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01.
arXiv (CS.LG) 2026-06-24

Hybrid Sequence Modeling and Reinforced Verification for Controllable Target-Conditioned Decision Making

arXiv:2508.16420v3 Announce Type: replace Abstract: Target-conditioned sequence models provide a simple interface for controllable offline decision making, but the requested target return can be an unreliable control signal, especially when the target return lies in underrepresented regions of the dataset. This paper proposes Doctor, a hybrid sequence modeling and reinforced verification framework for controllable target-conditioned offline decision making. Doctor trains a shared masked trajectory Transformer with two complementary objectives: masked trajectory reconstruction for candidate generation and in-sample value learning for action-value verification. At inference time, the model samples multiple nearby target returns, generates candidate actions in parallel, and selects the action whose verified value is closest to the requested target return. We analyze this verifier-guided selection rule and show that its value-level alignment error is bounded by candidate-value coverage around the target return and verifier accuracy. Experiments on D4RL and EpiCare show that Doctor improves target-return alignment under reduced high-return coverage, remains competitive on standard offline return-maximization benchmarks, and enables a single policy to modulate between conservative and aggressive operating points in a simulated clinical decision-making task. These results suggest that reinforced verification can improve the controllability of target-conditioned policies.

02.
arXiv (CS.AI) 2026-06-16

Multi-Sensor Fusion for UAV Classification Based on Feature Maps of Image and Radar Data

arXiv:2410.16089v2 Announce Type: replace Abstract: The unique cost, flexibility, speed, and efficiency of modern UAVs make them an attractive choice in many applications in contemporary society. This, however, causes an ever-increasing number of reported malicious or accidental incidents, rendering the need for the development of UAV detection and classification mechanisms essential. We propose a methodology for developing a system that fuses already processed multi-sensor data into a new Deep Neural Network to increase its classification accuracy towards UAV detection. The DNN model fuses high-level features extracted from individual object detection and classification models associated with thermal, optronic, and radar data. Additionally, emphasis is given to the model's Convolutional Neural Network (CNN) based architecture that combines the features of the three sensor modalities by stacking the extracted image features of the thermal and optronic sensor achieving higher classification accuracy than each sensor alone.

03.
arXiv (CS.CV) 2026-06-24

Point-Voxel Absorbing Graph Representation Learning for Event Stream based Recognition

Sampled point and voxel methods are usually employed to downsample the dense events into sparse ones. After that, one popular way is to leverage a graph model which treats the sparse points/voxels as nodes and adopts graph neural networks (GNNs) to learn the representation of event data. Although good performance can be obtained, however, their results are still limited mainly due to two issues. (1) Existing event GNNs generally adopt the additional max (or mean) pooling layer to summarize all node embeddings into a single graph-level representation for the whole event data representation. However, this approach fails to capture the importance of graph nodes and also fails to be fully aware of the node representations. (2) Existing methods generally employ either a sparse point or voxel graph representation model which thus lacks consideration of the complementary between these two types of representation models. To address these issues, we propose a novel dual point-voxel absorbing graph representation learning for event stream data representation. To be specific, given the input event stream, we first transform it into the sparse event cloud and voxel grids and build dual absorbing graph models for them respectively. Then, we design a novel absorbing graph convolutional network (AGCN) for our dual absorbing graph representation and learning. The key aspect of the proposed AGCN is its ability to effectively capture the importance of nodes and thus be fully aware of node representations in summarizing all node representations through the introduced absorbing nodes. Extensive experiments on multiple event-based classification benchmark datasets fully validated the effectiveness of our framework.

04.
arXiv (math.PR) 2026-06-16

The Backward Stochastic Partial Differential Integral Equations: Solvability and Comparison Principle

arXiv:2606.16237v1 Announce Type: new Abstract: The paper is concerned with the well-posedness of backward stochastic partial differential equations with jumps, also called backward stochastic partial differential integral equations. We start from the proof for the existence and uniqueness of solution to backward stochastic evolution equation with jump in the Gelfand triple framework. Then the well-posedness of both weak solution and strong solution to backward stochastic partial differential integral equation is obtained with the Gelfand triple replaced by specific Sobolev spaces. Finally, the comparison principle for backward stochastic partial differential integral equation is proved, which has potential applications in financial mathematics.

