Science & Mathematics

Many modern language models have adopted hybrid architectures that incorporate both linear-time recurrence and softmax attention. Modern recurrence layers provide a highly expressive mixing mechanism while ensuring high throughput by compressing contextual information into a fixed-size state, but underperform softmax attention in contextual information retrieval. In this paper, we reveal a Competing Learning phenomenon where different kinds of mixers compete to learn the same function, and when any layer learns a function, it suppresses the corresponding learning signal for other layers. Layer attribution analysis reveals that under typical data distributions, modern recurrence learns retrieval functions faster than softmax attention, causing attention to fail to learn retrieval in most cases. Stopping weight updates in recurrence in the middle of training helps attention learn retrieval. Based on these results, we propose a staged training procedure for pre-training hybrid architectures on natural language. Empirical results on models up to 1B parameters show that our method results in substantial improvement in language modeling loss, common-sense reasoning, as well as a wide range of retrieval-related tasks across different context lengths.

Large-scale search and recommendation systems derive much of their retrieval quality from rich, heterogeneous features, yet existing generative retrieval (GR) methods struggle to exploit such feature ecosystems efficiently. Static feature injection either encodes all available signals or places them according to predetermined schemes, increasing serving cost and introducing irrelevant or conflicting evidence. More fundamentally, existing methods cannot adaptively determine when a feature is needed, which feature to select, or where it should influence hierarchical Semantic ID (SID) generation. We propose Agentic Generative Retrieval (AGR), a tool-augmented paradigm that interleaves SID generation with on-demand feature acquisition. Conditioned on the request and decoded SID prefix, AGR decides whether to invoke a tool, which feature to acquire, and where its observation should influence subsequent decoding, thereby steering generation toward feature-consistent SID branches. To supervise this behavior, we construct tool-augmented trajectories based on feature applicability and information gain along the SID hierarchy, and train the model through SID pretraining followed by tool-augmented fine-tuning. Experiments on an industrial dataset and three public benchmarks, together with an online A/B test, consistently demonstrate the effectiveness of AGR.

Sontag conjectured in 1988 that global controllability of polynomial control systems with rational coefficients is undecidable, but that the controllable systems form a recursively enumerable set. We prove the first part of the conjecture and disprove the second. For every homogeneous polynomial vector field $F$ of odd degree with rational coefficients, we construct an explicit polynomial control system $Σ_F$, with one more state than $F$, that is globally controllable if and only if the origin is \emph{not} globally asymptotically stable for $\dot x=F(x)$. By a recent result, the homogeneous polynomial vector fields with a globally asymptotically stable origin form a set that is recursively enumerable but not decidable. Consequently, global controllability of polynomial systems is undecidable, and the controllable polynomial systems are not recursively enumerable. The same conclusions hold for systems of the form $\dotξ=f(ξ)+Bu$ with a polynomial drift and a constant input matrix.

Machine learning is widely regarded as a promising application in which quantum computing could offer a computational advantage. However, general quantum machine learning models with provable guarantees on performance, trainability, and efficient inference remain limited. In this work, we introduce quantum Hamiltonian embeddings, a supervised learning framework in which a classical training dataset is encoded into a single effective, parameterized Hamiltonian. Training optimizes the parameters of this data-dependent Hamiltonian, whose approximate ground state defines the classification rule. Once the ground state has been approximated using a quantum algorithm, inference can be performed either classically using a classical representation of the learned state, or with a quantum representation of the state. We establish efficient methods for gradient estimation and prove favorable generalization guarantees. Furthermore, under standard cryptographic assumptions, we show that Hamiltonian embeddings can realize hypothesis functions beyond the reach of efficient classical algorithms. We then demonstrate the framework at scale on IBM Heron processors using a standard benchmark dataset. Together, these results establish Hamiltonian embeddings as a new framework for quantum machine learning, combining theoretical guarantees with a path for experimental investigations at scale on quantum hardware.

