Binarization

Binary neural networks are very attractive for constrained deployment, enabling small footprint and low-power inference. For binary activations, the dot products become sign-controlled additions or subtractions, but the number of operations is unchanged. Indeed, every neuron or output channel still accumulates all of its input, even though only the sign will be retained, which is often wasteful. As the accumulation progresses, the running partial sum frequently drifts so far from zero that its final sign becomes highly predictable long before the last term is reached; every contribution evaluated after that point changes the value of the sum but not the final output activation. This paper turns this observation into a post-training early-stopping mechanism. We characterize the behavior of the running accumulations on the training dataset and use this information to predict the final sign as soon as possible. No model parameter is retrained. We count the number of operations under an idealized ordering of weights. On VGG11 applied to the CIFAR-10 dataset, the method removes $86.6\%$ of the accumulation terms of the deepest convolution for a $0.37$-point accuracy drop, and $25\%$ of the full-network arithmetic when used on the three deepest convolutions simultaneously, for a $1.36$-point drop.

The Rashomon effect describes the phenomenon that many models can achieve nearly equivalent performance on the same learning task, with significant ramifications for robustness, feature importance, and customizability. These use cases motivate the computation of Rashomon sets: the set of all models whose regularized loss is near-optimal. Decision trees are one of the few model classes for which Rashomon sets can be fully enumerated, but this computation has always been conditional on a binarization of the original data, either restricting which splits each tree is allowed to make or substantially increasing the complexity of an already difficult combinatorial problem. We introduce the first algorithm that exactly enumerates decision-tree Rashomon sets while exploiting the ordered structure of continuous features. We further develop a relaxation for approximate enumeration and an anytime algorithm that progressively refines the set of candidate thresholds, producing increasingly detailed approximations that converge to the continuous-feature Rashomon set. Experiments show that coarse binarization can miss many trees, important features, and predictive multiplicity; our algorithms achieve orders-of-magnitude speedups over existing enumeration methods, with approximations providing further speedups while maintaining near-perfect recall.

Survival analysis is an established framework for analyzing time-to-event data, yet many clinical machine learning studies still binarize the outcome before model training. This practice excludes censored patients, collapses temporal information into a single threshold, and can affect which features are selected as prognostically relevant. We examine the cost of this binarization in the context of Bayesian network (BN) feature selection, using two recent publications as case studies: one that applies BN-based feature selection to a head-and-neck cancer cohort and a second surgical cohort study that, while not BN-based, likewise binarizes its survival endpoint. We replace the binary scoring function with the Cox partial log-likelihood for feature-to-outcome edges, a modification we call the Survival-Aware Bayesian network, and recover prognostic features that binarization misses. Our ablation experiment confirms that the improvement is driven by the time-to-event scoring formulation rather than by retaining more patients. The results generalize across five endpoint-cohort combinations in head-and-neck cancer and extend to three further cancer types (breast, colorectal, and kidney). We propose that clinical studies with survival outcomes should use time-to-event methods by default, as binarization discards the prognostic signal retained by survival analysis.

Binarizing a polynomial Kolmogorov--Arnold Network (KAN) not only changes parameter precision, but also alters the function space available to each layer. When activations are restricted to ${-1,+1}$, all even powers reduce to $1$ and all odd powers reduce to $x$, causing the elementwise polynomial basis to collapse to constant and first-order responses. We refer to this structural failure as Spatial Orthogonality Collapse. Our proposed BiKAN addresses this critical issue by augmenting each binary KAN layer with selected degree-2 Walsh characters. Fixed circular channel rolls generate pairwise parities, and learned binary projections mix them using the same XNOR--popcount operations as the remaining W1A1 paths. This restores explicit pairwise coordinates without learned routing or multiplier-based feature generation. Experiments on CIFAR-10 confirms that removing parity reduces accuracy by $1.23$ points over five paired seeds ($p=0.003$), the gain increases as width decreases, and accuracy improves monotonically as more parity planes are added. At an equal $\sim$11.9M-parameter budget, parity outperforms conventional widening by $3.09$ points ($p<10^{-4}$). At W1A1, BiKAN reaches $99.48\%$, $84.38\%$, and $55.81\%$ on MNIST, CIFAR-10, and CIFAR-100, respectively. Post-route Zynq-7020 FPGA results show that the repair remains hardware-efficient; the convolutional design cuts DSP usage from 164 to 72 and estimated compute-core latency from 401 to 54.8 ms, while the power-of-two-aware dense design achieves zero-DSP inference with a 0.03-point accuracy loss. The BiKAN implementation is available at https://github.com/OSU-STARLAB/BiKAN.

