Computer Science (arXiv)

Dense retrieval has become a cornerstone of modern local-lifestyle e-commerce search by encoding queries and items into semantic embedding spaces. While recent advancements have transitioned from BERT-based embedding models to Large Language Models (LLMs), most approaches still treat LLMs as static text encoders, neglecting their inherent reasoning capabilities. Furthermore, standard dense retrieval models remain query-centric, which is insufficient in e-commerce scenarios where sparse and ambiguous queries create an intent gap that can only be bridged by the rich context of user history. Meanwhile, existing personalized retrieval methods typically rely on implicit embedding interactions, which lack the reasoning capability to effectively disambiguate user intent from noisy historical behaviors. To address these challenges, we propose Think-to-Personalize (TTP), a novel framework that unifies explicit user-centric intent reasoning with dense retrieval. By reasoning over the user's historical purchase sequence, TTP explicitly deduces latent personalized needs and generates an intent-enhanced query, which is then encoded into a unified dense embedding. Specifically, we design a two-stage training paradigm: (1) a Supervised Fine-Tuning (SFT) stage that establishes cold-start capabilities; and (2) a Reinforcement Learning (RL) stage that aligns the reasoning process with retrieval utility using Group Relative Policy Optimization (GRPO). Extensive experiments on both proprietary and public benchmarks demonstrate that TTP significantly outperforms state-of-the-art baselines. Furthermore, in online A/B tests, it achieved a +0.46% lift in order volume, validating its practical effectiveness and establishing a new paradigm for reasoning-driven personalized dense retrieval.

For graphs of rank-width \(w\), the algorithms of Bui-Xuan, Telle, and Vatshelle (\emph{Theor. Comput. Sci.}, 2013) for fixed finite/cofinite \((σ,ρ)\)-problems and of Bergougnoux and Kanté (\emph{SIAM J. Discrete Math.}, 2021) for Connected Dominating Set run in \(2^{O(w^2)}n^{O(1)}\) time. Bergougnoux, Korhonen, and Nederlof (STACS 2023) proved a matching lower bound under the Exponential Time Hypothesis (ETH) for \emph{Weighted} Dominating Set, but left the unweighted problem open. We prove that, unless ETH fails, Dominating Set admits no \(2^{o(w^2)}n^{O(1)}\)-time algorithm, even on split graphs and, separately, on bipartite graphs of diameter at most four, and even with a rank-decomposition or witnessing vertex order supplied. The proof replaces the earlier weights by a two-guard gadget and uses a low-rank equality gadget to carry \(k^2\) assignment bits through cuts of rank \(O(k)\). The construction also gives the same lower bound for Independent, Connected, and Total Dominating Set on restricted graph classes and applies to a broad family of \((σ,ρ)\)-set problems. This family includes cases in which \(σ\) is neither finite nor cofinite and contains the entire nontrivial cofinite--cofinite minimization regime. Every solution within the target budget has target size and corresponds bijectively to a satisfying assignment. Under the counting Exponential Time Hypothesis (\(\#\mathrm{ETH}\)), the same bounds therefore hold for counting solutions of size at most or exactly the target. Together with the known algorithms, our results show that the quadratic dependence on the rank-width \(w\) is optimal up to constant factors in the exponent for the classical problems above and throughout the covered finite/cofinite regime.

