Feed-Forward

Structured pruning of large language models (LLMs) offers hardware-efficient compression, yet existing methods require calibration data, gradient computation, or large auxiliary policy networks at pruning time. LILA (\emph{Latent-Informed Layer Analysis}) scores neuron importance via the Kolmogorov--Smirnov (KS) distance between empirical singular value distributions of the full and neuron-ablated feed-forward network (FFN) weight matrix, providing a closed-form spectral rule requiring no training, calibration data, or auxiliary network. Without any fine-tuning, LILA surpasses PruneNet (45M-parameter RL policy) by 1.57pp in zero-shot accuracy on LLaMA-2-7B at 25% sparsity, and outperforms WikiText-2-calibrated SliceGPT by up to 6.0pp across all sparsity levels, while preserving the original architecture. After one epoch of LoRA recovery fine-tuning, LILA achieves highly competitive performance, matching the heavily calibrated SliceGPT baseline to within a 0.48~pp margin across LLaMA-2-7B and Phi-2, despite using zero calibration data. A Neural Tangent Kernel analysis confirms a 22$\times$ reduction in functional distortion versus random pruning, providing theoretical grounding for the spectral importance criterion. Finally, extending LILA to dynamically allocate sparsity budgets via KS-scores yields state-of-the-art generative preservation at moderate compression, while uncovering fundamental single-layer architectural bottlenecks at higher compression regimes.

We present FIRE3D, a unified framework that takes a single RGB image or casual RGB video and transforms it into simulation-ready 3D scene assets for games and interactive applications in under a minute. At the core of FIRE3D is a feed-forward, end-to-end network that predicts a compositional scene representation from posed RGB-D observations estimated from the RGB capture, including the 6-DoF pose, bounding box, mesh, and texture for every object. By modeling the scene as a collection of discrete entities, FIRE3D produces amodally complete and simulation-ready environments where objects are physically decoupled and ready for interaction. Our framework requires no test-time optimization, runs orders of magnitude faster than prior interaction-ready methods, and provides object-level completeness beyond existing feed-forward 3D approaches. We demonstrate competitive or state-of-the-art results across pose accuracy, geometry completeness, and texture quality across various datasets while being orders of magnitudes faster. Project page: https://xiahongchi.github.io/Fire3D/

Recent work identifies a mid-depth band of verbalisable, causally potent representations in a standard feedforward transformer --- a functional analogue of a global workspace. Whether the same workspace functionality emerges when depth is implemented through recurrence rather than a stack of distinct layers remains unknown. Looped and depth-recurrent transformers provide a direct test of this question because they reuse the same weights across depth. We extend the Jacobian lens to iterated architectures using a virtual-unrolling adapter. We apply the full workspace suite --- lens fitting, readout, and eleven causal experiment families --- to Ouro-2.6B (48 layers looped 4 times, deeply supervised) and Huginn-0125 (a 4-layer core recurred 16 times, trained for latent reasoning), using Qwen3.6-27B (64 untied layers) as the standard baseline. We find that a workspace forms in the iterated part of each architecture, but that recurrence changes how it can be accessed. Ouro reconstructs workspace content in every loop, and linear transport cannot carry that content across loop boundaries; writes and ablations must therefore span every remaining loop. Huginn carries content forward across all sixteen recurrences, while reads, writes, and ablations act only within a sliding window of roughly two recurrences. Whether newly injected content can be verbalised tracks explicit per-iteration supervision; whether existing content can be steered does not.

Retrieval-Augmented Generation (RAG) is highly sensitive to retrieval noise: when retrieved documents mix informative and irrelevant context, LLMs are easily distracted, leading to hallucinations. To overcome this, we propose SCoNE (Selective Context-aware Neuron Editing), a training-free model editing approach that improves retrieval noise robustness by selectively strengthening context-aware FFN neurons that are identified by both high attribution and high cross-input variability. SCoNE requires only a small number of mining samples, no fine-tuning, and no inference-time overhead. Across various knowledge-intensive question-answering benchmarks and two LLM backbones, SCoNE consistently outperforms competitive baseline methods. Our code is available at https://github.com/HYU-ARK-Lab/SCoNE.

Feed-forward 3D foundation models reconstruct perspective scenes in one pass. Satellite photogrammetry needs a different product, one that domain adaptation alone does not deliver: dense surface height in an absolute geodetic frame under non-central rational polynomial cameras (RPCs). Perspective-pretrained features are not reliably observable along RPC height rays, absolute elevation carries a low-order height--datum gauge exchangeable with sensor bias to first order, and monocular and multi-view cues fail in different regions. \method{} treats all three. Lightweight ray-consistent adapters make a frozen backbone matchable along native RPC rays. An explicit datum mechanism separates relief from absolute level and is equivariant to the vertical origin by construction, so one trained model serves zero-, one-, and sparse-control inference. Calibrated inverse-variance fusion combines the two relief streams. \bench{}, our absolute-frame benchmark of eighteen systems across in-domain, cross-dataset, and cross-city tiers, scores absolute placement without registration or test-reference leakage. On 26 held-out US3D tiles, \method{} attains $2.99$,m absolute MAE at $91.9\%$ coverage, improves completeness-aware accuracy by $46.4$ points over the strongest compliant feed-forward baseline, remains the most accurate such system under both transfer shifts, and runs in $24$,s model-forward time per tile. Code and models will be released at https://github.com/HIT-SIRS/GeoRay

We show that smooth two-layer feed-forward networks (FFNs) expose an additional structural model extraction channel under a chosen-input raw-output oracle at the FFN branch; consider transformer FFN branches with GELU or SiLU activations under chosen-input raw-output access, without access to parameters, gradients, or internal activations; exploit a second-order leakage channel in which projected input Hessians form different mixtures of the same hidden symmetric rank-one factors induced by the FFN input weights. We formalize resulting Hessian collection as a partially symmetric decomposition to establish conditions for local identifiability and stability to exploit vector-output stencil reuse to reduce the structural query cost by a factor of 16. On independently trained CIFAR-10 vision transformers, only 16 projected Hessians, corresponding to 8193 black-box queries, recover the hidden FFN directions with average absolute cosine alignment above 0.91, with 86.7.1 % of GELU and 91.1 % of SiLU directions exceeding 0.90 alignment. Recovery remains high across independently trained models, repeated extraction runs, and all transformer blocks. The recovered structure supports functional extraction too. Keeping the recovered directions fixed and fitting only the remaining FFN parameters yields high-fidelity substitutes with more than 92 % top-1 agreement, while test accuracy remains within 1.24% and 0.57% of the GELU and SiLU targets. Output rounding and Gaussian noise substantially reduce recovery under a fixed attack configuration, but adapting the finite-difference step restores average alignment to 0.9188 and 0.9081. This is an end-to-end path from black-box second-order observations to hidden FFN-structure recovery and functional replacement. Under the stated oracle model, smooth FFN curvature exposes internal parameter geometry that behavioral fidelity alone cannot reveal.

Existing feed-forward 3D reconstruction methods typically process a bounded number of images and recover cameras and geometry in local or internally normalized frames. Extending them to large-scale UAV mapping requires scalable multi-chunk processing and reliable aggregation, while full Sim(3) alignment can become unstable for near collinear trajectories. We present GeoFF3D, which combines a coordinate-anchored model with a spatial large-scale reconstruction framework (SLRF). The model uses georeferenced camera translations and optional geometric priors to predict camera poses and dense point maps directly in a gravity-aligned Z-up metric frame. SLRF partitions images into spatially overlapping chunks, propagates shared-view priors, and aggregates local reconstructions hierarchically, while remaining applicable to different bounded-view models. Across nine aerial mapping blocks, GeoFF3D achieves the best average reconstruction quality, improving F@5 from 0.829 for Pi3X + SLRF to 0.877. On long UAVScenes sequences, it reaches 0.848, compared with 0.687 for Pi3X + SLRF and 0.451 for the strongest evaluated SLAM/streaming baseline. GeoFF3D reconstructs 2,000 images in approximately five minutes, demonstrating scalable and robust large-scale UAV reconstruction.The code is available at https://github.com/yanxian-ll/GeoFF3D.