Large Vision-Language Models (LVLMs) have achieved remarkable progress in multimodal understanding, yet their enormous parameter scale and cross-modal computation incur substantial memory and latency overhead, severely limiting real-world deployment on resource-constrained devices. Binarization offers an attractive solution by drastically reducing storage and computational costs. However, existing binarization methods neglect the varying importance of weights across different layers and modalities. This causes parameters irrelevant to downstream tasks to be unnecessarily retained, whereas modality-critical weights may not be adequately optimized, resulting in significant performance degradation. To address these challenges, we develop a novel \underline{S}ignificance-\underline{A}ware \underline{B}inarization for \underline{L}arge \underline{V}ision-\underline{L}anguage \underline{M}odels (SAB-LVLM). Specifically, after constructing Hessian matrices for textual and visual inputs, we propose a spatial significance map to distinguish full-precision weights activated under a single modality from those activated across modalities. We then devise a modality-guided integration strategy to obtain the significance-aware binarization map, which measures weight significance across layers and modalities. Subsequently, this binarization map is incorporated into the binarization objective as an error reweighting term, and binarization fitting is performed through an alternating significance-weighted update scheme. Extensive experiments illustrate the superiority of our SAB-LVLM over existing binary PTQ methods under an approximately 1-bit compression constraint. Our code is accessible at https://github.com/LyuQi127/SAB_LVLM.

Training binary neural networks (BNNs) from scratch is dominated by the straight-through estimator (STE), whose forward/backward mismatch produces severe accuracy degradation as networks deepen. We study an orthogonal axis: when and where binarization is enforced during training. We introduce StoMPP (Stochastic Masked Partial Progressive Binarization), which gradually replaces clipped weights and activations with their hard binary counterparts layer by layer from input to output, using stochastic partial masks with soft refresh. StoMPP delivers two complementary benefits. As a standalone training rule, it provides a fully STE-free procedure that improves over vanilla STE with gains that grow with depth (ResNet-50 BNN: +18.0/+13.5/+3.8 on CIFAR-10/100/ImageNet), and the pattern holds across ResNet-18/34/50, MobileNetV2, and BERT fine-tuning. Composed with surrogate gradients by applying STE only to frozen entries, it reaches +27.1/+19.8/+17.7 over vanilla STE on the same setting. Underlying both regimes is a single mechanistic finding: progression order is decisive. Forward layerwise progression prevents depth collapse, reverse progression collapses to near-chance, and binary-weight networks (without binary activations) are insensitive to order. We trace this asymmetry to activation-induced gradient blockades: a committed binary activation severs gradient flow upstream, and ordering controls when these blockades form. To isolate the progression's contribution from any benefit conferred by STE, we conduct all ablations in the STE-free regime; the resulting characterization (schedule, refresh, ordering, dynamics) thus reflects the progression itself rather than its interaction with surrogate gradients.

Degraded document image binarization is sensitive to domain shifts caused by paper aging, bleed-through, stains, shadows, and uneven illumination, and the foreground-background separation of recent learning-based methods can become unstable on unseen degradation domains. We propose DR-Mamba, a sample-conditioned detail-background suppression framework that performs automatic inference-time domain adaptation for document image binarization. Unlike test-time adaptation methods that require gradient updates or auxiliary data at inference, DR-Mamba adapts to each input document through input-dependent gates within a single forward pass, requiring no target-domain labels, no fine-tuning, and no test-time parameter updates. Instead of using Mamba-style selective scanning as a single generic feature path, DR-Mamba reinterprets it as fast-slow route modeling: a fast detail route captures local stroke structures, while a slow background route accumulates spatially persistent degradation responses. The two routes are integrated through an input-dependent subtractive gate that explicitly suppresses background interference rather than fusing features by addition or concatenation. We further add full-resolution detail-guided reconstruction and thin-stroke-aware supervision to recover fine strokes lost during downsampling. Evaluated under a leave-one-year-out protocol on DIBCO-style benchmarks, where each held-out year is treated as an unseen degradation domain, DR-Mamba shows that per-document, per-location subtractive suppression improves cross-domain robustness, with particularly strong performance on the most severely degraded held-out fold.