05.
arXiv (quant-ph) 2026-06-11

Quantum repeater segment with free-space coupled co-trapped ions using telecom photon interference

arXiv:2606.12313v1 Announce Type: new Abstract: A quantum repeater segment is a basic building block of a quantum repeater, generating buffered entanglement of quantum memories to connect quantum repeater cells. It also enables the connection between quantum computers. In the implementation we present here, photons emitted from two co-trapped free-space coupled $^{40}$Ca$^+$ ions are converted to the telecom-C band and interfered after transmission over 440$\,$m of optical fiber (220$\,$m per arm), where a photonic Bell measurement is performed to create entanglement between the memories. With this scheme we generate an entangled $\left|\Psi^+\right\rangle$ Bell state with $\ge 68(8)\,$% fidelity, highlighting trapped $^{40}$Ca$^+$ ions as a promising quantum repeater hardware platform.

06.
arXiv (CS.CL) 2026-06-24

On the Stability of Prompt Ranking in Large Language Model Evaluation

Prompt-based interaction has become a dominant paradigm for using large language models (LLMs), where multiple candidate prompts are evaluated and the top-ranked one is selected for downstream use. This workflow implicitly assumes that prompt rankings are stable under minor variations in evaluation conditions. In this paper, we systematically study prompt ranking stability under common sources of variability, including random seeds and limited evaluation subsets. Across three open-weight LLMs and two benchmark tasks, we find that while overall rank correlations are often moderate to high, the identity of the top-performing prompt frequently changes, leading to unreliable selection decisions. To address this issue, we propose a simple stability-aware selection strategy based on a lower confidence bound, which accounts for both performance and variance. Our results show that this approach improves robustness in unstable settings while remaining competitive in more stable regimes. These findings highlight the importance of accounting for evaluation uncertainty in prompt selection and LLM benchmarking.

08.
arXiv (quant-ph) 2026-06-16

Bi-qutrit entangled edge states of positive partial transposes with largest ranks

arXiv:2606.16265v1 Announce Type: new Abstract: Whenever $E$ is an eight dimensional subspace of the bi-qutrit quantum system whose orthogonal complement is spanned by a vector of Schmidt rank three, we show that there exist PPT entangled edge states with the range space $E$ whose partial transposes are of rank six, which is the largest possible rank. In this way, we exhibit a huge family of bi-qutrit PPT entangled edge states of type $(8,6)$. They make faces of the convex set of all PPT states, and we find bi-qutrit PPT entangled edge states of other types on the boundaries of such faces.

09.
arXiv (CS.CL) 2026-06-18

Breaking the Solver Bottleneck: Training Task Generators at the Learnable Frontier

The limiting resource for training agents via reinforcement learning (RL) is increasingly frontier task supply: valid, solvable tasks just difficult enough to train the current model. As reasoning and agentic models improve, fixed task distributions saturate, while naive synthetic generation yields tasks that are trivial, impossible, or ill-posed. Training a task generator with RL to optimize validity and learnability can address this bottleneck, but direct optimization requires repeated solver rollouts per candidate. For software-engineering (SWE) tasks, a single rollout can take tens of minutes; solver-in-the-loop generator training is intractable. We introduce PROPEL, a solver-amortized framework for training task generators at the targeted solve rate. PROPEL trains a lightweight activation probe on a one-time labeled corpus of generated tasks and solver outcomes. The probe predicts target-solver pass rate from a frozen generator reference model and serves as a proxy for solve rate during generator optimization, reducing generator evaluation to a single forward pass. Across math, code, and software-engineering at multiple model scales, PROPEL shifts generation toward the targeted solve rate: for coding, tasks generated at the learnable frontier increase from $10.1\% \rightarrow 20.0\%$ for a Qwen2.5-3B-Instruct solver and from $5.3\% \rightarrow 12.6\%$ for a Qwen2.5-7B-Instruct solver. For SWE, PROPEL increases the share of generations at the targeted solve rate from $9.8\% \rightarrow 19.6\%$ for Qwen3.5-27B on repositories not seen during training of probe and generator.

