Physics-informed neural networks (PINNs) commonly evaluate the spatial derivatives appearing in partial differential equation residuals using automatic differentiation (AD), whose computational and memory costs can become substantial when multiple or high-order derivatives are required. We perform a controlled comparison of spatial AD and Fourier spectral differentiation in periodic physical-space PINNs. Within each paired experiment, the neural representation, temporal differentiation, optimizer, sampling procedure, and training schedule are held fixed, so that the two cases differ only in the spatial differentiation procedure. For the Fourier variant, network outputs are evaluated on a uniform periodic grid and transformed to Fourier space, where spatial derivatives are obtained through spectral multiplication and the same Fourier coefficients are reused across derivative orders. We compare the two procedures in standard PINNs for the Allen--Cahn and Korteweg--de Vries equations and in Causal PINNs for the Allen--Cahn, Korteweg--de Vries, and Kuramoto--Sivashinsky equations. Across these five equation--framework settings, Fourier differentiation yields mean paired end-to-end training speedups ranging from $2.90\times$ to $18.52\times$ and reduces peak allocated graphics processing unit (GPU) memory by $68.7\%$--$94.1\%$. The final relative $L_2$ errors remain of the same order, with neither differentiation procedure showing a consistent accuracy advantage. For the one-dimensional periodic benchmarks considered here, Fourier spectral differentiation therefore provides substantially lower training time and memory usage than spatial AD while retaining comparable solution error, at the cost of requiring a uniform structured spatial grid.
Discrete visual tokenization, predominantly driven by vector, scalar, and product quantization, lacks a unified conceptual framework for understanding quantization tradeoffs. In this paper, we propose a unified rate--distortion perspective on modern discrete visual tokenization. By viewing quantization as lossy compression, we characterize the nominal fixed-length coding rate through token count and codebook size, and quantization error as the distortion. Within this framework, we resolve three central questions. First, we theoretically and empirically show that minimizing distortion, rather than maximizing codebook utilization, is the primary intrinsic objective for reconstruction fidelity, with a direct connection to the STE-induced gradient discrepancy. Second, we establish two critical fairness conditions for intrinsic quantization comparison: controlling latent feature statistics and enforcing identical coding rates. Third, under these conditions, we recover the VQ--PQ--SQ distortion hierarchy in modern visual tokenization and show empirically that modern VQ methods achieve the lowest distortion. This work provides a foundational rate--distortion reframing of modern discrete visual tokenization, resolves ambiguities in quantizer evaluation, and provides a controlled framework for isolating intrinsic quantization effectiveness under fixed-rate constraints.
Xianghong Fang, Wenlong Mou, Yuan Yuan et al.· 0 citations
To address the sequential and evolving nature of time series, the Online Time Series Forecasting (OTSF) task has been extensively studied in multiple domains. Existing research focuses on adapting to non-stationary environments by employing memory buffer-based retrieval strategies. However, we observe that such frameworks struggle with long-term adaptation and fail to generalize to unseen patterns. To this end, we introduce CoSPOT, an LLM-based online time series forecasting framework that leverages a pre-trained LLM as the backbone online forecaster, motivated by its strong few-shot capabilities. For efficient online adaptation, CoSPOT keeps the LLM frozen and employs compositional spectral prompts grounded in frequency-domain bases to guide the model with the overall distribution of the input, thereby substantially reducing the number of parameters updated during the online phase. Specifically, CoSPOT decomposes time series into frequency bases and composes the corresponding spectral basis prompts according to their amplitudes, allowing unseen patterns to be represented as new combinations of learned basis prompts. Our extensive experiments on real-world datasets demonstrate the superiority and practicality of CoSPOT across challenging online scenarios, including extended online phases and cross-dataset settings with substantial distribution shifts. Our code is available at https://github.com/seungyoon-Choi/CoSPOT.