This paper investigates the computational complexity of verification problems for Binarized Neural Networks (BNNs), in which activations and weights are binary. Specifically, we study three verification problems. First, we prove that checking the satisfiability of a linear property for a BNN is NP-complete via a reduction from the Boolean Satisfiability (SAT) problem. Second, we show that verifying robustness under non-uniform image occlusion is NP-complete through a reduction from SAT. Finally, we demonstrate that uniform occlusion induces a piecewise-constant structure in the network output, which enables the design of a polynomial-time algorithm for robustness verification.

This paper presents ERN-Net, an Evolving Reason Node-Net for efficient document image binarization. ERN-Net enhances degradation-sensitive regions, such as faint strokes, broken characters, and noisy backgrounds, through evolving reason nodes and multi-scale reasoning. We further compare ResNet-101, ConvNeXt-Tiny, and ConvNeXt-Base, and find that ConvNeXt-Tiny provides the best practical trade-off between accuracy and memory usage. In addition, DIBCO-based pretraining improves binarization performance without increasing model memory consumption, requiring only about 1.5 additional training hours. Experiments on DIBCO-style benchmarks show that ERN-Net is effective under low-data and low-memory settings.

Document image binarization aims to separate foreground text from degraded backgrounds while preserving thin, broken, and low-contrast strokes. Although deep learning methods have improved binarization performance, most existing approaches rely on convolutional, transformer-based, or generative architectures, while Mamba-based state space models remain largely unexplored for this task. In this work, we investigate Mamba-based feature propagation and observe that direct state-space propagation may dilute weak foreground cues during long-range modeling, especially faint ink traces, fragmented characters, and boundary-sensitive stroke details. To address this problem, we propose DeepMine-Mamba, a Mamba-based binarization framework equipped with a novel Anti-Dilution Gate that estimates propagation-induced feature changes and selectively restores stroke-sensitive local responses while suppressing unnecessary background enhancement. Experiments on DIBCO/H-DIBCO benchmarks under a strict leave-one-year-out protocol show that DeepMine-Mamba achieves competitive overall performance, with strong average FM and Fps across benchmark years. Ablation results further show that the Anti-Dilution Gate is the key component for mitigating propagation-induced foreground dilution and improving stroke preservation.

Precise parametric control over circuit geometry is essential for semiconductor inspection, yet obtaining sufficient real training data remains costly. Although generative models such as diffusion models and Generative Adversarial Networks (GANs) can augment training data, they cannot guarantee the nanometer-scale geometric accuracy required for metrology tasks. We propose a visual program synthesis framework in which a Vision-Language Model (VLM) converts inspection images into editable Domain-Specific Language (DSL) code describing circuit geometries, enabling controlled generation of training data with exact parameter manipulation. Because the VLM is trained solely on synthetic DSL-rendered data, a domain gap arises when processing real Scanning Electron Microscope (SEM) images. We bridge this gap with an input binarization strategy that strips SEM-specific texture and noise, letting the model focus on geometric structure. On the MIIC dataset, binarized inputs improve the mean Dice coefficient from 0.4393 to 0.5256 over the raw-input baseline, demonstrating that simple texture abstraction substantially mitigates the sim-to-real gap.

