Trainable Parameter

We study how physical-state inputs affect a 0.8B hybrid language model adapted for manipulation with 6.2M trainable parameters. Six conditions are trained on three LIBERO-Spatial tasks and evaluated over three seeds and 540 held-out rollouts. Conditioning recurrent decay gates on geometric increments yields 28.9% success, compared with 36.7% when those increments are shuffled during training and 24.4% without explicit object/goal geometry. Both geometry policies receive correct inputs at evaluation. A token adapter using the same increments scores 27.8%; differences vary across seeds and remain inconclusive. Token-clock conditioning scores 11.1%, including one seed that fails to converge. In separate robustness tests, a state-only relative-coordinate policy retains 7/10 success under frame relabeling, whereas all four tested visual policies fall to at most 3/20 after a 5 cm object displacement. These results show no reliable advantage from training-time geometric alignment under this recipe and illustrate the gap between coordinate invariance and physical-layout generalization. Episode records, seed-level analyses, and figure-generation code accompany the paper.

World models have made remarkable progress in action-conditioned future prediction for embodied agents, yet still struggle to model physically plausible interactions. Existing approaches address this limitation by constraining the generation process with external representations encoding motion, geometry, or semantics. Obtaining these spatiotemporally dense representations typically requires auxiliary estimators or manual annotations, limiting training scalability. We instead revisit the training objective and identify a supervision-allocation mismatch under the globally averaged mean squared error (MSE) denoising objective: prevalent static content dominates the optimization signal, leaving sparse dynamic-object regions critical to interaction generation disproportionately under-supervised. Motivated by this observation, we introduce IMPACT, a scalable Interaction-aware Model training framework with Prior-guided Attention Calibration and Targeting. IMPACT uses cross-attention associated with manipulated-object tokens as an internal spatiotemporal prior for action-conditioned changes. It samples candidate regions from this prior, calibrates them with detached local prediction errors to construct an interaction map, and uses the map to reweight denoising supervision, requiring neither external representations nor inference-time modifications. Extensive experiments on robot-arm and human-hand manipulation, spanning diverse control modalities and DiT backbones, show that IMPACT consistently outperforms the corresponding MSE-trained baselines, improving interaction fidelity, physical plausibility, and visual quality.

The clinical management of gynecological diseases often relies on medical imaging for diagnosis, treatment planning, and follow-up. Segmentation in this setting is challenging because successive tasks may differ in imaging modality, target anatomy, pathology, and annotation structure. Continual learning allows models to adapt to new tasks without simultaneous access to previous datasets. However, when successive tasks differ substantially, learning a new task can degrade performance on earlier ones, a problem known as catastrophic forgetting. Understanding where adaptation disrupts previous knowledge can help guide the design of more targeted continual-learning strategies. We investigate how forgetting changes as different parts of an encoder--decoder network are allowed to adapt. We progressively expand the trainable region of a 3D nnU-Net backbone from the bottleneck toward input- and output-proximal blocks. Under a shared learning rate, adaptation near the bottleneck largely preserves previous-task performance but provides limited current-task learning, whereas broader adaptation improves current-task performance but sharply increases forgetting. This trade-off persists even when the average change in trainable backbone parameters is approximately comparable. Assigning different learning rates to different blocks substantially reduces forgetting when part of the backbone is trainable, although this changes both the size and location of the updates. Forgetting still increases as more blocks are trained and remains severe when the full backbone is updated. These results show that forgetting depends not only on how much the model changes, but also on which parts of the model are allowed to change.

Variational quantum circuits have been central to many proposed near-term applications of quantum computing, but a growing body of evidence suggests that trainability and quantum advantage are fundamentally at odds: ansätze expressive enough to resist efficient classical simulation tend to exhibit barren plateaus, while structures that provably rule out barren plateaus typically render them classically simulable. We propose a stacked linear combination of unitaries (S-LCU) as a variational ansatz which provides a tunable trade-off between barren plateaus and classical simulability. Using a diagrammatic analysis, we bound the loss-landscape variance of the Free Fermion S-LCU, whose elements are fermionic Gaussian unitaries. We prove a variance lower bound of $Ω(1/(n k^{3l}))$, with a simulation cost of $O(k^{2l} n^3)$ using the best known classical algorithm, compared to a quantum gate complexity of only $O(lkn^2)$. The number of layers $l$ serves as a single dial that trades computational complexity against the rate of cost concentration. This offers practitioners a systematic method for constructing ansätze with a complexity-trainability trade-off that best suits their application and hardware.