Agent frameworks increasingly package procedural knowledge as skills: instruction files an agent reads on demand, while public libraries now hold thousands of them. Which skill to read has thus become a decision the policy itself makes in the middle of an episode, yet no existing signal trains it. We show that the default remedy, outcome-rewarded RL over the candidate slate, cannot teach it, for a structural reason we identify and name selector credit starvation: under a broadcast, sequence-level advantage, the few tokens that name the chosen skill carry a vanishing share of the loss, and the credit they inherit is increasingly wrong-signed as trajectories lengthen. A correct choice is punished whenever the execution after it fails, even though the choice itself is among the most valuable decisions in the trajectory. Auditing a completed run's own training artifacts confirms all three properties, each worsening monotonically with horizon. SkillGate removes the failure by construction: it partitions the token support into two disjoint credit channels, outcome credit reaching only execution tokens, and a separate action-local advantage reaching exactly the skill-naming tokens, positive only when a trajectory's single read is the correct one. On five agentic benchmarks under a 16-candidate slate, SkillGate lifts a 9B policy from 40.8% to 53.2% trial success, well ahead of the identical budget spent on outcome reward alone, while cutting exposure to misleading candidates by two thirds and reading fewer skills.

Convolution integrals widely exist in applications, and to enable fast and accurate computations, this paper introduces two general multi-stage neural operator learning frameworks. The first, Deep Collocation Neural Operator (DCNO), is a supervised approach that iteratively refines the operator approximation by learning residuals from input-output data pairs. The second, Deep Galerkin Neural Operator (DGNO), is an unsupervised framework applicable when the target operator can be represented by a PDE, leveraging the weak form of the PDE residual for training. Both methods progressively construct basis operators through multiple training stages to enrich the approximation space, leading to significantly improved accuracy over standard one-shot operator learning. We provide theoretical analysis for their approximation capabilities and implement them for learning convolutions. Extensive numerical experiments demonstrate that both DCNO and DGNO achieve high accuracy, approaching machine precision under single float for convolution problems, and offer substantial efficiency gains for numerous queries or parametric variations compared to traditional solvers. We also extend these frameworks to handle multi-input operator learning scenarios involving variations in both the density and kernel of a convolution.

Tabular foundation models (TFMs) achieve strong performance through in-context learning, but context-dependent inference imposes substantial latency and memory costs, hindering large-scale deployment. We propose GEAR (\emph{Generative Expansion and Real Anchoring}), a modular two-stage framework that distills TFMs into lightweight MLP or tree-based predictors that can be deployed on commodity CPUs. Stage 1 uses synthetic covariates solely as teacher-query locations and trains the student on soft TFM targets, expanding coverage beyond observed rows. Stage 2 re-anchors the student to the target distribution using real labels and out-of-fold teacher predictions, whitch avoids self-labeling leakage. We further derive a risk certificate characterizing the trade-off between generated-query volume and generator fidelity. Experiments on TALENT and TabArena demonstrate the broad applicability of GEAR. Two-stage MLPs outperform supervised MLPs by 1.81--2.00 AUC points on binary tasks and 1.19--1.35 points on multiclass tasks, with additional gains over real-data-only distillation of 1.76--2.19 and 2.09--2.40 points, respectively. On binary tasks, the gains also transfer to LightGBM and XGBoost, and all three student families outperform CatBoost, the strongest non-TFM baseline, in mean AUC. Ablations show gains beyond longer training or alternative warm starts, greater stability from staged than mixed optimization, and generator-dependent diminishing returns as query volume increases. Finally, GEAR reduces median inference time by 57--2866 times and peak prediction memory by 1.9--3.3 times, while retaining higher AUC than matched supervised baselines.

Last-mile delivery aims to handle dynamically arriving orders with couriers while modeling complex spatial and temporal correlations. Recent learning-based methods model spatiotemporal dependencies among orders to predict courier service sequences, but leave next-order decision making unexplained. Describing the current delivery state in language allows LLMs to reason explicitly about the spatial, temporal, and behavioral cues behind an individual decision. As direct predictors, however, LLMs remain sensitive to task presentation and often produce unreliable decisions. To address these challenges, we introduce ORBITER, an agentic Order Arbiter for next-order decision-making in last-mile delivery. ORBITER models courier service through decision points, each containing the courier's spatiotemporal state and visible orders and exposing local trade-offs for modeling and verification. Fixed proposers rank the candidates, and a structured report identifies where their rankings disagree. The LLM uses task-specific tools to gather evidence on the leading alternatives, while an independent critic checks the resulting decision against that evidence. We conduct extensive evaluations on data in four cities, where ORBITER outperforms existing state-of-the-art baselines by up to 9.2% on average showing its effectiveness.