We consider for an arbitrary fixed $ρ$ and for each positive integer $n$ a multilayer feedforward artificial neural network with $ρ$ layers, $n$ neurons in the first layer (the input layer) and only one neuron, the output neuron, in the last layer. Very roughly formulated, the main result is that if the distribution of weights of connections from a layer to the next are, for all large $n$, approximated well by a fixed continuous (but otherwise arbitrary) curve which does not depend on $n$, and if the values of the $n$ input neurons are independently and identically distributed with a continuous probability density function, then there is a number $ψ$ such that for all $\varepsilon > 0$ the probability that the value of the output neuron is in $[ψ- \varepsilon, ψ+ \varepsilon]$ tends to 1 as $n$ tends to infinity.

We establish convergence guarantees of gradient descent for general feedforward neural networks of arbitrary width or depth, with no special requirements on the initialization or dataset. We only assume that the activation functions are Lipschitz smooth, Lipschitz continuous, and linearly bounded--- properties that hold for linear, tanh, softplus, and sigmoid activation functions. For the loss function, we require that it is Lipschitz smooth in the model outputs, which is true for mean-squared error. The key theoretical insight is that the Lipschitz properties of the activation functions are partially preserved even through repeated compositions, leading to a novel generalized Lipschitz smoothness condition where the change in gradient is upper bounded by the change in the parameter space, multiplied by polynomial terms of the parameter norms at both endpoints. This type of condition holds for both the model function and the loss function, enabling a descent lemma where the loss decreases as long as the learning rate is small enough with respect to the parameter norms. By ensuring that the parameter norms do not grow too quickly to infinity, we prove that the minimum squared gradient norm converges to zero in $T$ iterations at rate $O(1/T^{1/L})$ for an $L$-layer neural network.

3D scene reconstruction, modeling, and rendering are highly relevant for numerous tasks, and 3D Gaussian splatting has become a standard choice in this context. Its feed-forward variants provide fast reconstruction from sparse input views but often produce per-pixel primitives, leading to highly redundant and thus inefficient representations. We present a structure-aware merging pipeline that takes per-pixel primitives from any feed-forward method and consolidates them into a compact, content-adaptive Gaussian set while largely retaining visual quality at just $\frac{1}{20}^\text{th}$ of the Gaussians of a per-pixel method. We group spatially coherent Gaussians of similar appearance into variable-size clusters via adaptive superpixel segmentation guided by a saliency map, which allocates fine segments to textured regions and coarse segments to homogeneous areas. We compress each cluster into a compact latent representation through a learned encoder, then match and consolidate representations across views based on geometric overlap and feature similarity via a learned merger. A level-of-detail decoder then produces the final Gaussians at a controllable resolution, enabling a flexible quality-efficiency trade-off at inference. As a post-processing module, the pipeline is backbone-agnostic, leveraging the strengths of existing feed-forward methods. This leads to better and more robust quality than achieved by previous approaches that target a reduction in primitive count, while providing a highly compact representation, that can be rendered efficiently.

Multimodal Large Language Models (MLLMs) have shown strong multimodal instruction-following ability, but adapting them to diverse visual-language domains typically assumes centralized data access and costly joint training. This is restrictive when data is distributed across private, domain-specific, or permission-limited clients. To this end, we propose DistMoE, a mixture-of-experts (MoE) approach for distributed visual instruction tuning. In each layer of the language decoder it augments the public feedforward network (FFN) with a client-specific private FFN expert, with the goal to acquire domain-specific knowledge. However, independent expert training causes the private FFNs to learn representation of different scale and magnitudes, making merging the experts difficult. To reduce client-specific drift, we introduce a public-anchored expert composition stage that updates only routers and lightweight private projection adapters on a mix of local client data and public data, via an isotropic regularization loss, therefore making it cross-client rehearsal-free composition. During inference, DistMoE performs modular routing over public and private experts, enabling token-wise domain composition without explicit domain labels. Experiments across diverse visual-language benchmarks show that DistMoE enables flexible expert reuse, effective domain adaptation, and competitive performance while preserving modular control over client-specific knowledge. Codes are available at https://github.com/mainaksingha01/DistMoE.

Vision foundation models (VFMs) such as DINO are pretrained for single-image representation, whereas remote sensing change detection requires reasoning over a bi-temporal pair. Existing VFM-based methods usually encode the two images independently and compare them only afterward, leaving the VFM backbone unaware of cross-temporal relations. To bridge this mismatch, we present AdaDINO, a pair-aware in-backbone adaptation framework that equips a frozen DINO encoder with bi-temporal interaction for efficient change detection. Its core component, Change-aware Gated Local Adaptation (CGLA), couples the two streams after selected frozen blocks and injects a shared temporal residual into them with opposite signs, enhancing genuine change responses while preserving the pair midpoint. Batch-Shared Chunk Selection (BSCS) further reduces feed-forward network (FFN) computation by retaining a batch-shared subset of channel chunks that can be executed as a compact dense FFN. A CGLA-Prior-Guided Refinement (CPGR) decoder reuses encoder-side change responses for coarse-to-fine prediction. Experiments on four remote sensing change detection benchmarks show that AdaDINO achieves competitive or superior performance against VFM-based baselines, with the largest gain on the category-agnostic SYSU-CD dataset. With 62.5% of the FFN hidden width removed, AdaDINO still achieves an F1 score of 85.29% on SYSU-CD while delivering a 1.41$\times$ throughput speedup. The code will be released.

Attention-only dynamical theories model Transformer residual directions as particles aggregating on a sphere. We extend this framework by incorporating the feed-forward network (FFN) term as a local steering field acting on each token state. The resulting theory predicts that the tangential component of the FFN field is necessary for motion in residual-direction space, that critical residual directions correspond to nonlinear projective equilibria, and that a commutator defect determines when a finite attention--FFN block can be accurately approximated by a parallel, additive flow. Across GPT-2, Pythia, Mistral, and Llama models, the extended theory improves one-step angular prediction relative to an attention-only baseline, with the contribution of the FFN increasing from GPT-2 to Llama-3-8B. Intervention experiments show that retaining only the tangential FFN component preserves most model quality, whereas retaining only the radial component causes performance to collapse. The tangential component also preserves output diversity under aggregation pressure. As a practical application, layers with small commutator defects can be approximately parallelized with only a modest increase in loss, whereas layers with large defects degrade rapidly. These findings support the interpretation of FFN layers as directional steering fields that shape Transformer residual geometry and govern the feasibility of block-level interventions.

Feed-forward networks (FFNs) account for a large fraction of Transformer parameters, yet their hidden width is usually constant across depth. We ask whether this capacity can instead be allocated from a forward-pass measurement of layer behavior. We view each FFN as transporting a cloud of token representations and quantify the induced geometric change using correspondence-preserving shift, Gromov-Wasserstein distortion, and degree-one persistent homology under raw and scale-normalized metrics. A layerwise approximation surrogate yields an exact fixed-budget optimizer. Across seven pretrained language models, raw Euclidean work largely tracks residual-norm growth, whereas normalized work is predominantly front-loaded. Gromov-Wasserstein work is more consistently associated with perturbation-based layer sensitivity than the finite-sample topological estimate. In paired 128M and 256M training runs, several normalized-work schedules reduce mean validation loss relative to both uniform width and a hand-designed cosine taper. With the amplified paired differences at 440M, the best geometry-based allocations improve over uniform substantially larger than the cosine taper, while the anti-topological raw control is worse than uniform.

We present MeshFM, an efficient feedforward framework for extracting rich features from 3D inputs. Our method distills 2D features from visual foundation models into 3D. We train a feedforward network to directly predict 3D features without requiring optimization during inference. The approach utilizes a two-stage training strategy. First, we optimize a feature field in 3D using only 2D feature supervision. Second, we train a network to regress this feature field. The entire procedure requires no 3D annotation, instead relying on the powerful information in 2D foundation models. We demonstrate that our learned features can be immediately applied to downstream tasks, including part segmentation, dense correspondence, and mesh deformation. Extensive experiments show that MeshFM, trained solely with 2D supervision, performs on par with methods trained explicitly with 3D supervision, even without task-specific fine-tuning. Moreover, our model is trained to be robust to extreme rotations of the input objects. Project page: https://threedle.github.io/MeshFM/

Feed-forward networks (FFNs) dominate memory traffic and computation in large language model (LLM) inference, making them a primary target for activation sparsification. However, existing training-free methods suffer substantial model-quality degradation at high sparsity due to limitations in their channel-selection strategies. We observe that the SwiGLU intermediate state provides a highly effective channel-selection signal, but obtaining it requires costly dense computation. To address this, we present \emph{Prox}, a two-stage training-free framework for sparse SwiGLU FFNs. Prox hinges on the key insight: sparse execution requires only the channel mask induced by the intermediate state, which can be constructed from the magnitude ranking of its entries rather than their exact values. Specifically, Stage 1 uses input sparsity and quantized proxy weights to construct a shared mask; Stage 2 computes the selected channels exactly, enabling sparse execution of all three projections. Across ten LLMs from six model families, Prox outperforms training-free baselines at all sparsity levels, achieves up to a $1.99\times$ end-to-end decoding speedup at 70% FFN sparsity, and is compatible with quantization and sparse attention.