10.
arXiv (CS.AI) 2026-06-25

Learning with a Single Rollout via Monte Carlo Pass@k Critic

arXiv:2606.25451v1 Announce Type: cross Abstract: Estimating token-level advantages in reinforcement learning (RL) for language models remains challenging because scaling up episodic experience collection is expensive. The difficulty intensifies for baseline advantage estimation methods, where repeated sampling causes trajectories to diverge into substantially different reasoning prefixes. In this context, RL algorithms such as GRPO prove limited: an outcome reward is too sparse to be attributed to specific actions like intermediate steps, and comparisons across sampled traces are non-trivial because they are heterogeneous. To mitigate both the computational cost of repeated sampling and the difficulty of credit assignment, we study single-rollout proximal policy optimization (SR-PPO) featuring token-level credit assignment in RL for language models. Instead of estimating advantages by normalizing episodic returns within the candidate group, we train a calibrated token-level credit critic using Monte Carlo outcomes from one rollout per prompt. Specifically, we use the critic to predict the Pass@k success probability at the prompt prefix, which is derived from a Pass@1 attempt. This choice yields a more selective learning signal than Pass@1: it discounts easily solved prefixes while prioritizing hard ones whose success probability remains marginal. We show that as $k$ increases, Pass@k converges to a reachability indicator, reflecting whether a prefix can lead to at least one successful continuation. In an explicit state graph, the limit ($k \rightarrow \infty$) can be computed in $O(|V|+|E|)$ time, offering a promising surrogate for direct credit assignment without the need to sample contrastive traces. As an initial validation, SR-PPO exhibits stable learning dynamics, along with consistent gains in Pass@128 success rates on mathematical reasoning benchmarks such as HMMT26 and AIME24.

11.
arXiv (CS.LG) 2026-06-12

Quantizing Time-Series Models As Dynamical Systems: Trajectory-Based Quantization Sensitivity Score

arXiv:2606.13300v1 Announce Type: new Abstract: We introduce the Trajectory-based Quantization Sensitivity Score (TQS), a metric that reframes post-training quantization (PTQ) through the lens of dynamical-systems stability. By modeling the network's rollout as a discrete-time dynamical system, TQS characterizes how quantization-induced errors propagate and amplify over the rollout horizon. Unlike conventional PTQ methods, where sensitivity analysis is often coupled to the quantization procedure, TQS enables a priori sensitivity estimation decoupled from quantizer selection and bit-width assignment. This separation allows for quantization budget planning even for black-box or compiled networks with fused operators. Building on this, we present TQS-PTQ, a flexible mixed-precision framework that requires no calibration data or costly second-order approximations. Our experiments show that a dynamical-systems perspective provides a robust, high-performing pathway for low-precision deployment in resource-constrained settings.

12.
Nature (Science) 2026-06-22

Will AI spark a scientific renaissance — or a diffuse monoculture?

作者:

Artificial intelligence’s ability to enrich science will depend not only on model capability, but also on whether researchers, reviewers and funders reward originality over speed. Artificial intelligence’s ability to enrich science will depend not only on model capability, but also on whether researchers, reviewers and funders reward originality over speed.

13.
arXiv (CS.CV) 2026-06-15

What Drives Test-Time Adaptation for CLIP? A Controlled Empirical Study from an Update Perspective

Vision-Language Models (VLMs) such as CLIP have become a standard backbone for open-vocabulary recognition, yet their zero-shot predictions remain vulnerable to distribution shifts encountered at deployment. Test-Time Adaptation (TTA) has recently been extended to CLIP as a lightweight solution, leading to a rapidly growing body of TTA4CLIP methods. However, empirical progress in this area has largely outpaced our understanding of what truly drives adaptation, where their gains originate, and under which shifts they remain reliable. In this paper, we take a step back from the pursuit of state-of-the-art accuracy and conduct a systematic controlled study of TTA4CLIP. We first organize existing methods into three unified paradigms according to what is updated at test time. We then introduce TTABC, an open-source TTA Benchmark for CLIP, which standardizes evaluation protocols and integrates more than 20 representative methods. Our controlled empirical analysis focuses on three key areas. First, we determine the driving factors in parameter-based methods, revealing that adaptation gains are primarily driven by test-time evidence and reliable proxies rather than heavy optimization. Second, we explore evidence utilization beyond heavy parameter tuning, showing that competitive and efficient performance can be achieved through cross- or current-sample evidence and lightweight prototype updates. Finally, we demonstrate that there is no silver bullet for TTA: no single adaptation paradigm is universally optimal, and the preferred paradigm depends on the nature of shift. We hope our benchmark and study provide a clearer understanding of the current TTA4CLIP landscape and establish a foundation for further research.