We introduce a physics-inspired continuous relaxation framework that yields substantially improved solutions for NP-hard combinatorial optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), binary sparse coding, and planted-solution Ising models. By parameterizing discrete binary variables as continuous wave-like states on the complex unit circle, we inherently smooth highly non-convex energy landscapes. We show that representing binary variables as complex phases reveals an implicit regularization mechanism that promotes convergence toward discrete states. Extracting this mechanism yields significant improvements even within standard real-valued optimization frameworks, using this regularizer explicitly. Empirically, this regularization yields vastly higher ground-state convergence rates than standard real-valued alternatives. Our models achieved zero error in large-scale 160x160 QUBO tasks under severe noise (sigma=0.25), and outperformed traditional algorithms (OMP and LASSO) in underdefined sparse coding with perfect recovery at sigma=0.15. The solver's robustness was further validated by recovering exact ground-state configurations in 8 out of 11 rigorously engineered planted-solution benchmarks.

Quasi-bimodal objects, such as text, road signs, and barcodes, play a basic yet vital role in daily visual communication. By boiling these down to clear silhouettes, binarization uses a minimal language to convey essential vision cues for maximum downstream efficiency, especially for tasks that require simple geometric, topological reasoning rather than heavy appearance modeling. The catch is that frame-based imaging often struggles on mobile platforms like drones, self-driving cars, and underwater vehicles, in which rapid motion causes severe motion blur and harsh lighting washes out scene details. To overcome these physical limits, neuromorphic vision via event cameras, featuring microsecond time resolution and high dynamic range, steps in as a natural solution. Building upon this event-driven paradigm, we propose a simple yet effective dual-modal approach that harnesses the synergy between frames and events for training-free, real-time, high-frame-rate binarization on CPU-only devices. Extensive evaluations show that it earns competitive performance against leading techniques in reducing blur artifacts and delivers impressive improvements under challenging illumination at a lower computational cost. Besides, its asynchronous nature bypasses long-standing event-scarcity issues that break traditional time-binning reconstruction at fixed time slots, maintaining clear target shapes even at extreme kilohertz frame rates. Its binary results further serve as reliable representations to facilitate a range of downstream tasks. This work paves the way towards lightweight perception and interaction in embodied intelligence on resource-constrained edge platforms.

We introduce Graph Normalization (GN), a principled dynamical system on graphs that serves as a differentiable approximation engine for the NP-hard Maximum Weight Independent Set (MWIS) problem. MWIS encompasses many combinatorial challenges, including optimal assignment, scheduling, set packing, and MAP inference in discrete Markov Random Fields. Unlike Belief Propagation, we prove GN always converges to a binary indicator of a Maximum Independent Set. GN realizes a fast quasi-Newton descent through an exact Majorization-Minimization step, systematically improving the MWIS relaxed primal objective. We establish an equivalence between GN and the Replicator Dynamics of a nonlinear evolutionary game, where vertices compete for inclusion in an independent set. While a non-potential game, the GN game follows Fisher's Fundamental Theorem of Natural Selection, where the average fitness equals the MWIS primal objective and strictly increases. This connection leads to a weighted extension of the Motzkin-Straus theorem, showing MISes are in bijection with the local minima of a quadratic form over a tilted simplex. For the Assignment Problem, GN acts as a variant of the Sinkhorn algorithm that naturally converges to a hard assignment while generalizing to arbitrary constraint graphs. We demonstrate GN's performance as a fast binarization engine for the state-of-the-art Bregman-Sinkhorn relaxed MWIS solver. On real-world benchmarks with up to 1M edges, GN identifies solutions within 1% of the best known results in seconds on a CPU. GN opens new avenues for deep learning architectures requiring differentiable, "hard" decisions under constraints, with applications in structured sparse attention, dynamic network pruning, and Mixture-of-Experts. Beyond core AI, the GN framework enables end-to-end learning of constrained optimization in computer vision, computational biology, and resource allocation.