We propose KronLSTM, a linear attention architecture based on the Kronecker Delta Rule, a novel update rule for associative matrix memories. KronLSTM extends the xLSTM family with a memory-revision mechanism that corrects targeted associations while modifying the memory only along a single direction in matrix space. This minimally invasive memory revision reduces interference with previously stored information compared with delta-rule updates, making it particularly well suited for long-context language modeling. The resulting memory dynamics can be mathematically described as a Markov chain that converges to a steady-state distribution, while the expected norm of the memory matrix remains uniformly bounded throughout the entire input sequence. Hence, KronLSTM ensures stable memory dynamics without requiring additional normalization and stabilization mechanisms for the memory state. Experiments show that KronLSTM is competitive with, and often outperforms, existing linear attention architectures, including models of the (Gated) DeltaNet family, with particularly strong performance on long context benchmarks. These results establish the Kronecker Delta Rule as an effective and analytically tractable foundation for stable associative memory in recurrent linear attention architectures. Our code (https://github.com/NX-AI/KronLSTM) and models (https://huggingface.co/collections/NX-AI/kronlstm) are open-source.

LLM agents that compute the right answer can still answer wrongly. Agent harnesses increasingly keep long tool outputs out of the context window, saving them to files that the agent searches or reads on demand. We ask where this costs accuracy with a real scientific tool: PHREEQC, a widely used geochemistry simulator from the USGS, whose reports reach 846.8k characters and whose determinism lets every printed value be traced. Agents use it to answer 158 execution-verified multiple-choice items. When agents read the simulator's report through a section index rather than in context, GPT-5.1 and GPT-5.2 lose 11.3 and 7.9 points of accuracy, while Claude Opus 4.6 and Claude Sonnet 4.6 show no detectable cost. Re-running all 11,007 logged simulator calls shows that both GPT models compute the keyed value about as often as before; what changes is the evidence they answer from. Under retrieval they often skip the report, answer from their own higher-precision output files, and misround to a neighboring option, a failure we call evidence substitution. With the simulation held fixed, retrieval still costs GPT-5.2 9.4 points. For GPT-5.4, more frequent correct simulations mask an evidence-use loss of about ten points, leaving a net change indistinguishable from zero. Naming the authoritative output raises accuracy by 6.3-7.9 points over plain retrieval for the three GPT models; for GPT-5.1 and GPT-5.2, inlining outputs that fit works as well, while asking for correct rounding does not. Context-management choices in agent harnesses should be judged by where accuracy is lost, not only by final accuracy.

Diffusion Transformers (DiTs) achieve high-fidelity image and video generation, but they suffer from substantial inference costs due to repeated transformer evaluations across many denoising steps. Feature caching reduces this cost by reusing features across denoising steps. Recent forecasting methods extend this idea by extrapolating features to skipped steps instead of reusing them. However, existing forecasting methods extrapolate the features they predict uniformly, even though the spatial-frequency components of these features change most at different stages of denoising. They also overlook that denoising progresses nonuniformly, so equal step intervals can correspond to very different amounts of change. These mismatches amplify forecast errors as more steps are skipped, limiting the achievable acceleration. We propose SpecKCast, a training-free method that forecasts the model output in the frequency domain. SpecKCast applies a 2D discrete cosine transform (DCT) to the output and tracks each coefficient with a lightweight Kalman filter along a band-specific time coordinate derived from the noise schedule. The filter tracks each coefficient's value and rate of change, and the transformer is evaluated only when the filter's forecast uncertainty exceeds a threshold. Experiments on FLUX.1-dev, Qwen-Image, Wan2.1-14B, and HunyuanVideo show that SpecKCast achieves a better trade-off between acceleration and fidelity than existing caching and forecasting methods, reaching up to 6x speedup with less than 0.05 GiB of additional memory.

EHR foundation models promise scalable clinical prediction across health systems, yet their deployment is constrained by a tokenization bottleneck. The same clinical concept can appear as different ontology codes, local identifiers, synonyms, or free-text descriptions, which standard EHR tokenizers treat as unrelated symbols. A model trained on MIMIC-III with a closed-vocabulary tokenizer can use only 13% of eICU events. We introduce MEDIATOR, a discrete ontology-agnostic tokenizer that maps any clinical concept expressed as text into a shared vector-quantized codebook, turning EHR harmonization into open-vocabulary tokenization without manual mappings or a fixed vocabulary. Trained with synonym supervision and guided by enriched concept descriptions, code co-occurrence, and relation graphs, MEDIATOR collapses equivalent expressions while organizing distinct concepts in a medically meaningful discrete space. Used as the token interface of an EHR Transformer, MEDIATOR improves mean AUPRC over the strongest prior tokenizer by 4.0 points (8% relative) on 20 MIMIC-III tasks and by 8.6 points (29% relative) in zero-shot transfer to 14 eICU tasks, where it uses all events. The transfer gain combines coverage and representation, as MEDIATOR remains the best tokenizer under identical inputs (+1.0 and +1.9 points on operational and subcohort-mortality tasks). Same-encoder controls show that the text encoder drives in-domain accuracy, while the learned objectives of MEDIATOR drive transfer robustness and entity-linking quality. MEDIATOR also enables transferable attribution across hospitals.