We investigate whether symbolic regression can discover explicit neural network weight-update rules that outperform standard hand-designed optimizers on small symbolic regression benchmarks. Candidate update rules are represented as fixed-depth symbolic expressions over operands derived from common optimizers, including gradient, momentum, adaptive-gradient, and moment-estimate quantities. Across 30 benchmark/neural network combinations, the symbolic regression procedure found an update rule outperforming the best hyperparameter-tuned established optimizer in 25 cases, with an aggregate MSE reduction of 44.47% over the improved cases. The discovered rules do not all share a single common symbolic form, but many combine adaptive normalization, momentum-like quantities, nonlinear transformations, and rational expressions. These results suggest that symbolic regression can serve as a lightweight mechanism for discovering compact optimizer variants, while also highlighting the need for larger-scale validation.

Feed-forward networks hold two thirds of a transformer's non-embedding parameters, yet the architecture has not received a necessity test that controls parameters, compute, and depth at once. We pretrain attention-only decoder transformers (Simple Attention Networks, SANs) against standard transformers matched separately for parameter count, training FLOPs, and depth (2 to 48 layers), for up to 105B tokens at 6M to 87M parameters. Deleting feed-forward layers in place is costly: the standard transformer leads by 0.47 nats at matched depth and 0.26 nats at matched FLOPs. Reallocating the freed budget into attention depth closes the gap: at matched parameters the difference is 0.006 nats (0.27 percent of loss), reproducible to one part in ten thousand across seed pairs, shrinking across 5B, 30B, and 105B budgets, and holding near 0.02 nats across a 29x size range. Three measurements localize the remaining gap to parametric recall: attention-only models are better on context-grounded answers and worse where knowledge must come from weights. Weight spectra show why: routing matrices (Q/K) crystallize early, content matrices accumulate rank slowly, and removing feed-forward layers relocates this accumulation to the attention output projection. QK-normalization, not feed-forward layers or residual gating, keeps 48-layer attention-only stacks trainable. The deficit concentrates on low-context query prediction and localizes there entirely by the largest budget. A pre-registered test confirms the account: it predicts a 0.02 to 0.05 nat gap on knowledge-dense web text; a matched pair trained on fineweb-edu measures 0.040. Within the tested regime, attention does the rest.

Compositional visual question answering requires Vision-Language Models (VLMs) to execute multiple reasoning operations like object selection, spatial relation resolution, and attribute verification. Despite strong aggregate performance, the mechanistic basis of VLM failures on this task remains underexplored. To address this gap, we analyze vision-operation misalignment in VLMs by examining how failures relate to specific reasoning operations and the internal computational pathways through which they arise and propagate. We introduce an Operation-centric mechanistic framework that decomposes VLM failures by both the reasoning operation where they originate and the internal computational pathway through which they propagate. Our analysis reveals four mechanistically distinct failure modes: grounding failure, reasoning failure, attribute extraction failure, and language prior dominance failure. Each characterized by a unique relationship between visual grounding strength and answer correctness. Through three complementary causal interventions applied across all transformer layers, we further demonstrate a pathway dissociation: grounding failures route exclusively through the feedforward network, reasoning failures route through late-layer attention, and attribute extraction failures localize to the answer-position feedforward computation. This dissociation demonstrates that different failure types require fundamentally different corrective strategies, providing a principled foundation for targeted improvements to VLM reliability in multimedia reasoning.

Kolmogorov--Arnold Networks (KANs) replace fixed node activations with learned one-dimensional edge functions, offering an explicit interface for interpretation and a possible alternative to transformer feed-forward networks. We test these claims separately. In a six-layer, 10M-parameter B-spline KAN, we reconstruct all 884,736 feed-forward edges: 87.8% exceed (NLS>0.1) and 0.4% are inactive. Pruning the lowest-activity 20--25% causes negligible loss increase, although structured MLP neuron pruning tolerates comparable sparsity. The audit replicates on BabyLM, but grid-size sweeps show that near-total fPCA compression and high closed-form-fit coverage are properties of the low-capacity grid-2 basis, not universal KAN behavior. For replacement, we evaluate MLP, SwiGLU, grouped Chebyshev, and rational GR-KAN networks on BabyLM. The KAN-family and gated variants improve validation loss over the GELU MLP, but this ordering does not transfer to standardized benchmarks: across ten seeds and 59,875 BLiMP pairs, accuracies span 62.4--63.1%, EWoK remains at chance, and a (+0.7)-point GR-KAN effect on BLiMP reverses on the supplement. Larger tests are also cautionary: parameter-matched MLPEdge underperforms the MLP on Wikitext-103, and 286M-parameter GR-KAN remains below a SwiGLU ClimbMix baseline after stabilization. Thus, small-basis KANs provide a practical, corpus-transferable interface for auditing learned scalar transformations, but the tested replacements show no consistent benchmark, quality, or latency advantage over strong MLP baselines.

Interpreting a neural network requires understanding what its internal features extract from a particular input. Feature inversion seeks to express a selected feature in the input domain, but canonical iterative methods search for an input whose re-encoded representation matches the target. Because many inputs can satisfy this constraint, target matching alone does not specify the inverse associated with the sample that generated the feature. We formulate source-grounded feature inversion by conditioning the inverse on the source-local network geometry at the target-generating input. At each boundary of the computational DAG, backpropagation provides the correct reverse dependencies but transports an adjoint signal rather than an upstream-state estimate. We locally repair this signal with a closed-form matrix Wiener map from a mean-seed VJP to the upstream state, followed by a second Wiener map for the JVP forward-consistency residual, and compose the repaired states through the same DAG in one finite reverse pass. One calibrated zero-intercept map family supports new inputs, depths, channels, and channel groups across diverse CNN and Transformer architectures, tensor components, and visual distributions without query-specific optimisation. Matched target and source controls verify that each inverse depends on the selected feature and the local operators of the sample being explained, rather than a target-independent image template. Prediction-conditioned feature atlases align these visualisations with independent interventions on the corresponding internal features. Together, source-grounded feature inversion opens the model's hidden feature hierarchy to inspection at the level of individual layers and channels, linking what the network extracts from an input to the internal evidence that shapes its decision.

We present RegHead, a framework for constructing semantic blendshape sets for animatable non-humanoid head avatars. With a fixed expression vocabulary, semantic blendshapes provide a low-dimensional and interpretable animation interface and support cross-identity retargeting. Building such blendshape sets remains expensive because (i) expression-consistent supervision is scarce, (ii) generated 4D assets typically lack correspondence, and (iii) facial motion is highly localized. We propose (1) a large-scale dataset of non-humanoid identities paired with a shared expression vocabulary, obtained by expanding a small artist-rigged library via fine-tuned image editing; (2) a dense stochastic anchor motion representation tailored to localized facial deformations; and (3) a fast feed-forward registration model that converts unregistered expression meshes into a corresponded blendshape basis by predicting anchor-based deformations from the neutral shape. Experiments show that our approach produces higher-fidelity expression meshes than baselines, while running orders of magnitude faster than optimization. We further demonstrate real-time retargeting from human face tracking signals to non-humanoid characters, capturing both head pose and localized facial motions. Our project page is available at https://snap-research.github.io/RegHead/.

Feedforward network (FFN) blocks account for a large fraction of the parameters and computation in Transformer architectures, yet their internal structure remains difficult to interpret due to the additive superposition induced by the residual stream. We examine whether the activation of an FFN neuron can be explained by a sparse set of preceding neuron activations and attention outputs. We introduce a training-free attribution method that estimates the relative influence of upstream neurons and attention outputs on a target neuron's activation. Empirically, across models and layers, we find that small subsets of preceding activations and attention outputs suffice to preserve neuron activations with high fidelity when all remaining inputs are masked with their average values. Effective sparsity is even greater when accounting for the inherent activation sparsity of upstream layers. Moreover, applying the neuron-specific masks in all layers simultaneously, such that the induced deviations propagate through the network, leaves model perplexity largely unchanged at moderate sparsity levels. These results demonstrate that, despite dense parameterization, FFNs exhibit sparse and structured inter-layer dependencies at the neuron level. Our method provides a practical, scalable tool for circuit-level interpretability and identifies candidate sparse pathways with potential implications for efficient inference.