A central challenge in quantum machine learning is understanding the scaling behavior of parameterized quantum circuits (PQCs). In particular, it remains unclear how their performance on unseen data changes as the number of trainable parameters increases. Prior works have derived formal generalization guarantees for quantum models, but it is well-known that many such results do not fully characterize generalization behavior in practice. In this work, we show that gradient-based PQCs can exhibit improved performance on unseen data as model size increases, displaying the phenomenon of double descent. This contrasts with the traditional view that larger models lead to degraded generalization. We provide analytical results rigorously underpinning this behavior by leveraging add-one-in perturbation techniques and spectral properties of random matrices. We support these results with numerical experiments on re-uploading PQCs across several data sets and training set sizes, consistently observing the predicted double descent behavior. While other obstacles on the path toward practical quantum machine learning remain, our finding that deeper parameterized quantum circuits do not necessarily exhibit degraded performance provides reasons for cautious optimism.

A LoRA adapter is a few megabytes that almost everyone treats as a skill rather than a record of the data behind it. We put that assumption on a scale. Extending compression-based memorization analysis to the frozen-base setting, we measure directly, in bits, how much a low-rank adapter writes into a model it never changes. The answer is both smaller than full fine-tuning and less lawful than parameter counting would predict. Adapters store a couple of bits per trainable parameter, well short of a full model's budget, but that figure turns less on how many parameters an adapter carries than on where they sit. Move the same parameter budget from attention into the MLP and it holds nearly twice as much; strip the frozen base of its structure and the capacity all but disappears. Applied to realistic fine-tunes of Qwen2.5, the same instrument shows privacy leakage rising with the bits an adapter writes rather than the parameters it nominally has, and it draws a clean line between supervised and reinforcement learning: the secrets that supervised fine-tuning copies down verbatim, an adapter trained on verifiable rewards never records. Measuring what fine-tuning writes, rather than attacking it after the fact, turns a piece of folklore into a quantity one can design against.

Active visual agents solve fine-grained image tasks by interleaving reasoning with image-grounding actions across multiple turns. However, deployment-time rollout budgets are rarely fixed: some requests permit long rollouts, while others require the agent to act under a tight turn limit. Existing methods train the policy as if the rollout budget were hidden, so when the available budget is smaller than the trajectory the agent prefers, the interaction is often truncated before any valid answer is produced; we term this failure \emph{catastrophic truncation}. To overcome this challenge, we present AdaTurn, a budget-aware framework that conditions the agent on the allowed number of turns and explicitly trains the boundary behavior induced by the budget. Our key component, Forced-Answer DAPO (FA-DAPO), converts the over-budget event from a masked or penalized failure into a trainable final-decision step, teaching the model to synthesize partial evidence when further tool use is no longer possible. We further randomize rollout budgets during both training and inference and introduce a load-balanced scheduler that makes such operations practical. AdaTurn substantially improves low-budget accuracy, for example raising VisualProbe-Medium from 36.7% to 47.6% at four turns, while preserving strong scaling at larger budgets and transferring effectively to multiple backbones and general multimodal benchmarks.

We present a theoretical framework to explain the emergence of inductive reasoning abilities in Transformer language models. While previous works on Transformer learning dynamics have so far been mostly tied to specific tasks, we study a generalized class of inductive tasks that unifies several synthetic tasks known in the literature, including in-context n-grams and multi-hop reasoning. In this class, we theoretically prove that the training dynamics of attention models can be confined to a highly interpretable, low-dimensional invariant manifold. On this manifold, the learning dynamics are captured by a handful of interpretable coordinates rather than millions of parameters, making both theoretical and empirical analysis more tractable. Using this framework, we characterize how data statistics govern the competition between in-context and in-weights learning, we study how random initializations determine the `winning' circuit when multiple solutions are possible, and we demonstrate that the coordinate frame associated with the manifold can be used to automatically detect which circuits have been learned in trained models. By casting circuit formation as a low-dimensional dynamical phenomenon, we take a step toward a predictive theory of how Transformers learn.

Recent work identified Super Weights, individual parameters whose removal degrades model performance by orders of magnitude. We show that this degradation due to pruning Super Weights does not universally apply to all LLMs. Furthermore, if these parameters are so important, Super Weight-aware training should be effective. We show the opposite. Training Super Weights in isolation (100 to 8,192 parameters) drops accuracy to random-guessing levels on both OLMo-1B and OLMo-7B, and expanding to local neighborhoods of up to 36K parameters provides no improvement. The failure is specific to Super Weight coordinates: training an equal number of randomly chosen positions in the same down_proj layers instead improves over the baseline, so the collapse comes from targeting Super Weights, not from sparsity itself. Vanilla LoRA, updating every position in attention weight matrices through low-rank structure, succeeds with only 0.16% of parameters, and applying the same low-rank update to down_proj succeeds as well. A 10-seed ablation confirms that constraining LoRA updates at positions corresponding to Super Weight coordinates yields statistically indistinguishable results. These findings establish that parameter importance does not imply parameter trainability in isolation, and that effective fine-tuning relies on structured decompositions over entire layers rather than targeting individually important weights.