Copy-protection encodes a functionality in a reusable quantum state that cannot be split into two states (freeloader adversaries) which remain simultaneously useful. Prior plain-model results handle only independently sampled challenges; the more natural identical-challenge notion, also tied to unclonable bits and copy-protection of point functions, has remained open. We strengthen these definitions and prove plain-model security for our new stronger notions. For single-decryptor encryption (SDE) we define correlated challenge security, show it implies all previous SDE notions including identical-challenge security, and prove that the construction of Kitagawa and Yamakawa (TCC'25) achieves it assuming iO and one-way functions. We also nearly fully characterize the relations among prior SDE notions. For general functionalities we define correlated challenge unclonable puncturable obfuscation (UPO), allowing arbitrary correlations among challenge points and puncturing bits plus auxiliary information before and after splitting, and requiring only conditionally uniform bits and $λ^c$ average conditional min-entropy in each point separately (thus, in particular, the points may be identical). Assuming post-quantum iO and quantum-hard LWE, we construct correlated UPO for polynomial-size keyed circuits with input length at least $λ^c$, answering an open question of Ananth, Behera, Huang, Kitagawa, Yamakawa (EUROCRYPT'26) and of Cakan-Goyal (EUROCRYPT'26). We also obtain the first plain-model copy protection for point functions, $k$-point functions, and compute-and-compare programs, and identical-challenge copy protection for general puncturable functionalities.

Indoor scene synthesis provides essential environments for embodied AI, robotic manipulation, and simulation-based policy learning. Recent code-based scene generation methods produce editable and extensible environments, yet they remain focused on visual construction and object-level articulation, leaving the functional usage of scenes largely unmodeled. To address this problem, we present RoomWright, an agentic usage-driven framework for generating 3D scenes represented entirely as code for embodied interaction. RoomWright performs usage-driven object reasoning, which treats each anchor as a task centre and admits task-required objects and their affordances. A code agent further enables multi-part interaction by compiling each interaction into a trigger, condition, effect rule that updates structured object states, capturing causal dependencies across objects. Moreover, since manipuland orientation is ambiguous and hard to recover from pixels, RoomWright alleviates this via annotation-informed usage-guided orientation. Extensive experiments demonstrate the effectiveness of our method. The resulting scenes are executable, editable, and simulation-ready, providing interactive environments for embodied AI and policy learning.

We consider a fundamental problem of \emph{mixedness testing}: Given $n$ copies of an $N$-qubit state $ρ$, determine whether $ρ= \mathbb{I}_d/d$ or $\|ρ-\mathbb{I}_d/d\|_1 \geq \varepsilon$ with high probability, where $d = 2^N$. In particular, we focus on performing this task in the practical setting of single-qubit measurements, where measurements are prepared independently on each qubit. We provide a nearly complete picture of single-qubit mixedness tesing by showing $n = \widetildeΘ\left(\sqrt{10}^N/\varepsilon^2\right)$. To establish our lower bound, we introduce a new measurement-dependent lower bound framework for adaptive single-copy state certification. For the upper bound, we present a randomized Pauli basis measurement protocol, which relies on a new primitive for computationally efficient uniformity testing of correlation-concentrated distributions on the Boolean hypercube.

We study makespan minimisation on two identical parallel machines that share a single server for both loading and unloading. Each job must be loaded, processed without interruption on its assigned machine, and unloaded immediately after processing, with a common positive integer duration for all loading and unloading operations. We prove that the decision problem is NP-complete for every fixed server-operation duration and strongly NP-complete when this duration is part of the input. We then analyse ordinary list scheduling and the longest-processing-time rule in the non-unit setting. List scheduling has a tight supremum ratio of two. For the longest-processing-time rule, we obtain the exact worst-case ratio when all processing times are at least the server-operation duration, and derive new parameter-dependent lower and upper bounds for unrestricted instances. The results show that both processing-time granularity and blocking generated by short jobs shape the approximation behaviour of the common-server problem.