Large language models (LLMs) have driven major progress in NLP, yet their substantial memory and compute demands still hinder practical deployment. Binarization can compress weights to 1 bit, fundamentally lowering compute and bandwidth cost. However, existing methods cannot address activation heavy tails and thus must keep activations in high precision, preventing true end-to-end acceleration. To overcome this limitation, we propose BWLA (Binarized Weights and Low-bit Activations), the first post-training quantization framework that preserves high accuracy while achieving 1-bit weight quantization together with low-bit activations (e.g., 6 bits). The Orthogonal-Kronecker Transformation (OKT) learns an orthogonal mapping via EM minimization, converting unimodal weights into symmetric bimodal forms while suppressing activation tails and incoherence. The Proximal SVD Projection (PSP) then performs lightweight low-rank refinement through proximal SVD projection, further enhancing quantizability with minimal overhead. On Qwen3-32B, BWLA reaches a Wikitext2 perplexity of 11.92 under 6-bit activations (vs. 38 from SOTA), improves five zero-shot tasks by more than 70%, and delivers 3.26 times inference speedup, demonstrating strong potential for real-world LLM compression and acceleration.

Deploying large language models (LLMs) in resource-constrained environments is hindered by heavy computational and memory requirements. We present LBLLM, a lightweight binarization framework that achieves effective W(1+1)A4 quantization through a novel three-stage quantization strategy. The framework proceeds as follows: (1) initialize a high-quality quantized model via PTQ; (2) quantize binarized weights, group-wise bitmaps, and quantization parameters through layer-wise distillation while keeping activations in full precision; and (3) training learnable activation quantization factors to dynamically quantize activations to 4 bits. This decoupled design mitigates interference between weight and activation quantization, yielding greater training stability and better inference accuracy. LBLLM, trained only using 0.016B tokens with a single GPU, surpasses existing state-of-the-art binarization methods on W2A4 quantization settings across tasks of language modeling, commonsense QA, and language understanding. These results demonstrate that extreme low-bit quantization of LLMs can be both practical and highly effective without introducing any extra high-precision channels or rotational matrices commonly used in recent PTQ-based works, offering a promising path toward efficient LLM deployment in resource-limited situations.

Discretizing raw features into bucketized attribute representations is a popular step before sharing a dataset. It is, however, evident that this step can cause significant bias in data and amplify unfairness in downstream tasks. In this paper, we address this issue by introducing the unbiased binning problem that, given an attribute to bucketize, finds its closest discretization to equal-size binning that satisfies group parity across different buckets. Defining a small set of boundary candidates, we prove that unbiased binning must select its boundaries from this set. We then develop an efficient dynamic programming algorithm on top of the boundary candidates to solve the unbiased binning problem. Finding an unbiased binning may sometimes result in a high price of fairness, or it may not even exist, especially when group values follow different distributions. Considering that a small bias in the group ratios may be tolerable in such settings, we introduce the epsilon-biased binning problem that bounds the group disparities across buckets to a small value epsilon. We first develop a dynamic programming solution, DP, that finds the optimal binning in quadratic time. The DP algorithm, while polynomial, does not scale to very large settings. Therefore, we propose a practically scalable algorithm, based on local search (LS), for epsilon-biased binning. The key component of the LS algorithm is a divide-and-conquer (D&C) algorithm that finds a near-optimal solution for the problem in near-linear time. We prove that D&C finds a valid solution for the problem unless none exists. The LS algorithm then initiates a local search, using the D&C solution as the upper bound, to find the optimal solution.

Deploying large language models (LLMs) is challenging due to their massive parameters and high computational costs. Ultra low-bit quantization can significantly reduce storage and accelerate inference, but extreme compression (i.e., mean bit-width <= 2) often leads to severe performance degradation. To address this, we propose Squeeze10-LLM, effectively "squeezing" 16-bit LLMs' weights by 10 times. Specifically, Squeeze10-LLM is a staged mixed-precision post-training quantization (PTQ) framework and achieves an average of 1.6 bits per weight by quantizing 80% of the weights to 1 bit and 20% to 4 bits. We introduce Squeeze10LLM with two key innovations: Post-Binarization Activation Robustness (PBAR) and Full Information Activation Supervision (FIAS). PBAR is a refined weight significance metric that accounts for the impact of quantization on activations, improving accuracy in low-bit settings. FIAS is a strategy that preserves full activation information during quantization to mitigate cumulative error propagation across layers. Experiments on LLaMA and LLaMA2 show that Squeeze10-LLM achieves state-of-the-art performance for sub-2bit weight-only quantization, improving average accuracy from 43% to 56% on six zero-shot classification tasks--a significant boost over existing PTQ methods.