We present MMD-Reg, a novel correspondence-free approach to point-cloud registration that is differentiable and has linear computational complexity in the number of points. We model registration as a nonlinear least-squares problem based on the Maximum Mean Discrepancy, approximated using random Fourier features. The resulting objective can be solved efficiently with standard methods such as Levenberg-Marquardt, and the solution is differentiable via the implicit function theorem. This allows MMD-Reg to be used as a differentiable optimization layer within end-to-end trainable models, supporting registration under challenging conditions such as poor initial alignment and partial overlap. We demonstrate this Neural MMD-Reg formulation by integrating the layer with a set transformer, training the resulting model in supervised and unsupervised settings, and comparing its performance against recent learning-based methods. We also evaluate standalone MMD-Reg, comparing its accuracy and scalability against widely used non-learning-based registration methods.

Training-free neural architecture search promises efficient discovery of high-performance networks without costly training. However, existing zero-cost proxies rely on fragmented heuristics that fail to capture the fundamental question: what makes an architecture trainable? This paper introduces Intrinsic Trainability (InTrain), a unified theoretical proxy that formalizes trainability as an architectural invariant emerging from two synergistic components: geometric capacity and optimization resilience. We operationalize intrinsic trainability through analysis of neural information processing. Geometric capacity is quantified via the participation ratio of activation covariance eigenspectrum, capturing the effective dimensionality of representation manifolds. Optimization resilience is measured through cumulative gradient health, assessing the robustness of backpropagation across network depth. InTrain synthesizes these dimensions through a scale-invariant multiplicative coupling, which we hypothesize is essential for capturing their synergistic, non-additive relationship. Extensive experiments on standard NAS benchmarks and search spaces demonstrate that InTrain achieves ranking correlations on par with state-of-the-art ensemble-based proxies and outperforms other single-metric methods.

Text-conditioned 3D human motion models now synthesize plausible motions from prompts, but practical animation and embodied-agent workflows rarely stop at text: a character may need to follow a sketched root path, hit an end-effector target, or satisfy a multi-joint trajectory while still preserving the gait, style, and intent described by language. This exposes a control trade-off. A trajectory controller should be precise without overwriting the pretrained text-conditioned motion prior, yet existing solutions either duplicate large portions of the generator to regain per-layer control access or move much of the cost to test-time optimization. We introduce KV-Control, a compact attention-side control interface for frozen masked text-to-motion transformers. The key idea is to make geometric constraints available as memory inside self-attention rather than injecting them through a global pose token or enforcing them only at the output side. To support this interface, we co-design a part-tokenized motion substrate and controller: \textbf{PartVQ} learns anatomy-aligned part codebooks, T-Concat exposes each frame--part token as an attention-addressable site, and KV-Control injects control-conditioned key/value memories at every self-attention layer while preserving the pretrained query stream, text cross-attention, FFN, and all backbone weights. The resulting adapter adds only trainable injection parameters atop a shared trajectory encoder, yet tracks root and multi-joint constraints with sub-centimeter accuracy under the inherited refinement protocol while retaining text-conditioned motion quality. KV-Control reframes trajectory conditioning as lightweight memory retrieval, providing a small, precise, and transparent control interface for text-to-motion generation.

Trainable input embedding tables are a standard component of modern language models. We ask whether they are actually necessary at the input interface. For a vocabulary of size $V$, exact token identity requires only $K=\lceil \log_2 V\rceil$ bits. We replace the usual trainable $V\times d_{\text{model}}$ input embedding matrix with fixed minimal binary token codes and a zero-parameter lift to model width. In our main setting, $V=65{,}536$, so $K=16$, and tokens are represented by fixed 16-dimensional binary codes tiled to $d_{\text{model}}=1024$. We also evaluate a fully table-free variant in which codes are generated from token IDs on the fly and randomly recoded by an invertible affine transform over $\mathbb{F}_2^K$. Across matched 32-layer decoder-only models trained on approximately 17B tokens and evaluated over three independent training seeds, fixed minimal codes achieve comparable held-out validation perplexity to a standard learned-input baseline while removing 67.1M trainable input parameters. The fixed-code runs have a lower mean validation perplexity in our experiments, 2.36 versus 2.44, but the observed gap is within the measured seed-to-seed variation of 4.8%; we therefore interpret the result as evidence that the trainable input table is not necessary, rather than as a statistically resolved superiority claim. The table-free affine-recoded variant remains close at 2.39 despite a slightly shorter training run. These results show that, in this regime, a trainable input embedding table is not necessary for useful language modeling. The output projection remains standard and trainable.