Utilities lose a substantial share of treated water to leakage, yet rarely trust artificial-intelligence localizers to dispatch crews: guessing everywhere cannot justify excavation. The gap is accountability, not accuracy: no method proves when it should not act. Here we recast leak localization as decision-making under verifiable abstention. A physics-grounded executor agent falsifies hypotheses (leak, demand, sensor, valve) against a digital twin; an independent supervisor agent, with a large-language-model (LLM) auditor, checks evidence against a code-verifiable contract, then certifies a dispatch, requests evidence or abstains. Under field-grade noise, a 32% forced baseline becomes 96% decision precision on acted events. On an independently generated benchmark it acts on only 4 of 33 leaks, all correct. A 194-event register of audited real leak locations with twin-simulated pressures and flows yields five excavation dispatches, three correct, and 44% survey recovery at full district precision. Accountable abstention offers a defensible route to autonomous water-infrastructure operation.

Medical vision-language models (VLMs) can achieve high accuracy but remain unreliable: they are systematically overconfident, benefit little from test-time reasoning, and lack the ability to reliably calibrate trust in their own responses. We introduce EVADE (Evidence-Verified Agentic Diagnosis with Escape), an inferential, non-training method that enhances the safety of deploying a single frozen VLM. EVADE responds and, when uncertain, localises the region most diagnostically relevant, re-answers on a zoomed view, and commits only when both the entire image and the zoomed view responses agree; otherwise, it abstains. To directly address verification hallucination in single-model self-checking, our main idea is to verify gate consistency across different image views rather than re-reading the model's own text. Experimental evaluation on VQA-RAD, SLAKE, and PathVQA using Qwen2.5-VL-7B reports that EVADE is the only method that simultaneously improves both calibration and selective risk while maintaining accuracy, reducing expected calibration error (ECE) by up to 45% compared to zero-shot. Chain-of-thought, self-consistency, and self-verification all fail at least one axis. A grounding analysis reports that self-proposed regions perform better at diagnostic structure localisation than centres or random crops. However, a 7B VLM cannot use this localisation to revise answers. Therefore, reliability gains come from the consistency gate and calibrated abstention.

Audio-driven lip synchronization manipulates the mouth region of a talking-face video to match the driving audio while preserving head pose, identity, and background. Although the task is inherently local editing, prevailing approaches reconstruct the entire lower face with heavy GAN- or diffusion-based decoders, incurring substantial latency and, more critically, hallucinating intra-oral details such as teeth and lip wrinkles instead of preserving authentic textures. We contend that the bottleneck in identity preservation is not the scarcity of reference frames, but the lack of a mechanism that faithfully transfers the genuine textures they already contain. We therefore present EfficientSync, a real-time deformation-based framework that retains reference textures rather than resynthesizing them. First, the Dynamic Texture Mixer reformulates multi-reference fusion as channel-wise selection, evaluating each spatially aligned reference in a global context and aggregating them by channel-wise weighted summation, preserving textural integrity at low cost. Second, Spatio-Temporal Shifted Adaptive Masking decomposes the source frame into lip-generation conditions and an independent background prior, suppressing lower-face leakage while blending the synthesized mouth seamlessly into the background. Third, STAR Sampling, a zero-overhead pre-processing step, retrieves the sharpest and most topologically diverse reference frames. Experiments on HDTF and VFHQ show state-of-the-art visual quality and identity preservation at 166 FPS on a single GPU. Video demos: https://alunaticat.github.io/EfficientSync/index.html.