14.
arXiv (CS.CV) 2026-06-12

CD-RCM: Generalizable Continuous-Depth Novel View Synthesis for Reflectance Confocal Microscopy

Reflectance confocal microscopy (RCM) provides noninvasive, cellular-resolution "optical biopsies" of human skin in vivo by acquiring en-face images at successive depths, forming a sparse z-stack. Due to optical limitations, these stacks are anisotropic 3D volumes with lateral resolution (0.5 $\mu$m) $\sim$6 times higher compared to axial resolution, which is defined by the optical sectioning (3 $\mu$m), limiting the interpretation of tissue. Our goal is to provide continuous-depth visualization by interpolating intermediate sections and making the 3D volume isotropic. Such a representation permits arbitrary-direction sectioning, including histopathology-like cross-sectional examination, without requiring per-patient optimization. To that end, we introduce the first RCM-specific novel-view synthesis (NVS) approach, CD-RCM, a feedforward model that predicts realistic, unseen depths from sparsely sampled RCM stacks. Classical neural rendering methods focus on reconstruction from surface-level multi-view observations. In contrast to surface-level camera views, RCM can acquire optically sectioned en-face images of tissue beyond the surface up to 200 $\mu$m. However, during visualization of the RCM stacks, observations of the shallower sections (towards the surface) obscure the deeper ones. This unique axial imaging geometry and layer-dependent anatomical organization motivated our development of a tailored architectural and training framework that explicitly accounts for RCM's depth-resolved, occlusive imaging physics. Experiments demonstrate that CD-RCM achieves high-fidelity novel-view synthesis with sub-second inference time.

15.
arXiv (quant-ph) 2026-06-11

A Cryogenic Uniaxial Strain Cell for Quantum Devices

arXiv:2606.11485v1 Announce Type: new Abstract: Mechanical strain is a powerful resource for tuning quantum systems, but existing piezoelectric strain cells are generally optimized for fragile, high-aspect-ratio single crystals rather than the thick, square-profile chips typical of semiconductor quantum devices. Furthermore, adapting these cells for qubits requires accommodating dense RF and DC wiring while maintaining strict electrical isolation from high-voltage piezo actuators. Here, we present a piezoelectric uniaxial strain cell designed to homogeneously strain thick, square-profile substrates. We introduce a highly symmetric dual-chip loading configuration that effectively suppresses flexural deformation and shear stress. The cell integrates a high-density RF/DC interposer to support standard wire bonding and encloses the actuators in a grounded Faraday cage to prevent unwanted Stark shifts in the device layer. Finite element simulations confirm that combining stiff actuators with this symmetric mounting drastically improves strain homogeneity. Finally, we validate the apparatus experimentally by applying uniaxial strain to a 200 $\mu$m thick silicon die. Surface strain measurements demonstrate an applied strain of 215 $\mu\epsilon$ for 200 V applied piezo bias.

16.
arXiv (quant-ph) 2026-06-12

Quasi-local Edge Mode in XXX Spin Chain/Circuit with Interaction Boundary Defect

arXiv:2603.17835v2 Announce Type: replace-cross Abstract: We study the Heisenberg spin-1/2 model on a semi-infinite chain - or, equivalently, a trotterized unitary SU(2) symmetric six-vertex quantum circuit - with a boundary defect where the interaction between the two spins nearest the edge differs from that in the bulk. For sufficiently strong boundary interaction we explicitly construct a conserved operator quasi-localized near the boundary using a matrix-product ansatz. This quasi-local edge mode leads to non-decaying boundary correlation functions, corresponding to a nonzero boundary Drude weight. The correlation length of the edge mode diverges at a finite critical value of the boundary interaction, signaling a transition to ergodic boundary dynamics for subcritical interactions.

17.
arXiv (CS.LG) 2026-06-12

A unified complexity bound for logconcave sampling

arXiv:2606.12694v1 Announce Type: cross Abstract: We give a simple, unified, and nearly tight bound for sampling arbitrary logconcave distributions from a warm start using the In-and-Out algorithm along with exponential lifting. The main new ingredient in the analysis is an improved bound on the Poincaré constant of a lifted distribution. As a consequence, the resulting convergence rate is nearly tight for both constrained settings (e.g., Gaussian restricted to a convex body) and well-conditioned settings (e.g., strongly logconcave and smooth densities).