Bilevel optimization provides a framework for machine learning tasks such as hyperparameter optimization, data reweighting, and meta-learning. Existing Newton-based bilevel methods typically rely on the classical hypergradient formula, which is generally unavailable when lower-level solutions are nonunique and the lower-level Hessian is singular. We develop two Newton-based methods beyond lower-level strong convexity by exploiting curvature shared by the lower-level and multiplier updates. Newton-based GALET handles potentially singular lower-level curvature under a positive spectral-gap condition, exploiting its range structure to avoid the squared-Hessian multiplier system used in GALET. Newton-based BAMM uses a strongly convex aggregation model when the lower-level objective is convex and the upper-level objective is strongly convex in the lower-level variable. We establish convergence guarantees and improved complexity bounds relative to GALET and sl-BAMM under the corresponding assumptions. We further introduce GNBO, a generalized Newton-based framework that captures the shared-curvature structure of the proposed methods and several existing Newton and quasi-Newton bilevel methods. Experiments on synthetic problems, data hyper-cleaning, and GPT-2 data reweighting evaluate the proposed methods across different bilevel learning tasks.

Systems that combine several large language models (LLMs) often use one context for many questions. When the context is passed between models as text, the receiving model processes all of its tokens again for every question. Avoiding this cost requires a context representation that is compact, reusable across questions, and readable by a different LLM. Existing compression and latent communication methods each provide only some of these properties. We introduce LatComm, a Latent Communication interface that provides all three by separating encoding from reading: the context is encoded once without the question, and the receiver selects what to read for each question. A frozen context encoder LLM compresses the context into a fixed-size packet and sends it to a different frozen receiver LLM, which reads the packet through cross-attention, with gates computed from its prompt. On 12 multiple-choice question-answering datasets, LatComm improves average accuracy over single-vector baselines by up to 10.2 points. On QuALITY, it reduces the receiver's input by 57x and answers the questions of an article 3x faster.

Phase modulated continuous wave (PMCW) radar is an attractive choice for automotive sensing due to its high dynamic range, interference robustness, and support for integrated communication and sensing. In multiple-input multiple-output (MIMO) PMCW radar, code division multiplexing (CDM) separates transmit signals, but non-ideal auto- and cross-correlation properties increase range sidelobes and degrade dynamic range. This paper proposes a Doppler-compensated space-time coding (STC)-based MIMO PMCW radar framework that separates transmit signals before range correlation, eliminating cross-correlation terms under perfect compensation and allowing the same binary sequence to be used across transmit antennas. The Doppler influence on STC decoding is analytically characterized, showing that chip-wise and inter-STC-slot phase distortions increase range sidelobes and generate ghost components in the direction-of-arrival (DOA) spectrum. To mitigate these effects, Doppler is estimated first, followed by joint fast-time and STC-slot compensation before decoding. Residual STC leakage under imperfect Doppler estimation is quantified, and the processing is extended to multiple moving targets through Doppler-bin-dependent compensation. Theoretical analysis and simulation results demonstrate reduced range sidelobes and suppression of DOA ghosts, while maintaining flexibility in code sequence design.

The goal of a world model is to capture the dynamics of an environment. This has the great appeal that it allows agents to plan and simulate a course of actions with the help of a world model. For these uses to be reliable, however, the learned dynamics must behave well beyond the specific state-action combinations observed in expert rollouts. Despite this, the relationship between data coverage, dynamics generalization, and downstream planning performance remains underexplored. We study this relationship through the lens of compositional generalization: can a world model recombine familiar state and action factors into valid dynamics? To answer this, we introduce AnyGoal, a benchmark of goal-shifted task variants built from widely used world-model environments, together with an open-source library. Each task is designed to be within reach of a world model that has learned the underlying dynamics: individual state factors and actions remain within their training support, but their combinations are underrepresented in expert trajectories. Across multiple environments and world model families, we find that current models consistently exhibit failures under these recombinations. By examining dynamics and representation failures across model families, interaction regimes, and evaluation metrics, we study where current world models generalize and where challenges remain for goal-shifted prediction and planning. Together, this framework, benchmark, and analysis provide a basis for evaluating progress toward world models that generalize to new planning tasks.