Reward function design remains a bottleneck in reinforcement learning. While large language models (LLMs) have enabled automated reward generation, existing methods generate and revise reward functions as monolithic programs, making it difficult to reliably preserve and reuse effective components discovered in earlier iterations, leading to unstable performance across iterations. To address this, we propose Module Level Reward Evolution Framework (MLREF). At the core of MLREF is a module pool, a persistent repository of reusable reward components. MLREF treats the module pool as the primary optimization object: the pool evolves across iterations by accumulating successful modules, refining underperforming ones, and reusing proven components; while reward functions are constructed as linear combinations of modules drawn from this pool. To drive this evolution, MLREF integrates three mechanisms: reflection-based refinement, hybrid credit assignment, and a merge strategy with rollback, which together improve the effectiveness and robustness of reward optimization. Experiments on 17 tasks show that MLREF outperforms strong baselines by 25.2% in locomotion and 6.6% in manipulation, with more stable optimization dynamics.

Medical automatic speech recognition (MedASR) requires adaptation to specialised terminology, limited annotated clinical data, and multilingual use cases. Although large-scale pretrained ASR models such as Whisper achieve strong generalisation, their behaviour after medical and multilingual adaptation remains insufficiently understood beyond word error rate (WER). This paper investigates how multilingual medical adaptation reshapes the internal representations of Whisper models through layer-wise encoder analysis. We compare zero-shot decoding, English-only fine-tuning, German-only diagnostic fine-tuning, two-stage EN->EN+DE continuation, and direct EN+DE fine-tuning across Whisper model sizes. Fine-tuning substantially improves MedASR performance, but the best model depends on the adaptation setting: Whisper-Medium gives the lowest English WER (7.72%) and the lowest combined EN+DE WER under direct EN+DE training (26.30%); German-only Whisper-Large-v3 gives the lowest German WER (44.96%), but as a within-corpus diagnostic on 86 single-speaker training utterances rather than robust generalisation. Layer-wise analysis of the two-stage Whisper-Small trajectory shows that English medical fine-tuning produces the dominant encoder shift, whereas multilingual continuation largely preserves the adapted representation space. Domain and language information remain highly recoverable across layers, while linearly recoverable error-predictive cues weaken as WER improves.

Large language models can propose proofs for interactive theorem provers, but a successful build does not show the surrounding verification task was preserved. We study this problem in an Isabelle development of a sampled-data double-tank controller. The work began with nine theories and ten unfinished obligations, grew to a 16-theory build without sorry, oops, added axiomatisation, or oracle use, and accumulated 23 stable and 36 broken proof states. A retrospective audit found material changes in 16 of the 100 original declarations, including a weakened end-to-end assurance theorem that assumed three of the four requirements in its conclusion. We used CAPRI, a contract-aware proof-repair tool, to govern a reconstruction by combining Isabelle acceptance with an independent check of repository changes against machine-readable edit contracts. The reconstruction discharged all ten scoped obligations within the original nine-theory structure. A secondary replay by a co-author reproduced the R10 build, contract checks, control tests, and principal audit findings; independent replication remains future work. Operational end-to-end verification remains incomplete: we still need to connect operational executions to the reconstructed quantitative trace contract, a task requiring an extended contract.

The logical reconstruction of argument graphs from natural language text is challenging because of the prevalence of enthymemes (i.e., arguments with implicit premises). There are natural language processing methods for identifying enthymemes in text, and there are symbolic methods based on abduction for identifying missing premises in a logical representation of enthymemes. However, there is a need for methods to generate implicit premises to logically show a known entailment or contradiction relationship between a pair of statements. To address this, we propose a neuro-symbolic pipeline that uses large language models (LLMs) to generate intermediate implicit premises that are translated into logical formulae and used with logical formulae representing explicit premises and explicit claims to show the logical relationships between them (entailment, contradiction, or neutrality). Our approach is evaluated on the Microtext Argumentative Corpus.