Backpropagation is the computational engine of deep learning, yet its mathematical structure is typically treated as a procedural traversal of computational graphs. We present a global operator theory of the \emph{F-adjoint} framework, which reformulates the layerwise backward recursion of an $L$-depth feedforward network into a single linear system $(I-\cB)\Xs=\bG$, where $\bG$ is a source vector. We prove that the global backward operator $\cB$ is strictly block upper-triangular and nilpotent of index at most $L$. This nilpotency guarantees the exact termination of the Neumann series solution after at most $L$ terms, revealing classical backpropagation to be mathematically equivalent to block back-substitution on an upper bidiagonal system. We formalise \emph{F-symmetry} -- the condition in which the backward pass perfectly mirrors the forward pass -- identifying orthogonal weight matrices as canonical examples. Through worked numerical examples, we demonstrate how this operator perspective exposes the single-path collapse of strictly feedforward networks and its breakdown in residual architectures. Finally, we leverage this compositional structure to rigorously derive the mechanics of residual networks (gradient highways) and transfer learning (gradient truncation). This framework elevates backpropagation from an algorithmic recipe to a global nilpotent-operator formulation.

Large language models increasingly operate as tool-using agents, where small format, argument, or function-call errors can invalidate otherwise plausible responses. We study inference-time feed-forward network (FFN) intervention for improving structured outputs without retraining model weights. Our project began with Orthogonal Residual Projection (ORP), a direction-changing repair attempt that revealed sensitive SwiGLU FFN intervention sites but often caused more harm than fixes. We therefore propose Amplitude Gating (AG), a non-destructive alternative that preserves pretrained FFN weight directions and modulates only activation magnitudes during generation. We define a fine-grained intervention system spanning P1/P2/P3 and branch-specific P1s/P2a/P2b sites, and introduce an evaluation protocol that separates combination-oracle headroom from fixed configurations and learned gates, enforces sample-level accounting, and uses task-aware metrics for binary and partial-credit datasets. Across Qwen3.5-9B, Qwen3-8B, and Qwen2.5-7B, AG is weakly positive in aggregate but strongest on tool-structured tasks. On Qwen3.5-9B, a category-level learned gate improves tool/structured/agentic performance from 38.66% to 42.92% (+4.27 percentage points), with Hermes function-call tasks reaching about +7.6 points. On Qwen3-8B, Hermes JSON mode improves by +11.36 points. Qwen2.5-7B retains oracle headroom but current learned gates fail to capture it, showing that deployment requires model- and category-specific routing. Comparisons of entropy AG with Newton-Schulz-windowed AG show that neither family is uniformly dominant. These results identify tool-structured inference as the most credible first target for safe FFN-level inference optimization, while prospective online validation and broader cross-model evaluation remain necessary.

Driven by next-token prediction, NLP shifted from task-specific models into powerful generalist foundation models. What, then, is the equivalent catalyst needed to achieve a general-purpose model in computer vision? In this paper, we contend that large-scale text-to-video generation serves as a strong pre-training paradigm for computer vision, providing the necessary spatiotemporal priors, vision-language alignment, and scalability required for general visual intelligence. We introduce GenCeption, which leverages a pre-trained video generative diffusion backbone to define a feed-forward perception model, capable of performing various vision tasks steered by text instructions. Empirical results demonstrate that GenCeption achieves state-of-the-art performance across a diverse suite of tasks, including depth, surface normal, and camera pose estimation, expression-referring segmentation, and 3D keypoint prediction, often matching or surpassing specialized models (e.g. DepthAnything3, SAM3, D4RT, VGGT-Omega, Sapiens, David, Genmo, and Lotus-2). Furthermore, the video generative pretrained backbone outperforms alternative pretraining paradigms (e.g., V-JEPA, and Video MAE) under comparable settings. Importantly, GenCeption exhibits preliminary data and model scaling properties along with exceptional data efficiency, where it achieves comparable performance with leading models like D4RT and VGGT-Omega with 7 to 500 less training data. Finally, GenCeption also exhibits intriguing emergent behaviors: a model trained exclusively on synthetic human videos generalizes to real-world footage and out-of-distribution object categories (e.g., animals and robots). These findings suggest that video generation is not merely a synthesis tool, but a foundational path toward generalist vision intelligence for the physical world. Project page: https://genception.github.io

A companion paper showed that a transformer's feed-forward layer can be rebuilt from explicit fuzzy set operations - intersection, set-difference, and a self-forgetting sequence quantifier - so its hidden units read as named logical operators at no cost to language-model quality. That left the other half of the transformer opaque. Here we carry the same idea into attention and join the two into one model. The mechanism is minimal: a head's value is passed through a sigmoid, so each value channel becomes a readable detector of whether a feature holds at a token. This adds no parameters and leaves the standard head otherwise untouched. A Boolean variant goes further, restructuring the value into an explicit within-token intersection and negation-capable set-difference. In both designs the output projection is left free, not tied to the vocabulary, which is the load-bearing decision: bounding what a head detects while leaving what it writes unconstrained yields selective detectors, whereas constraining the write does not. A bounded value is shaped into a readable detector by two selectivity pressures - one for sparse firing, one for decisive firing at the rails - and which a design wants is not universal. Across five specialized-attention designs at 125M parameters, 44 to 62 percent of value channels become crisp, contextually selective detectors, and their legibility rises with depth rather than crystallizing only on punctuation. Language-model quality is at parity with a conventional baseline. Finally, we couple the Boolean attention to the legible feed-forward layer and train an end-to-end legible-by-construction language model at benchmark parity: its feed-forward units are named set and quantifier operations throughout, and we can take a token it generates and read the named units that compose to produce it.

Inverse rendering aims to recover both 3D geometry and physically meaningful material properties from images, enabling applications such as relighting and novel view synthesis. Optimization-based methods achieve high fidelity but require costly per-scene fitting, while image-space learning-based approaches often suffer from multi-view inconsistencies and lack an explicit 3D representation for stable novel view rendering. We present a feed-forward multi-view reconstruction framework for inverse rendering that directly predicts a structured 3D Gaussian representation with intrinsic material attributes. Each Gaussian primitive is parameterized by mean, normal, opacity, rotation, scale, albedo, metallic, and roughness, enabling a disentangled and physically grounded scene representation. Our model integrates priors from a material estimation network with a multi-view 3D reconstruction backbone, allowing joint prediction of geometry and reflectance parameters in a single forward pass. Experiments on synthetic and real-world datasets demonstrate improved multi-view consistency compared to 2D baselines, accurate material recovery, and stable novel view rendering. Our representation further supports physically-based relighting and more faithful modeling of view-dependent effects compared to existing RGB-based feed-forward reconstruction methods. Our project webpage is: $\href{https://poliik.github.io/invsplat/}{\text{https://poliik.github.io/invsplat/}}$.

In practice, most commercial LLM providers do not publicly release details of underlying LLM architectures. However, prior work has shown that given limited API access to an LLM (namely, top-$k$ logits and/or a logit bias function), one can recover certain architectural details of an LLM, such as the hidden dimension of the feed-forward network. Perhaps in response to these results, most commercial LLM providers have restricted their APIs to expose only the single logit for each decoded token, and they no longer give users the ability to bias logits. We show that even under current restrictive APIs, several architectural parameters are still recoverable. We present NightVision, an attack that uses restrictive black-box API access to estimate the hidden dimension, depth, and parameter count of an LLM. Algorithmically, NightVision relies on a novel common set prompting technique in which multiple prompts expose log probabilities for the same set of output tokens; a spectral analysis of these results is used to infer hidden dimension. NightVision additionally uses end-to-end time to first token (TTFT) measurements and the estimated hidden dimension to estimate depth and parameter count. We empirically evaluate NightVision on 32 open-source LLMs, recovering hidden dimension to within 23% average relative error across all models (9% on MoE models), and depth and parameter count to within 53% for models exceeding three billion parameters. We run extensive ablations to demonstrate how these accuracies scale with token budget and model properties. Overall, our results suggest that current LLM APIs are not sufficiently restricted to fully obfuscate the architectural details of their underlying models.