A seemingly reasonable push in Sokoban can make the puzzle unsolvable. To avoid such mistakes, an agent has to anticipate the consequences of its actions before execution, especially when feedback from the real environment is sparse or actions are irreversible. We introduce Agentic Imagination (Agima), a training framework that trains an agent to imagine before acting, i.e. to be imaginative. Agima trains a single omni model to propose actions, generate images of their outcomes, and then reason over these imagined futures to decide what to execute in the real environment. Rather than committing to a single plan, the agent can simulate a sequence of actions, explore alternatives, and compare possible futures. We first use supervised fine-tuning (SFT) to unify policy and world modeling within a single omni model. This enables the agent to predict future outcomes and perform basic forms of imagination, such as forward thinking and counterfactual branching. We then use agentic reinforcement learning (RL) to teach the agent to reason with its imagined futures and use them effectively for planning. Across four environments spanning Maze2D, Sokoban, Pacman, and PushT, Agima generalizes to harder settings unseen during training. Trained with SFT alone on two-box Sokoban, Agima solves 40% of four-box puzzles while seeing the real board only once every five moves, compared with an action-only planner that only solves 2%. After RL, new behaviors emerge in how Agima uses its imagination: it learns a new unified format that was unseen during the SFT stage, learns to conduct forward thinking only when necessary, and branches more frequently at critical decision points. An agent that can picture where its actions lead can learn when and where to look ahead, that is, to plan. Project page: https://agima.net/.

Recent advances in multimodal models have enabled GPT-6 Astra to perform robotic manipulation through in-context learning. Yet contact-rich control and tactile perception are often regarded as strengths of specialist policies, leaving open whether Astra can directly understand and use tactile observations. We provide, to our knowledge, the first demonstration that Astra directly interprets vision-based tactile images and uses their contact cues for manipulation. Tactile RGB images enter through its existing visual interface, enabling few-shot closed-loop control on nineteen simulated UniVTAC and OpenViTac tasks with 210 sampled scene seeds per setting. With visuo-tactile input, Astra achieves mean success rates of 93.8% and 81.8%, exceeding the strongest reported specialist baselines in our comparison by 22.9 and 13.1 percentage points, respectively. Vision-only performance also leads these baselines, reaching 76.3% and 80.6%. Trajectory analysis reveals active probing, cautious grasping, contact-guided alignment, and recovery, alongside difficulties with tangential loading and corrective execution. Our findings challenge the exclusivity of specialist policies in contact-rich manipulation and show that fine-grained vision can partially compensate for missing touch. They also identify vision-based tactile sensing as an interface for scaling contact understanding with foundation models and reveal signs of benchmark saturation. These results motivate joint visual-tactile pretraining, harder contact-rich evaluations, and physical-robot validation.

Long-horizon agents must learn heterogeneous capabilities from interleaved trajectories. Updating shared parameters to learn new capabilities can degrade previously acquired ones, resulting in catastrophic forgetting. As a trajectory unfolds, different stages may require different capabilities, yet conventional joint training and static adapter merging maintain a fixed parameter configuration throughout execution. We introduce WeAct (Weight-level Internal Actions), which trains independent capability-specific LoRA adapters over a frozen backbone and adds adapter selection to the agent's action space. These internal actions use the model's native tool-calling interface for on-demand capability composition in a shared context. Across eight deep-research benchmarks, Qwen3-32B with WeAct improves average accuracy by 6.2% relative to full fine-tuning counterparts despite using less compute, and by 27.5% relative to the strongest static LoRA-merging method. WeAct also supports modular continual adaptation, by adding a new code computation adapter to expand the agent's capabilities and updating the existing writing adapter to improve report quality. Both updates leave the backbone and other adapters unchanged, supporting modular continual adaptation in agents.