Seungyoon Choi, Hyunchul Kim, Jae-Gil Lee et al.· 0 citations
We present TropicalCycloneNext (TC-Next), a multimodal deep learning model that forecasts tropical cyclone track and intensity at $6$-$24$ h leads by leveraging a foundation model's forecast fields of atmospheric kinematic and thermodynamic fields and GridSat infrared satellite imagery. Trained only on GraphCast forecasts over the Western Pacific (WP), yet reliant only on generic atmospheric variables, TC-Next on GraphCast lowers track error by $15$-$44\%$ and intensity error by a factor of $3$-$6$ relative to a conventional, rule-based tracker, TempestExtremes; applied without retraining to the forecast fields of Pangu-Weather and IFS HRES, it stays ahead of TempestExtremes on both. Applied zero-shot to the generic weather fields of WeatherNext Cyclones on the 2025 WP season, TC-Next attains lower intensity error at every lead time, and lower or comparable track error, compared to that model's specialized direct tracker in a deterministic comparison. Our ablation studies show that our multimodal model is able to utilize the additional modality to improve performance in tracking errors at every lead time and in intensity prediction at longer lead times.
Zhe Wang, Sijie Chen, Yiming Luo et al.· 0 citations
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Removing complete transformer layers preserves a standard serving architecture, but existing depth-compression methods can lose substantial quality, and the loss varies unpredictably across models. We introduce XMerge, a post-training method with two components. Cross-axis selection identifies a block with low relative-magnitude and angular hidden-state change, and local boundary reconstruction re-fits the adjacent surviving block to match the original two-block output. XMerge uses no task labels or end-to-end fine-tuning, and it introduces neither architectural changes nor additional inference-time parameters. Across seven Llama and Qwen backbones (0.5B-8B), five published baselines, and three layer-reduction levels, its advantage over baselines is largest at the most aggressive removal: at k=4 it ranks first on six of seven backbones on CORE (a 22-task aggregate) and, separately, on six of seven on MMLU (five of seven on both at once), while avoiding the large perplexity increases of several competing operators. In a task-level bootstrap, the 95% confidence intervals for the three largest CORE margins exclude zero; the remaining margins are consistent with ties. Across the 14 (model, regime) cells it is also the only evaluated operator that never collapses, ranking top-2 in both zero-shot and in-context regimes; on a first calibration probe (one backbone) it is the best-calibrated operator. Ablations show that local reconstruction provides most of the gain, while cross-axis fusion helps when the two selection axes disagree. The additional construction cost is recovered through per-token decode savings after roughly tens of thousands of requests.
Probabilistic multivariate time series (MTS) forecasting is crucial for modeling complex dynamical systems. However, existing diffusion-based methods rely on task-specific conditional paradigms that lack flexibility and struggle with inherent "information heterogeneity"--the significantly varying noise levels and evolutionary patterns across variables. To address this, we propose DynG-Diff, a variable-sensitive dynamic guidance diffusion framework for probabilistic multivariate time-series forecasting: (1) DynG-Diff adopts a two-stage separated training strategy and uses an unconditional diffusion backbone to model the joint distribution of multivariate time series. (2) DynG-Diff introduces a lightweight state-aware policy network that adaptively infers variable reliability from real-time noisy states and one-step denoising estimates, outputting a dynamic guidance strength matrix. (3) DynG-Diff mathematically formulates this dynamic weight as the local precision of the observation distribution, enabling precise guidance for high-confidence variables during inference while filtering out interference from anomalous noise. Extensive experiments on real-world benchmarks demonstrate competitive probabilistic forecasting performance against state-of-the-art conditional diffusion models and improved robustness under severe observation corruption.The implementation code is available at: https://github.com/TT-20011031/DynG-Diff
LLMs latent-state reasoning methods replace discrete intermediate tokens with continuous states, such as weighted mixtures of token embeddings, to retain multiple possible reasoning directions rather than committing to one. Yet pretrained language models often fail to preserve these mixtures. We study why through a combination of theoretical analysis and controlled empirical investigations on a variety of models. We identify three independent, distinct sources of failure. First, transformer architectures already distort mixture geometry, and training substantially amplifies this effect. Moreover, the failure can occur even if the model transports mixtures perfectly linearly: the softmax readout and autoregressive feedback form a dynamical system that either amplifies small differences until one component of the mixture dominates or contracts different mixtures until they become indistinguishable. We verify this theoretical prediction empirically: the observed transition between contraction and amplification occurs near the theoretical threshold derived by our analysis, and pretrained-model rollouts lie predominantly on the amplifying side. Finally, we generalize to mixtures of many components and show that exact preservation generally requires context-dependent correction, whose required dimensionality can grow with the number of components.