Transformers have revolutionized machine learning and deploying attention layers in the model is increasingly standard across a myriad of applications. Further, for large models, it is common to implement Low Rank Adaptation (LoRA), whereby a factorized parameterization of them is trained, to achieve a surprisingly beneficial accuracy-size trade-off. In this work, via a unified framework we rigorously establish trainability of such models under stochastic methods. We prove that for any mild regularization, the empirical regression loss on a attention layer and LoRA on a shallow neural net, both induce Poincaré inequality for the corresponding Gibbs' measure. Then it follows via invoking recent results that a certain SDE, which mimics the SGD, minimizes the corresponding losses. In both the cases, our first-of-its-kind results of trainability on attention and nets, do not rely on any assumptions on the data or the size of the architecture.

LoRA-MoE has emerged as an effective paradigm for parameter-efficient fine-tuning, combining the low training cost of LoRA with the increased adaptation capacity of Mixture-of-Experts (MoE). However, existing LoRA-MoE frameworks typically adopt a fixed and uniform expert configuration across heterogeneous Transformer modules (\eg, attention query/key projections and MLP gating networks), ignoring their distinct functional roles and capacity requirements. This design leads to localized over-provisioning, redundant trainable parameters, and unnecessary optimizer-state overhead. Moreover, prior methods enforce load balancing among experts throughout training. Although beneficial in the early stage, this constraint becomes restrictive once routing patterns stabilize, limiting expert specialization on downstream tasks. In this paper, we propose DMEP, a novel LoRA-MoE fine-tuning framework based on Dynamic Module-wise Expert Pruning. DMEP tracks expert utilization during training and physically removes low-utility experts on a per-module basis, yielding a more compact expert structure tailored to different modules. The pruned model then continues training without the load-balancing constraint, freeing the remaining experts to focus entirely on the downstream task and develop specialized expertise. By jointly adapting module-wise expert capacity and eliminating unnecessary balancing, DMEP improves both parameter efficiency and training efficiency. Extensive experiments on multiple reasoning benchmarks show that DMEP reduces trainable parameters by 35%--43% and improves training throughput by about 10%, while maintaining or surpassing the downstream reasoning accuracy of uniform LoRA-MoE baselines.

Product mapping, the task of deciding whether two e-commerce listings refer to the same product, is a core problem for price monitoring and channel visibility. In real marketplaces, however, sellers frequently inject promotional keywords, platform-specific tags, and bundle descriptions into titles, causing the same product to appear under many different names. Recent LLM-based and multi-agent frameworks improve robustness and interpretability on such hard cases, but they often rely on expensive external APIs, repeated retrieval, and complex inference-time orchestration, making large-scale deployment costly and difficult in privacy-sensitive enterprise settings. To address these issues, we present EPM-RL, a reinforcement-learning-based framework for building an accurate and efficient on-premise e-commerce product mapping model. Our central idea is to distill high-cost agentic reasoning into a trainable in-house model. Starting from a curated set of product pairs with LLM-generated rationales and human verification, we first perform parameter-efficient fine-tuning (PEFT) on a small student model using structured reasoning outputs. We then further optimize the model with Reinforcement Learning (RL) using an agent-based reward that jointly evaluates output-format compliance, label correctness, reasoning--preference scores from specially designed judge models. Preliminary results show that EPM-RL consistently improves over PEFT-only training and offers a stronger quality--cost trade-off than commercial API-based baselines, while enabling private deployment and lower operational cost. These findings suggest that reinforcement learning can turn product mapping from a high-latency agentic pipeline into a scalable, inspectable, and production-ready in-house system.

Generative image models can now produce high-quality images, follow complex instructions, and support precise edits, but they still struggle to preserve who or what is being depicted. When generating or editing images of a specific subject, identity may drift as the pose, expression, appearance, viewpoint, or surrounding scene changes. Existing subject-driven methods make fundamentally different choices about where identity is represented: through the input context (GPT-Image-2, NB2), as trainable subject-specific model parameters (LoRA), or as a persistent identity layer (PHOTA IDENTITY) reusable across generations and edits. We systematically benchmark these paradigms across subject-driven generation, editing, restoration, and multi-subject settings, with tasks designed to increasingly stress identity preservation. Our results show that identity preservation remains a distinct limitation of current generative foundation models: strong image quality and instruction following do not necessarily imply strong identity fidelity, and identity degradation becomes more pronounced under iterative edits, small subject scales, severe image degradation, and multi-subject composition. Persistent identity substantially reduces this degradation across generation, editing, and restoration, consistently improving identity preservation when applied to different foundation models while maintaining comparable instruction adherence and perceptual image quality. These results suggest that identity does not simply emerge from increasingly capable generative models, but can instead be represented as persistent subject knowledge that is composed independently with the underlying generative model.