Arguments often omit premises or claims, forming enthymemes. We study pairwise logical selection between two candidates for the omitted component. Existing natural language methods can identify or generate candidates but often do not expose how the selected candidate completes the inference, while logic-based approaches usually assume that the required formulae and background knowledge are available. We extend a prior neuro-symbolic pipeline from missing-premise to missing-claim selection and replace binary entailment outcomes with logical-resistance scores. Top-Link uses weighted Partial MaxSAT under a single configuration of highest-confidence semantic links. We then introduce Possible-World Atom-Link Formalization (PWAL), which keeps translated formulae fixed and marginalizes logical resistance over alternative cross-formula semantic-link configurations. We evaluate PWAL on five tasks: ARCT and a CDED-derived task for missing-premise selection, iDebate- and AAE2-derived tasks for missing-claim selection, and alphaNLI for abductive hypothesis selection. Relative to Top-Link, PWAL raises strict accuracy by 2.95-30.86 percentage points and reduces tie rates by 4.57-58.00 percentage points on all five tasks. When ties receive half credit, accuracy still increases by 0.45-6.04 percentage points. PWAL also records the translated formulae, sampled link configurations, and resistance components for every comparison, providing a transparent trace of each score.

Recent Visual-Language Models (VLMs) have enhanced the capabilities of pre-trained LLMs by adding vision tokens alongside text, with approaches like LLaVA showing impressive results. However, the computational burden of processing up to 576 or 729 visual tokens makes edge deployment challenging. While various token pruning techniques require retraining, some are training-free and thus can easily adapt to architecture changes. We introduce ClustRS, a two-part, training-free algorithm for robust token pruning. Its first component is an attention-weighted, clustering algorithm that selects representative tokens from each semantic cluster. The second component, Residual Shrinkage, is a one-pass denoising step on the selected tokens. These training-free lightweight steps make LLaVA ready for real-world data, improving robustness to a wide range of image-noise types and intensities. Experimental results on the ScienceQA-IMG and MM-VET benchmarks show our method outperforms attention- and diversity-based methods by up to 20\% under extreme noise and token conditions (reducing tokens by 97\%, down to 16 tokens) on LLaVA 1.5 7b and achieves exceptional results on LLaVA-OneVision, where we match baseline performance with fewer than one-third of their tokens under mild noise conditions. Our study demonstrates a simple yet powerful alternative to both score-only and diversity-only pruning rules, paving the way for compute-efficient and noise-resilient VLM deployment.

Graph neural networks (GNNs) are widely used, but how parameter sparsity affects the expressivity of relational (RGNNs) and temporal (TGNNs) variants is poorly understood. The Strong Expressive Lottery Ticket Hypothesis (SELTH) posits the existence of sparse GNNs that preserve Weisfeiler-Leman (WL) expressivity on static graphs. We generalize this existence result to a probabilistic statement for multi-relational and temporal domains via the relational WL (RWL). We prove that sufficiently parameterized RGNNs contain sparse subnetworks that maintain 1-RWL expressivity and derive a lower bound on the probability that a random pruning yields such a subnetwork. We show that common TGNNs and cross-graph message passing schemes admit RGNN reformulations such that they inherit these guarantees and, moreover, that the expressivity of a sparse RGNN is connected to its optimization behavior under common update regimes. Experiments instantiate the bound, compare it to empirical probabilities on synthetic data, and study how pre-training expressivity relates to optimization and prediction quality metrics on temporal and molecular benchmarks.