18.
arXiv (CS.LG) 2026-06-25

Learning Structural Hardness for Combinatorial Auctions: Instance-Dependent Algorithm Selection via Graph Neural Networks

作者:

arXiv:2602.14772v2 Announce Type: replace Abstract: The Winner Determination Problem (WDP) in combinatorial auctions is NP-hard, and no existing method reliably predicts which instances will defeat fast greedy heuristics. The ML-for-combinatorial-optimization community has focused on learning to replace solvers, yet recent evidence shows that graph neural networks (GNNs) rarely outperform well-tuned classical methods on standard benchmarks. We pursue a different objective: learning to predict when a given instance is hard for greedy allocation, enabling instance-dependent algorithm selection. We design a 20-dimensional structural feature vector and train a lightweight MLP hardness classifier that predicts the greedy optimality gap with mean absolute error 0.033, Pearson correlation 0.937, and binary classification accuracy 94.7\% across three random seeds. For instances identified as hard – those exhibiting ``whale-fish'' trap structure where greedy provably fails – we deploy a heterogeneous GNN specialist that achieves ${\approx}0\%$ optimality gap on all six adversarial configurations tested (vs.\ 3.75–59.24\% for greedy). A hybrid allocator combining the hardness classifier with GNN and greedy solvers achieves 0.51\% overall gap on mixed distributions. Our honest evaluation on CATS benchmarks confirms that GNNs do not outperform Gurobi (0.45–0.71 vs.\ 0.20 gap), motivating the algorithm selection framing. Learning when to deploy expensive solvers is more tractable than learning to replace them.

19.
arXiv (CS.LG) 2026-06-17

A Diffusion Approximation for Temporal-Difference Learning with Linear Features under Markovian Noise

arXiv:2606.18183v1 Announce Type: cross Abstract: Temporal difference (TD) learning with linear function approximation is a core method for policy evaluation. Its classical continuous-time description is an ordinary differential equation (ODE), which captures the asymptotic mean dynamics but neglects stochastic fluctuations determining the error floor. We introduce a stochastic differential equation (SDE) approximation for linear TD(0) under Markovian noise. The resulting model distinguishes the contraction dynamics governed by the projected Bellman operator from the influence of Markovian sampling. As a consequence, the model explains the constant-stepsize error floor through the interaction between Markovian long-run covariance and the contraction geometry of the projected Bellman operator.

20.
arXiv (math.PR) 2026-06-19

Towards practical PDMP sampling: Metropolis adjustments, locally adaptive step-sizes, and NUTS-based time lengths

arXiv:2503.11479v2 Announce Type: replace-cross Abstract: Piecewise-Deterministic Markov Processes (PDMPs) hold significant promise for sampling from complex probability distributions. However, their practical implementation is hindered by the need to compute model-specific bounds. Conversely, while Hamiltonian Monte Carlo (HMC) offers a generally efficient approach to sampling, its inability to adaptively tune step sizes impedes its performance when sampling complex distributions like funnels. To address these limitations, we introduce three innovative concepts: (a) a Metropolis-adjusted approximation for PDMP simulation that eliminates the need for explicit bounds without compromising the invariant measure, (b) an adaptive step size mechanism compatible with the Metropolis correction, and (c) a No U-Turn Sampler (NUTS)-inspired scheme for dynamically selecting path lengths in PDMPs. These three ideas can be seamlessly integrated into a single, `doubly-adaptive' PDMP sampler with favourable robustness and efficiency properties.

21.
arXiv (quant-ph) 2026-06-16

Synthesizing Arbitrary Non-Hermitian Hamiltonian with Stochastic Floquet Engineering

arXiv:2606.15664v1 Announce Type: new Abstract: The conventional Floquet engineering scheme synthesizes a given target Hamiltonian with a deterministic temporal periodic driving field. In this work, we introduce the stochastic Floquet engineering scheme that can synthesize an arbitrary non-Hermitian target Hamiltonian using a time-periodic driving field with noisy amplitude. Our method is rooted in the Hermitian dynamics taking noise as a valuable quantum resource with no need for loss or gain in prior. We apply our method to engineer a cavity Hamiltonian with dissipative coupling between Fock states, and to prepare a given quantum state from a generally arbitrary quantum state. The stochastic Floqut engineering also provides a way to generate non-unitary quantum gates, which take advantage in certain tasks compared to unitary quantum computing, without the need for ancillae or state-dependent updating.