Recursive Feature Machines (RFMs) are a class of kernel machines that utilize the Average Gradient Outer Product (AGOP) as a mechanism for feature learning. They have been shown to effectively replicate the learning dynamics and feature representations of Feedforward Neural Networks (FNNs) across various settings. However, despite comparable capacity for feature learning and the similarities in the features they acquire, RFMs exhibit significantly lower performance than neural networks in certain data-corrupted scenarios. In this work, we investigate these limitations in mathematical problems. As a solution, we introduce a remarkably effective transformation applied to the training labels which promotes learning in noisy, complexly represented, and class-imbalanced data. This simple yet powerful adjustment enables RFMs to close the performance gap with FNNs and, in some cases, even surpass them.

Low-resolution face recognition (LR-FR) remains a challenging task due to poor feature extraction and aggregation, as probe images often contain limited identity information resulting from extreme degradations such as blur, occlusion, and low contrast. Additionally, the domain gap between high-resolution (HR) gallery images and low-resolution (LR) probe images poses a significant challenge. A single feature encoder struggles to generalize effectively across both domains when fine-tuned on an LR dataset, and this issue is further magnified by catastrophic forgetting. To address these challenges, we propose FaceMoE, an effective adaptation of Mixture of Experts (MoE) transfomer architecture for low-resolution face-recognition . Specifically, we introduce multiple specialized feed-forward network (FFN) experts and incorporate a top-k router, which dynamically assigns tokens to appropriate experts. This design emergently promotes specialization across experts for different semantic regions of the face, which enables FaceMoE to perform resolution-aware feature extraction. Moreover, the top-k router facilitates sparse expert activation, enabling the model to preserve pretrained knowledge when finetuned on a LR dataset, while increasing model capacity without proportional computational overhead. FaceMoE is trained with a combined face recognition loss, router z-loss, and load balancing loss to ensure expert specialization and stable training. To the best of our knowledge, this is the first work leveraging MoE for LR-FR. Extensive experiments across eleven datasets, spanning HR, mixed-quality, and LR benchmarks, demonstrate that FaceMoE significantly outperforms state-of-the-art methods. Code: https://github.com/Kartik-3004/FaceMoE

We study layered models, including feedforward networks, ResNets, and transformers, by limiting each layer to a width of $d = 3$, i.e., $\mathbb{R}^3$ as representation space. This allows us to track how a neural network changes low-dimensional topological invariants through its layers. Just about any topological structure may be simplified or even trivialized by simply increasing dimension; e.g., any knot is equivalent to an unknot in $\mathbb{R}^4$. By restricting to $\mathbb{R}^3$, we not only isolate the effects of activation and depth from that of width, we work in a space that lends itself to easy visualization. We focus on linking number here, deferring other invariants like link groups, Milnor's $\barμ$-invariants, knot types, ambient cobordisms, to a sequel. We provide full proofs and empirical experiments to justify the following insights: When measured by their power to effect changes in linking numbers, the layer-skipping feature in ResNets is as powerful as the attention mechanism in transformers; both ResNets and transformers are strictly more powerful than feedforward neural networks with monotonic activations, which are in turn more powerful than invertible and flow-based models; but replacing monotonic activation with a nonmonotonic one elevates a feedforward network into the same expressivity class as ResNets and transformers. These results suggest that low-dimensional topology can be a useful tool to guide designs of AI architectures. We also generalize our results from $d = 3$ to arbitrary $d > 3$.

A transformer's feed-forward (FFN) sublayer materializes the distinctions attention gathers, yet gives no account of what it computes. In a parameter-neutral replacement, each hidden unit is an explicit fuzzy set operation on sigmoid-bounded [0,1] memberships: intersection AB and set-difference A(1-B), the latter a bounded positive negation ("A but not B") that gated/bilinear units lack -- a negation-capable FFN (NC-FFN). On N-bit parity they are the most parameter-efficient reasoning basis at shallow depth; at scale (125M, OpenWebText) NC-FFN ties the GELU baseline's perplexity, every unit carrying explicit logical form. Two limits share one cause: two-operand logic localizes to layer 0 and erodes under training, and the one robust grammatical deficit concentrates in licensing and quantifiers, beyond within-token operators. We resolve both with a small block of sequence quantifiers: a soft existential and a soft proportion, each with a per-unit learned forgetting rate from a sticky init. This recovers the deficit at epoch one (halving the wider epoch-two gap), modestly leads on LAMBADA, and makes the FFN legible: the structure now holds and migrates into depth; the decay un-learns its stickiness (median half-life ~1.5 tokens; zero latch units); and at the semantic layers the units read, without dictionary learning, as grammatical licensing detectors: each fires on a licensor (a comparative, a passive participle, a negative-polarity item) and carries its memory forward to predict the licensed word (than, by, nor). This legibility is localized and free only up to a partition (a fully Boolean FFN diverges in training), but the result is a parameter-neutral, language-model-quality transformer with a readable, interpretable-by-construction grammatical mechanism -- an account not just of what a feed-forward layer represents but how it licenses.

Low-rank adaptation (LoRA) is commonly viewed as an update-space approximation to full fine-tuning, yet this view is incomplete for self-gated Transformer feed-forward networks. In gated FFNs, a low-rank residual can change not only projected features but also the nonlinear selection weights that determine which channels contribute to the output. We formalize this effect as selection misalignment and connect it to the local effective homogeneity of self-gated activations. This motivates a nonlinearity-aware principle for parameter-efficient fine-tuning: low-rank updates should allocate capacity to gate channels whose nonlinear states remain responsive and should shape the temporal evolution of selection. We propose NA-LoRA, a training-only method with two lightweight mechanisms: a derivative-based temporal-importance mask for gate-related LoRA updates and an activation-specific step-scaling rule when a meaningful coarse effective-homogeneity partition is available. NA-LoRA adds no auxiliary loss and incurs no inference-time overhead. Experiments on language-model fine-tuning and vision-language transfer benchmarks show that NA-LoRA consistently improves over vanilla LoRA and is competitive with or better than strong PEFT variants.

We present RenderFormer++, a scalable and physically grounded feed-forward neural rendering framework for global illumination in mesh scenes. Existing Transformer-based neural rendering methods such as RenderFormer achieve promising cross-scene generalization, but suffer from limited physical consistency and poor scalability due to the quadratic attention complexity of triangle-level tokenization. To address these issues, we introduce Physics-Informed Transport Guidance (PITG), which embeds rendering-equation inductive biases into the attention mechanism and enforces transport consistency loss, enabling physically consistent light transport modeling. We further propose Hierarchical Object-Centric Tokenization (HOCT), which aggregates triangle-level features into compact object-level tokens via cross-attention with learnable queries, substantially reducing computational and memory costs while preserving geometric and radiometric information. Extensive experiments demonstrate that RenderFormer++ achieves scalable, stable, and generalizable feed-forward global illumination rendering across complex large-scale scenes with improved physical accuracy and efficiency over prior neural rendering methods.

Recent advances in 3D scene reconstruction have highlighted the intricate trade-offs among rendering quality, inference efficiency, and data dependency. To address the challenge of rapidly reconstructing detailed 3D indoor scenes from minimal input, we introduce FastPano3D, an end-to-end framework that directly generates renderable 3D Gaussian representations from a single panoramic image. Unlike perspective-based methods, panoramic images inherently suffer from equirectangular projection distortions and spatially non-uniform feature distributions, making direct feed-forward Gaussian generation particularly challenging. In contrast to existing Gaussian Splatting based methods that rely on multi-view supervision or per-scene optimization, FastPano3D employs a lightweight feature encoder, adaptive Gaussian sampling, and a point-cloud-guided refinement strategy to achieve efficient and accurate scene generation without any test-time optimization. Our approach reconstructs high-fidelity 3D scenes within seconds, achieving up to 156 times faster inference than prior state-of-the-art methods such as Pano2Room, while using only half the parameters. Extensive experiments demonstrate that FastPano3D delivers rendering quality comparable to NeRF- and 3DGS-based reconstructions, establishing a new benchmark for rapid, single-view 3D scene inference.

We present FFAvatar, a Transformer-based 3D Gaussian framework for fast construction of high-quality and animatable 4D head avatars from one or more reference portrait images. Unlike existing feed-forward approaches that require a fixed number of input views, FFAvatar supports incremental reconstruction, progressively refining the avatar representation as additional reference images become available. At the core of our method is an alternating attention mechanism that disentangles identity appearance from expression and viewpoint variations, enabling the reconstruction of a canonical 3D appearance that remains consistent across poses and facial expressions. To balance visual fidelity and computational efficiency, we introduce a sparse-to-dense learning paradigm. Coarse appearance features are first learned using sparse primitives anchored to the FLAME vertex level and are subsequently densified in the UV domain to capture fine-grained geometric and texture details. We further propose a plug-and-play motion refinement module that enables subject-specific dynamic personalization by modeling residual motion beyond parametric deformation. Extensive experiments demonstrate that FFAvatar efficiently produces high-fidelity and controllable 4D head avatars, achieving superior flexibility, driving efficiency, and identity-consistent rendering across diverse expressions and viewpoints.