AI hallucinations - that is, outputs which are made up, cannot be verified, or contradict the source material - are generally regarded as an engineering flaw to be dealt with. This paper contends that they also have philosophical significance when it comes to the question of machine consciousness. We examine the known causes of hallucinations in large language models - such as source-target divergence, discrepancies between training and inference, and overfitting - and we present two empirical investigations. In the first, we apply successive generations of the GPT model to ambiguous factual questions under different temperature settings, finding that higher temperatures result in plausible but incorrect answers while lower temperatures lead to factually accurate ones. The sampling parameters that cause a model to seem creative or spontaneous and thus more likely to pass behavioral tests of intelligence are the same ones that increase its hallucination rate. In the second, we look at an encoder-only model that has been trained on encyclopedic data and which answers questions of the same type factually and without embellishment, indicating that hallucinations are due to exposure to subjective and socially diverse training data rather than to the development of any cognitive ability. Using references to Turing, Searle's Chinese Room, the frame problem, and the cybernetic tradition of Wiener and Ashby, we claim that a model's self-reports of emotion or sentience come within the definition of hallucination, and that any future occurrence of machine consciousness might remain epistemically inaccessible since it would be indistinguishable from a sufficiently advanced hallucination.

In the last years, a number of proofs of the fact that $O_2$ is a multiple context-free grammar (MCFG) were given. Such results can be exploited in the fields of both computational linguistics and of computational algebra. Here, we focus on a recent such proof spelled in terms of factorizations of string tuples, and give a new result with a stronger characterization of such factorizations than in existing theorems.

An optimizer is usually chosen before training a deep neural network and then kept fixed. Treating optimizer choice as a hyperparameter could boost performance, but it requires several complete training runs and discards all but the winner. Repeated Optimizer Resampling (ROR) instead searches during one evolving run. Every $b$ epochs, each candidate optimizer scouts from the current model weights for $s$ epochs. The best scout continues for the remaining $b-s$ epochs, and that completed segment becomes the new incumbent if it improves the validation objective. This design allows the preferred optimizer to change as training progresses. We compare two variants of ROR on MNIST, Fashion-MNIST, and two motor insurance claim-count models. Nine fixed optimizers and both ROR variants are evaluated with the same ten seeds. One-epoch ROR uses 24\% to 35\% of the aggregate training needed to identify the best fixed optimizer exhaustively and remains close to that optimizer on all four tasks. These results support short scouting as a practical way to search over optimizers without completing every candidate run.

This paper introduces Tensor Field Models (TFMs), realization-level Mathematical Structures in which a learned Operator maps a product of admissible component-section families to a prescribed family of time-dependent tangent sections on a Generative State Manifold. Analytic and dynamical restrictions are encoded through the choice of admissible families rather than imposed by the root definition. Constructed, component-separable, and Tensor Bundle TFMs provide structured refinements of this common object. In the conditional realizations considered here, a structured condition $c=(c_1,\ldots,c_n)$ is mapped componentwise to a reusable collection $\mathbf H_c=(H_{c_1}^{(1)},\ldots,H_{c_n}^{(n)})$. In the architectures evaluated here, the component representations remain distinct and are combined only by the Field Operator to produce the generated Vector Field. All learned models are trained using Flow Matching. Experiments show that TFMs can improve performance and that amortized sampling enabled by reusable condition representations can accelerate generation.

Efficient continual learning remains a fundamental challenge for deep neural networks. While catastrophic forgetting and loss of plasticity are widely considered the primary obstacles to overcome, we show that these two issues cannot fully explain the performance gap between naive sequential training and offline joint training. In this paper, we highlight data co-observation as a distinct factor influencing continual learning performance. By decoupling the constraints of separate data access from stability and plasticity, we systematically investigate the representational benefits gained by observing training data together. Empirically, we demonstrate a consistent performance difference between joint and separate training across both supervised and self-supervised paradigms in generic data-incremental "chunking" scenarios, whilst mitigating forgetting and controlling for plasticity. Our findings indicate that simultaneous observation of training data (co-observation) yields benefits to the learner's generalization that extend well beyond mere knowledge retention, and that this effect does not require a specific continual distribution shift. Furthermore, we contextualize prominent continual learning mechanisms through this lens: while distillation-based approaches act only as effective knowledge retention mechanisms, our results suggest that the empirical success of memory replay goes beyond the mitigation of forgetting, actively reintroducing the benefits of data co-observation into the learning process.