Large language model (LLM) agents for long-horizon interactive tasks typically follow a ReAct-style protocol, issuing one primitive action per LLM round. While this enables frequent replanning, it is inefficient for long-horizon tasks where many rounds are spent on routine action sequences. A natural alternative is to let the agent emit variable-length action chunks. However, naively training such policies with standard reinforcement learning fails: the agent either collapses to single-action behavior or over-commits to excessively long sequences. Both failures share a common root cause: the inability to learn chunk boundaries. We propose SPACE, which addresses this challenge by distilling chunk-boundary supervision from trajectory-induced programmatic skills. We induce two-level programmatic skills from successful trajectories, where subskill boundaries serve as direct chunk-boundary supervision. This temporal structure is then distilled into a primitive-chunk policy via hybrid on-/off-policy optimization with chunk-aware credit assignment. Experiments on ALFWorld and ScienceWorld show that SPACE improves success rates by 7.0%-31.3% over the strongest baseline in each setting while reducing average LLM decision rounds by up to 78.9%.
Yanting Yang, Can Jin, Jinman Zhao et al.· 0 citations
Class unlearning aims to remove a model's ability to recognize designated forget classes while preserving performance on retain classes. However, low forget accuracy after unlearning does not necessarily mean the class structure has been erased. Approximate unlearning methods can alter classifier decision boundaries while leaving recoverable structure in the representation. Prior work has shown that forget classes can be recovered, but existing approaches require real forget or retain samples, auxiliary data, or reference checkpoints. We study class relearning in a strictly source-free setting, asking whether a forget class can be recovered through a classifier-head update using only the unlearned model. Our approach rests on a theoretical analysis establishing a sufficient alignment condition under which a single gradient step on a synthetic probe set increases the expected logit margin of the forget class. Building on this, we propose a white-box Source-Free Relearning Audit (SFRA), which generates candidate embeddings in representation space and uses model-guided confidence filtering to construct high-confidence retain probes and low-confidence boundary-adjacent probes that are relabelled as the forget class. Gaussian sampling and Softmax confidence are used by default, while ablations with alternative proposal distributions and uncertainty criteria show that recoverability is not specific to these choices. To quantify recoverability, we introduce the Relearning Score (RS), which jointly measures forget-class recovery and retain-accuracy preservation, and report class-matched $\Delta$RS relative to a retrained reference. Experiments on CIFAR-10, CIFAR-100, and TinyImageNet with ResNet-18, ViT-B/16, and Swin-T show that several unlearning methods exhibit substantial source-free recoverability, and that for a subset of methods this recoverability exceeds the matched retrained reference.