Metric feed-forward 3D reconstruction for panoramic data remains under-explored due to the lack of large-scale panoramic RGB-D training data. We present Realsee3D, a hybrid dataset of 10K indoor scenes (1K real, 9K synthetic) with 299K panoramic viewpoints and precise metric annotations, and Argus, a feed-forward network trained on it for metric panoramic 3D reconstruction. In the sparse unordered capture setting of Realsee3D, a poorly chosen coordinate anchor can cause global pose drift. Argus addresses this with a learned covisibility module that selects the geometrically optimal reference view to anchor the metric world frame. To further improve multi-task learning, we decompose the bidirectional pixel-to-world mapping into interpretable sub-steps with per-step supervision and cross-coordinate joint constraints, reinforcing geometric consistency across prediction branches. On the Realsee3D benchmark, Argus achieves state-of-the-art metric performance in camera pose estimation, depth estimation, and point cloud reconstruction. Project page: https://argus-paper.realsee.ai.

We present CLEAR-MoE, a four-phase post-training pipeline that converts a frozen pretrained Vision Transformer (ViT) into a sparse Mixture-of-Experts (MoE) model without updating backbone weights. The pipeline (i) scores feed-forward network (FFN) layers by sparsity, clusterability, and output sensitivity; (ii) decomposes selected layers into a shared low-rank SVD basis and per-cluster residual experts using k-means clustering; (iii) trains lightweight routers supervised by cluster labels; and (iv) dispatches tokens through pluggable CUDA backends. On Imagenette with DeiT-Small, CLEAR-MoE retains 99.9% of the dense model's accuracy (86.70 +/- 0.02% versus 86.73%). Extensive ablation studies reveal a consistent empirical finding: the shared SVD basis is the primary factor responsible for preserving accuracy. Random routing, learned routing, and three different router architectures produce nearly identical performance, with accuracy varying by at most 0.06 percentage points (86.62%-86.68%). Accuracy also remains stable across different SVD ranks, expert counts (2-8), calibration set sizes (50-500), and random seeds. This behavior generalizes across five ViT backbones (DeiT-Tiny, DeiT-Small, DeiT-Base, ViT-Small, and ViT-Base), covering models from 5.7M to 86.6M parameters, with accuracy differences <= 0.10 percentage points from their dense counterparts. On a GTX 960 GPU, routing and scatter-gather overhead make the CLEAR-MoE FFN 1.3-1.7x slower than the dense implementation. A dispatch microbenchmark further shows that routing is an order of magnitude more memory-bound than expert matrix multiplications, identifying fused dispatch kernels as a promising direction for future optimization.

Mixture-of-Experts (MoE) language models scale model ability with sparsely activated experts, making this architecture a standard recipe for modern large models. However, sparse activation does not remove the deployment burden of storing and serving all experts, and the available deployment budget can vary substantially across devices, users, and workloads. Existing MoE compression methods are still largely fixed-budget, typically optimizing one compressed endpoint at each chosen target budget. We study a different setting: converting a large pretrained MoE LLM into a nested family of deployable subnetworks across budgets. Our method first ranks expert FFN channels by their importance, then lets each expert learn a discrete action to prune its channels. By gradually increasing cost pressure, a single action-training run exports a series of action masks from high to low budgets, each of which identifies a reliable smaller subnetwork nested in the ranked base model. Moreover, we use a single recovery fine-tune at a mid pruning budget (40%) to recover degraded model quality and transfer the recovered model to other unseen budgets. Overall, our framework surpasses recent MoE compression baselines. Specifically, on Qwen2-57B-A14B, our method retains ~99.8% of base performance while pruning 50% of routed expert parameters even without fine-tuning. For deployment, our pruned subnetworks deliver real memory reduction and throughput gains, and further support realtime online budget switching with kernel-level co-design.

Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes. While powerful, this perspective is incomplete: it primarily captures complexity through regularity, and therefore does not distinguish intuitively simple and complicated objects with comparable regularity, such as the square-root function and a typical Brownian path. The guiding message is that neural networks should be viewed not only as flexible basis functions, but also as models of computation. If a function is computable by a real-valued circuit over a prescribed elementary gate language, then it can be computed to comparable accuracy by an NN with explicit depth, width, and non-zero-parameter bounds controlled by the depth, width, gate count, and gate structure. Thus, neural-network complexity is not governed by regularity alone, but also by algorithmic complexity. We then show that any definable NN model satisfying a natural parallelization condition, allowing possibly multivariate non-linearities such as attention or layer normalization, is a universal approximator if and only if it contains a non-affine nonlinearity. The scope of our theory is illustrated by deducing universal approximation guarantees for continuous functions, minimax-optimal approximation guarantees for Besov classes, logarithmic-error complexity for holomorphic functions, and by showing that NNs can emulate numerical algorithms such as Newton-Raphson root finding and power iteration without architecture-specific arguments. Its precision is illustrated by shortest-path computation on $k$-vertex graphs: compiling the tropical dynamic-programming circuit yields NNs with O(log(1/ε)) non-zero parameters, exponentially improving in 1/ε over the generic $O(ε^{-c k^2})$ Lipschitz-approximation scale, for a constant c>0.

We propose a complete architectural blueprint for safe artificial general intelligence based on a closed reentry loop (D <-> I cycle). In contrast to feedforward networks, which are directed acyclic graphs (C=0, S=0) incapable of self-reference, the proposed architecture contains a structural cycle (C >= 1) with self-sustaining amplification (rho > 1), mathematically guaranteeing the emergence of a self-model, instrumental self-preservation, and unprogrammed goal-directed behaviour. The agent's goals are encoded as a non-textual D-vector in the architecture itself, making them immune to reinterpretation and prompt injection. We present the S-measure -- a polynomial-time [O(N^3)] computable alternative to Tononi's NP-hard Phi -- with machine-verified Lean 4 proof that S>0 implies positive integrated information. The work provides full Python/NumPy implementations (Tarjan-based cycle complexity, Delta-S barrier), industrial horizontal scaling via Apache Kafka and Docker Compose, a taxonomy of six epochs of AI evolution, a zoo of future reentry architectures (RAS, diffusion attractors, fractal loops), gauge-invariant networks for safe swarms, fault-tolerance and recovery protocols, and eight falsifiable predictions. All formal proofs are machine-verified in Lean 4. This architecture is deployable today and represents a topologically protected, safe-by-design approach to AGI.

We introduce FiCA, a Feed-forward, instant Gaussian Codec Avatar generation pipeline that creates lifelike avatars from a single portrait image. Generating a photorealistic and drivable avatar from just a single image is significantly challenging due to the limited visual information available to accurately infer the 3D appearance and geometry of human heads. To address this, we develop a novel system that combines human-centric vision foundation models with a diffusion model. This system is designed to fully exploit partial visual observations to generate lifelike human avatars. Our proposed diffusion model learns a generative mapping from these partial observations to complete and authentic 3D mesh reconstruction. Additionally, we introduce a feed-forward mesh refinement network that enhances the fidelity and identity preservation of the generated avatars, eliminating the need for person-specific test-time optimization. By leveraging a universal prior model that decodes a generated mesh into a set of 3D Gaussians, we generate a photorealistic 3D Gaussian avatar, capable of being driven with novel expressions in real-time. Our experiments demonstrate that the avatars generated by our feed-forward approach faithfully represent diverse identities and surpass the visual quality of avatars produced by recent competing methods.

Learning Entropy (LE) has recently been extended to image analysis through Spatial Learning Entropy Maps (SLEMs), which are two-dimensional LE distributions that highlight unusually high learning activity across an image. Unlike conventional image descriptors, SLEMs are generated by incremental, sample-wise learning of a pretrained feedforward MLP network, where local pixel neighborhoods are presented sequentially in a fixed spatial order to predict the corresponding central pixels. Consequently, the learning activity at each image location depends not only on its local structure but also on the knowledge acquired from previously processed locations. This paper introduces Learning Entropy Signatures (LES), an image descriptor derived from SLEM using the K largest LE locations. LES captures the spatial organization of learning-relevant image structures and provides a compact representation of image content based on learning weight behavior. Experimental evaluation on image classification tasks shows that a relatively small number of K largest LE locations preserve substantial discriminative information. The results indicate a close relationship between the learning of neural weights and information relevance, extending the role of Learning Entropy from time series to images and, within images, from structural point extraction to compact image representation and classification.