22.
medRxiv (Medicine) 2026-06-24

INCREASED REMOVAL SIGNALS ON ERYTHROCYTES OF ANEMIC CANCER PATIENTS

BACKGROUND: Anemia is a negative factor in cancer, influencing the prognosis, quality of life and financial situation of cancer patients. Recent studies have shown that anemia in cancer is provoked by augmented erythrocyte removal. OBJECTIVE: In this study we sought to investigate the molecular bases for erythrocyte removal in cancer patients with anemia. In particular, we explored the levels of erythrocyte CD47, lactadherin, calreticulin and MCP1. METHODS: Thirty five anemic cancer patients (25 women, aged 66.4 +/-11.35 years old) and twelve healthy non-anemic controls (8 men, aged 61.1+/-9.98 years old) participated in our study. Red blood cells were isolated throug multiple centrifugations, and were lysed with the use of Triton-X 100. The levels of CD47, lactadherin, calreticulin and monocyte chemoattrractant protein 1 were determined by ELISA. RESULTS: Erythrocytes of anemic cancer patients display reduced CD47 (p

23.
arXiv (CS.CV) 2026-06-15

GarmentSketch: Large-scale Sketch-to-Fashion Benchmark

Fashion sketching is a cornerstone of design workflows, allowing rapid visualization of creative concepts prior to physical prototyping. Yet, progress in sketch-based fashion image synthesis has been hindered by the absence of large-scale, high-quality paired resources. To bridge this gap, we present GarmentSketch, a novel dataset comprising 26,249 fashion sketches across 21 garment categories, each paired with detailed textual descriptions. Captions were produced through a multi-stage pipeline that integrates multiple multimodal large language models (MLLMs) with human-in-the-loop refinement, ensuring both semantic accuracy and descriptive richness. We benchmark GarmentSketch on state-of-the-art generative models, providing baseline performance for sketch-guided text-to-image generation. Our experiments reveal both the promise and the current limitations of existing methods. By offering a comprehensive and richly annotated resource, GarmentSketch establishes a foundation for advancing sketch understanding, fine-grained fashion image generation, and creative human-AI collaboration in design. The dataset will be available at: https://khangbdd.github.io/garmentsketch.

24.
arXiv (quant-ph) 2026-06-11

Exact Entanglement Dynamics Beyond Nearest-Neighbor Dual-Unitary Floquet Systems

作者:

arXiv:2606.11311v1 Announce Type: new Abstract: Exact results using dual-unitarity largely rely on nearest-neighbor structures, while finite-range interactions typically lead to complications. Going beyond the usual nearest-neighbor setting, we introduce an analytically tractable family of finite-range kicked Ising models that admit exact closed-form entanglement dynamics. The construction is based on a staggered structure in which dual-unitarity is present on sublattices that are then coupled to each other. The central observation is that these inter-sublattice couplings do not obstruct the dual-unitarity of the resulting model. For the minimal interaction range of $r= 2$, we derive exact expressions for all the $n-$Rényi entanglement entropies at all times and show that the result is the sum of the two coupled sublattice contributions. Our framework extends naturally to larger finite interaction ranges and to systems with heterogeneous local Hilbert spaces, without additional assumptions. It thus provides a controlled setting for studying exact entanglement growth beyond strictly nearest-neighbor dual-unitary models.

25.
arXiv (CS.AI) 2026-06-16

When Generator Replay Degrades: Projected Rehearsal Orchestration for Heterogeneous Federated Class-Incremental Learning

arXiv:2606.15695v1 Announce Type: cross Abstract: Federated class-incremental learning (FCIL) becomes substantially harder when clients observe different label subsets, progress through tasks at different stages, and provide uneven supervision for the same semantic concepts. Existing FCIL methods often preserve old knowledge through input-space synthesis, but they can be fragile under heterogeneous task streams and difficult to transfer across modalities. To alleviate such issues, we propose PRO, a framework that replaces synthetic input replay with projected rehearsal orchestration. To remove external pretraining, we evaluate all methods under the same warmup. After this, PRO maintains compact class-level projected memories on the server and allows clients perform balanced pseudo multi-task training over current examples and old projected memories. To handle stronger representation drift, we further introduce PRO-MAX, which augments PRO with neighborhood-weighted memory alignment while preserving the same server-light principle that the server only aggregates model updates and memory statistics. Across image, text, and graph benchmarks, PRO and PRO-MAX improve retention and final utility under heterogeneous streams while remaining competitive in homogeneous FCIL. Even when baselines are given expanded replay budgets, they degrade under supervision imbalance and stage misalignment, indicating that replay quantity alone does not resolve replay-quality failures. Additional weak-task diagnostics further show that larger replay mismatch is associated with larger downstream degradation, while our method keeps projected memories better aligned with the evolving representation.