Zahra Dehghani, Pablo Piantanida, Mohammadhadi Shateri· 0 citations
A compressed student has two shapes that need not agree: the weight it deploys at inference and the weight family its training can reach. We show that a state-of-the-art weight-inheritance distiller, Low-Rank Clone (LRC), deploys a full-width student MLP but ties training to a teacher-induced slice, leaving 62.5-81.4% of each deployed matrix's independent linear degrees of freedom unreachable-paid for at inference, never trainable. Our principle is one line: train what you deploy. From the identical LRC warm start, we make the training object the entire deployed matrix, with no change in deployed shape, deployed parameter count, or inference FLOPs, via two mergeable realizations (Dense-LRC and CORE-LRC) that both collapse to one deployed weight. This recovers stranded capacity: taking the stronger realization per teacher, +2.36/+2.71/+10.45 Avg9 over matched-budget plain-LRC baselines across three teachers (Llama3.2-3B, Llama3.1-8B, Qwen2.5-3B), with the largest gain on the widest teacher (Qwen), where it reaches the original recipe's approx. 20B-token accuracy at 10B tokens (2x token efficiency); there the strictly same-lineage arm still recovers +6.39, the fully controlled figure. Controls strongly support attributing the gain to the enlarged reachable set, rather than to added parameters or the recipe. From approx. 10B distillation tokens plus a short SFT, a half-parameter 1.5B student matches its approx. 9T-token teacher's 9-task macro-average, within evaluation noise and with a residual MMLU deficit, and a 2.7B student beats Meta's own official compression of Llama3.1-8B at ~900x fewer compression tokens (a token count under unmatched recipes, not a compute claim). All results are from single-seed runs on the LRC backbone.
Wen-Hui Chen, Zhi-Feng Li, Jie Zhou et al.· 0 citations
Magnetic core loss originates in the hysteresis loop: the energy dissipated per excitation cycle equals the loop area, and frequency, temperature, and waveform shape set the loss by reshaping the loop geometry. Most existing models let these conditions act only on a terminal scalar - empirical equations fold them into fitted exponents, and data-driven predictors append them to encoded features - so no intermediate hysteresis representation remains for the conditions to reshape. This paper proposes CAHR-Net, a condition-adaptive hysteresis reconstruction network that injects the operating conditions where they physically act. It preserves the interpretable chain from flux density waveform to magnetic field reconstruction, loop-area integration, and power loss estimation, and uses feature-wise linear modulation to inject frequency, temperature, and waveform statistics into the intermediate reconstruction representation. A matched large-batch training protocol based on AdamW, cosine scheduling, and a staged reconstruction-to-power-loss objective is also reported, because the modulation pathway takes effect only within it. On the MagNet final A-E material protocol, CAHR-Net attains an average p95 relative error of 6.89% with only 1874 parameters, the lowest among all compared methods, together with a lower worst-material p95 than the strongest black-box solution at about 48x fewer parameters; it reduces the average p95 of the physical reconstruction backbone from 7.47% to 6.89% and the p95 of material D, the most difficult material, from 16.40% to 14.87%. Ablation and condition-slice analyses attribute the improvement to the coupling of physical loop reconstruction, structured condition modulation, and the matched optimization trajectory.
Data-driven process simulation aims to generate realistic case trajectories from historical event logs without requiring an explicitly specified model of the underlying dynamics. Deep sequence models can capture complex temporal dependencies through next-activity probabilities and conditional time distributions. However, event logs provide only a partial view of the underlying process state, often recording activity completions without the corresponding service-start times. Consequently, the same observed process history may be consistent with multiple plausible latent process conditions, whereas standard recurrent models compress each process prefix into a single deterministic recurrent state. We propose a Unified Particle Filter LSTM (Unified PF-LSTM) that maintains and sequentially updates a weighted set of recurrent-state hypotheses. We summarize this particle belief using its weighted mean and learned features based on the moment-generating function. The resulting representation is used to predict a categorical distribution over the next activity and conditional quantiles of the current activity's sojourn time. The framework is trained end-to-end from event-log data and evaluated on three real-world emergency department datasets. The results show that the proposed framework consistently outperforms the considered data-driven baselines in reproducing routing, duration, and system-level behavior across all datasets, with particularly strong gains in settings where complex process dynamics are only partially reflected in the available event logs.
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
A new method for surgically removing training examples from a model reveals that as datasets grow, the link between what a model learns and what it produces dissolves.