We present MeshLoom, a feed-forward registration network that directly reconstructs vertex deformations across mesh sequences. Our approach advances non-rigid registration beyond existing models, which are typically constrained by costly per-instance optimization, narrow object categories, pairwise-only inputs, or merely intermediate outputs. The network is simple and efficient, registering multiple meshes within seconds. At its core lies a topology-aware encoder--decoder design. Specifically, we first introduce a topology-aware point representation that encodes the anchor (reference) mesh's topology into its per-vertex features. This representation strengthens the network's understanding of the anchor-mesh geometry and disambiguates points that are Euclidean-close yet geodesically distant. We then propose a multi-modal encoder that fuses this anchor-mesh representation with complementary cues from each frame, such as shape latents and image features. These multi-source signals are compressed into a compact global motion embedding that captures dense inter-frame correspondence. A lightweight decoder then queries this global embedding with the anchor-mesh point representation, retrieving per-vertex deformations at target timestamps. Through extensive experiments across diverse motions and object categories, we show that MeshLoom achieves state-of-the-art results on non-rigid registration. In addition, we find that our global embedding-then-query paradigm naturally enables the network to generate deformations at intermediate timestamps, which extends MeshLoom to motion interpolation and mesh morphing. Project page: https://meshloom.github.io/ .

Transformer feed-forward networks (FFNs) are often treated as nonlinear stores of computation, yet how nonlinear a trained FFN block actually is has rarely been measured. We treat each FFN as a position-wise input-to-output map and split it into the exact least-squares linear approximation plus a residual. The held-out variance the closed-form linear map explains defines a block's linear recoverability (R^2_lin), an optimiser-free measure of its linearity. Across all twelve blocks of GPT-2, Pythia-160m, and llama-160m, R^2_lin is highly heterogeneous and non-monotone with depth, ranging from near-linear (>0.99) to strongly nonlinear (<0.3) between adjacent blocks, and is not set by the activation function: same-width GELU models GPT-2 and Pythia-160m have sharply different profiles, so recoverability is a learned property of individual trained blocks, not an architectural one. A low-rank bilinear probe of the residual recovers only a few points of R^2, with gain uncorrelated with residual nonlinearity: the unrecovered computation is not a single position-wise product but higher-order or distributed structure. The measurement also serves as a targeted compression signal: recoverable blocks admit large single-layer replacements (GPT-2's early FFN at 8x fewer parameters for +0.77 perplexity), while low-recoverability blocks flag where this is unsafe. It further exposes a methodological pitfall: trained linear baselines can badly under-converge on ill-conditioned transformer activations, so we report the exact closed-form least-squares ceiling throughout.

While recent advancements in generative AI have substantially accelerated static 3D model creation workflows, the synthesis of category-agnostic 3D animations remains a significant bottleneck in 3D asset production. Current methods for category-agnostic animation generation exhibit critical limitations in inference speed, motion quality, and adherence to textual prompts, thereby leaving the process dependent on labor-intensive manual artistry. To address these challenges, this paper introduces AnimaSpark, a novel pipeline for category-agnostic 3D animation generation. Our approach is motivated by the key insight that for many fundamental motions in the 3D world, the corresponding joint transformations can often be effectively modeled within a two-dimensional subspace. The pipeline begins by rendering a rigged static 3D model into multi-layered image representations of its mesh and skeleton, which are subsequently fed into a video generation model. We then employ a keypoint tracking algorithm on the generated video to capture the motion of the skeletal joints projected onto the camera's viewing plane. In the final stage, we distill the planar translations and rotations from these tracked keypoints and lift them from the 2D domain into 3D space to animate the character. Comprehensive evaluations reveal that our method achieves superior performance over existing state-of-the-art techniques across key metrics, including text-motion alignment, quality of motion, and computational efficiency.

We study dense-to-sparse continual training as a way to construct channel-sparse large language models from dense checkpoints. Starting from a Qwen2.5-8B dense backbone, we continue training at 32K context and introduce a predictor-gated sparse SwiGLU FFN in the 32K stage. For each token and layer, we use a low-rank predictor to produce FFN-channel routing logits. We then apply a bank-wise top-k rule to retain 16 channels in every 64-channel bank, yielding 4x sparsity in the FFN intermediate activation. Unlike post-hoc sparse inference methods, the routing module is placed on the main language modeling path and optimized during continual training, enabling the dense model to be upcycled into a hardware-oriented sparse model. We report the architecture, training recipe, benchmark performance, and training lessons. We also identify a layer-local long-context failure mode on RULER-CWE and propose a single-layer repair algorithm that substantially improves the affected length range.

Mixture-of-Experts (MoE) models achieve strong performance through conditional computation, but their large parameter footprint poses deployment challenges. Prior MoE compression approaches catastrophically fail when evaluated on general-purpose benchmarks beyond commonsense reasoning. We trace this failure to the granularity of compression: important capabilities are distributed across experts but concentrated in FFN sparse intermediate dimensions. To identify these dimensions, we use Fisher importance which outperforms activation-, router-score-, and magnitude-based alternatives, and identifies tiny sets of task-critical dimensions: in Qwen1.5-MoE, removing as few as 12 of 1.35M routed-FFN intermediate dimensions collapses GSM8K accuracy while largely preserving factual-knowledge performance. Building on this, we propose Fisher-MoE, which operates within FFN to remove intermediate dimensions ranked by Fisher importance. At the same 50% MoE compression ratio, Fisher-MoE preserves model capability, while reducing weight memory by ~45% and improving inference throughput by 21%. These findings suggest intermediate dimension granularity is an effective unit for both compression and ranking where capability concentrates in MoE models.

Recent works have explored unifying SLAM with geometric foundation models (GFMs). However, directly using GFM predictions for tracking is highly sensitive to model capability and uncertainty, as geometric inaccuracies in the predictions can adversely affect pose estimation. To address this limitation, we propose a decoupled framework that integrates classical feature-based SLAM with GFMs, which achieves higher quality and more consistent dense reconstruction. In brief, we use classical visual SLAM for robust low-latency tracking and use GFMs exclusively for mapping. By anchoring mapping to poses produced by the SLAM module and optimizing across depth scales, the proposed design avoids propagating inaccuracies from GFM predictions into pose estimation while imposing geometric constraints on the reconstruction. The system builds submaps from multiple posed keyframes and enforces scale consistency via lightweight frame and submap scale optimization. It also performs projection-based point cloud fusion within each submap, and updates submaps online to reflect trajectory updates from the feature-based SLAM. To evaluate tracking and reconstruction of our method, we introduce a loop-rich, building-scale indoor dataset with accurate sensor trajectories and LiDAR ground-truth. Experiments show that our approach achieves superior trajectory accuracy while improving reconstruction precision by 10%-20% over existing methods, with about 2 cm reconstruction error per 10 m chunk on building-scale dataset. On large-scale outdoor datasets, it attains 10 cm error per 30 m chunk (w.r.t LiDAR ground-truth models). Code and dataset: https://github.com/ori-drs/ScaRF-SLAM

We propose a machine learning approach for image regression from sparse experimental measurements. We show the application of the proposed method on film cooling studies in propulsion system development, aiming to reduce the need for extensive physical testing. Our method employs a lightweight feed-forward neural network with positional encoding to generate images conditioned by input parameters. Validated on real and synthetic data, it achieves high image similarity (RMSE < 8 %, SSIM > 93 %) while maintaining accuracy with a 30 % reduction of measurements. We further propose a knowledge-informed extension for local adaptability of the generated images. This approach significantly reduces required tests while preserving high-quality data, enabling efficient optimization of coolant injector configurations with applications beyond aerospace.

