlow, a single framework for conditioning stochastic processes, with no learned neural approximations and no training. Our starting point is to write the stochastic process as the deterministic image of a tractable latent innovation, $f_0 = T_{\vartheta}(\xi_0)$, with $\xi_0$ sampled from a simple reference distribution. This reduces process-level conditioning to latent-space inference: pull the likelihood back through $T_{\vartheta}$, sample the resulting latent law with a tractable guided probability flow, and push the samples forward. This construction is provably exact at the level of the target law; in practice, approximation enters only through finite terminal noising, Monte Carlo guidance, and time discretisation of the continuous-time dynamics, each of which is explicit and systematically reducible. As LatentFlow is training-free, conditioning reduces to solving a single reverse-time SDE. This enables conditional sampling in seconds on a single desktop CPU across model classes that have never shared a scalable method: classical spatial priors, nonlinear stochastic dynamics, mechanistic models from the physical and life sciences, stochastic PDEs, heavy-tails and extremes, point and discrete-state processes, and neural or simulator-defined processes.
Louis Sharrock, L. Astfalck, Henry Moss· 0 citations
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
MIT News · Artificial Intelligence· news.mit.eduAug 24, 2026