Recent work in random matrix theory (RMT) has developed the notion of deterministic equivalents: typically linear surrogate models that approximate the spectral behavior of large nonlinear random matrices, such as nonlinear feature maps in neural networks (NNs). Such equivalents make theoretical predictions tractable by reducing a complex model to a simpler one with properties that fall under the umbrella of classical RMT tools. However, this leaves open the question of whether this idealized linear equivalence remains meaningful for classification of high-dimensional nonlinearly separable data. Motivated by this, we consider the conjugate kernel (CK), which is the nonlinear feature map of a one-layer feedforward NN, under a canonical nonlinearly separable dataset for the XOR problem; and we use the study of informative outlier eigenvalues in the CK and whether their corresponding eigenvectors asymptotically align with XOR labels as a proxy for nonlinear learnability. We develop a robust quadratic equivalent of the CK matrix that enables a precise analysis of emergent informative spikes, as one modifies various knobs common in ML practice: sample complexity, signal-to-noise ratio (SNR), nonlinear activation choice, and pretrained features. We identify regimes in which these knobs move the CK beyond the linear equivalent and produce BBP-type transitions to label-aligned outlier eigenspaces. Our analysis helps bring deterministic-equivalence tools from RMT to bear on problems of practical relevance in ML.

We investigate the computational complexity of neural network verification in quantised settings. We distinguish three classes of Feedforward Neural Networks (FNNs): rational FNNs with exact rational weights, quantised FNNs whose weights come from a finite-width arithmetic, and dynamically quantised FNNs in which rational networks are evaluated with respect to a given finite-width arithmetic. We consider two types of specifications used in the literature. Linear programming (LP) specifications are conjunctions of linear constraints, while bit-vector (BV) specifications allow reasoning at the bit level and can express non-linear constraints. Our results give a complexity landscape of these verification problems. For quantised FNNs with fixed arithmetic precision, we show that verification under both LP and BV specifications remains NP-complete, matching the complexity of the rational case. For dynamically quantised FNNs with BV specifications, we establish upper bounds, complementing a previously known PSPACE-hardness result.

Feed-forward networks (FFNs) dominate the parameter count and computation of modern language models, yet existing pruning methods often struggle to convert sparsity into hardware-friendly inference efficiency gains. We introduce \textbf{PrunePath}, a budget-adaptive structured sparsification framework for FFN layers. Built on MoEfication, PrunePath replaces independent expert-wise thresholding with a softmax-normalized routing distribution and activates important experts under a cumulative-mass threshold. This formulation imposes a token-level probability budget, enabling adaptive expert counts and a direct inference-time sparsity knob from a single checkpoint. Across NLU, NLG, and instruction-tuning evaluations, PrunePath achieves a favorable sparsity--performance trade-off compared with existing static pruning and MoEfication-based methods. We further implement Triton kernels for KV-cache decoding to translate the resulting structured sparsity into practical memory savings and measurable decoding-speed improvements. These results demonstrate the superior performance of PrunePath for building highly sparse, deployment-friendly large language models.

Feedforward network (FFN) layers account for a large fraction of parameters and nonlinear expressivity in Transformer-based large language models (LLMs). Despite the evolution from ReLU and GELU to gated variants such as SwiGLU, most FFN designs still use a single fixed activation function, applying the same nonlinear transformation to all tokens. In this work, we propose Mixture of Activations (MoA), a token-adaptive FFN design that mixes a dictionary of activation functions using lightweight input-dependent gates while sharing the same linear projections. As an input-independent counterpart, we also introduce learnable activations (LA), which form linear combinations of activation functions for both ReLU-type and SwiGLU-type FFNs. Theoretically, we establish strict finite-width expressive separations among fixed-activation FFNs, LA, and MoA: LA strictly contains fixed-activation FFNs, while MoA strictly contains LA, with the additional expressivity arising from input-dependent nonlinear hybridization. Empirically, we evaluate MoA through extensive pre-training experiments on dense and MoE language models ranging from 0.12B to 2B parameters under different token budgets, optimizers, and learning rate schedules. MoA consistently achieves lower terminal loss and exhibits more favorable scaling behavior than well-tuned baselines, with minimal parameter and computational overhead. These results suggest that token-adaptive activation mixing is a simple and effective mechanism for improving FFN expressivity in LLMs.

In many reasoning tasks, large language models (LLMs) rely on structured external knowledge, such as graphs and tables, which is typically linearized into sequential token representations. However, even when sufficient knowledge is available, LLMs can still produce hallucinated outputs, and the underlying mechanisms behind such failures remain poorly understood. We investigate these mechanisms and find that hallucinations arise from systematic internal dynamics rather than random noise. First, attention disproportionately concentrates toward shortcut-like structural cues rather than distributing across the full context. Second, feed-forward representations fail to ground the provided knowledge, causing the model to revert to parametric memory. Moreover, our results indicate that hallucination is consistently associated with failures in semantic grounding within feed-forward layers, while attention allocation exhibits greater task-dependent variability. Finally, we show that these mechanistic patterns generalize beyond single-hop graphs to multi-hop and tabular settings, enabling effective hallucination detection across structured knowledge formats.

Capturing relightable 3D assets from real-world objects is a widely researched problem. Several per-scene optimization-based methods, based on 3D Gaussian splatting (3DGS), support relighting; however, they usually require dense input views, and their overfitting nature makes it difficult to generalize across scenes. Unlike per-scene optimization methods, generalized feed-forward models can directly reconstruct Gaussians from sparse input views. However, the resulting assets have baked-in illumination and cannot be easily used for relighting. In this paper, we present F-RNG, a feed-forward framework that directly generates relightable 3DGS assets from sparse-view inputs. Training such a model from scratch can require massive data and computing resources, and it is especially challenging to generate relightable assets in a feed-forward manner with acceptable cost. We develop F-RNG upon an existing large reconstruction model (LRM) to extract relightable representations, while also utilizing priors from an intrinsic decomposition model (IDM). Specifically, we first introduce a latent-interpolated fine-grained geometry synthesis to enhance the LRM's geometry representation. Second, we propose a prior-guided relightable appearance distillation to extract relightable neural representations by incorporating IDM priors. Finally, a universal neural renderer enables flexible and high-fidelity relighting. F-RNG requires neither re-training nor fine-tuning of the underlying LRMs, thus can automatically benefit from better LRMs and IDMs in the future. With only small networks that can be trained with affordable data and computational resources, F-RNG avoids the repetitive inference of large models under different light conditions. By comparison to the state-of-the-art LRM-based relighting method, F-RNG achieves 25x faster relighting, as well as superior quality (+2.0 dB).

In the paper we show that there is an analogy between the operations occurring in a layer of a transformer (projections and layer normalizations, disregarding the feedforward neural network) and a step in the power method. Coherently with this analogy, we show that passing through a layer the tokens tend to be tilted towards the principal eigenvector of a matrix which is the product of the output and value weight matrices of that layer. In the special case of a transformer with shared weights (i.e., in which all layers have identical weights) then the alignment with this principal eigenvector is particularly evident empirically, and can also be shown analytically. The analogy also suggests a method to steer the output of the transformer towards an arbitrary desired direction in token space.

We present a novel framework for embedding hard constraint satisfaction into neural network (NN) architectures, specifically feedforward neural networks and transformers, with input-dependent affine constraints of arbitrary cardinality. Traditional constraint enforcement approaches either rely on penalty-based soft constraints, which offer no guarantee of satisfaction, or on post-processing methods that enforce constraints after the NN is trained, which may lead to suboptimality. We introduce a trainable constraint-affine (CAffine) layer into NNs, yielding CAffNet, which goes beyond enforcing affine constraints via fixed orthogonal or parallel projections and enables joint optimization with network parameters. Moreover, we impose no restrictions on the constraint space dimensions and establish that our construction preserves the universal approximation properties of NNs, while providing provable guarantees on constraint adherence for all inputs. Experimental validation demonstrates robust performance across diverse domains requiring guaranteed constraint satisfaction.

Recently, Belief-Attention \cite{Guoqiang25BeliefAttention} has been proposed by first performing an orthogonal projection of the softmax-based weighted summation of $V$ vectors with respect to the original $V$ vectors and then taking the perpendicular component as the residual signal in Transformer for performance improvement. In this paper, we first conduct an ablation study showing the projected component also carries information about the token correlation, which should not be ignored. We then propose to extend Belief-Attention by making use of both the perpendicular and projected components. In particular, the projected component goes through certain activation function and then a linear mapping before merging with the considered token. Conceptually speaking, the neural block for the projected component can be viewed as a two-layer feedforward network (FFN) within the new attention block. It is also noted that standard attention captures the token correlation via the inner-product matrix $QK^T$. We propose to introduce an additional inner-product matrix $ZZ^T$ to $QK^T$ to capture richer token correlation. We refer to the new module as Belief2-Attention. It can be easily shown that Belief2-Attention is more expressive than standard Attention. We then verify the effectiveness of Belief2-Attention for vision tasks of image classification and segmentation.