Conditional Random Fields

Weakly Supervised Semantic Segmentation (WSSS) learns pixel-level predictions from image-level tags. Recent work focuses on improving coarse CAMs extracted from large vision-language models (commonly CLIP), but does little to improve their accuracy along segment boundaries. That job is instead delegated to a post-processing method like DenseCRF. However, because DenseCRF relies on low-level colour cues, it can flip correct labels to incorrect ones when neighbouring pixels share similar colours. SAM has recently been adopted as a natural alternative, yet it simply takes on DenseCRF's role as an intermediate "refinement" step that outputs one-hot pseudo-labels in prior work. By discarding the valuable uncertainty in CAMs, these one-hot pseudo-labels turn borderline errors into confidently wrong targets. Our key insight is that CAMs should supervise training alongside SAM boundaries, each through its own loss, rather than being fused together into a single hard target. Inspired by CRF potentials, we propose a framework that disentangles soft pseudo-labels as unary supervision and binary edge maps as pairwise supervision. We realize our framework in a single-stage model, DS-CRF, using CAMs from dino.txt and boundaries from SAM. DS-CRF sets a new state-of-the-art of 56.5% mIoU on MS COCO.

Learned mask refiners improve segmentation accuracy, but it is hard to tell how much of the improvement comes from explicit structure rather than from extra capacity, and whether it holds up when the mask generator or its error distribution changes. UnfoldCRF treats refinement as inference in a conditional random field over pixel labels and latent region variables. Its energy has a corrected unary term, learned local pairwise interactions, and image-conditioned latent-region consistency, with a null state that lets a region with weak label agreement withdraw from the consistency term; inference unrolls damped mean-field updates on this one energy. To isolate the effect of structure, we compare against recurrent black-box refiners that read the same inputs and receive the same parameter budget, stage count, and supervision. On COD10K, UnfoldCRF beats the strongest matched control by 1.0 $F^ω_β$ point, improves all four COD metrics, and lowers the fraction of images made worse from 11.7% to 8.5%. Under a train-once protocol over five datasets and several mask sources, the 2.6M-parameter variant gains 4.2 mean $Δ$IoU against 2.0 for its control, and a variant built on frozen DINOv2 features matches the strongest foundation-model refiner with about a seventh of its resident parameters while staying ahead of its own control. On mask generators never seen in training, the gain is 2.0 $F^ω_β$ points against 0.6 for the control. Zeroing individual messages shows where the corrections come from: the pairwise messages mostly fix boundaries, the region messages mostly fix non-boundary errors. Code and supporting materials will be publicly released.

Automating the analysis of whole-slide images has high clinical value, since characterizing cancers requires examining them in detail. Such analysis increasingly relies on vision-language models that provide patch-level zero-shot predictions. However, these predictions remain noisy and must be refined with a few annotations. A promising paradigm for this refinement is few-shot transduction. Rather than treating each patch independently, these methods leverage the relations between patches, together with a few annotations, to refine all predictions jointly. However, current transductive methods are evaluated under conditions that overlook key properties of whole-slide images: (i) datasets consist of independent patches extracted from multiple slides, ignoring the complex tissue organization; (ii) datasets are mostly balanced, whereas a single whole-slide image exhibits severe class imbalance, with several classes absent; and (iii) annotations are sampled at random, without reflecting how a pathologist annotates a limited number of regions. To align the transduction paradigm to realistic whole-slide settings, we introduce the following contributions. First, we propose SlideCRF, which adapts conditional random fields for whole-slide images by combining spatial and biological cues while accounting for classes that may be absent from a given slide. Second, we provide a set of realistic annotation protocols, based on spatially localized clicks and scribbles, modeling different pathologist interactions, such as the iterative correction of model errors. Across four datasets, we show that SlideCRF outperforms current transductive methods in macro F1, improving over the zero-shot predictions by +24.2% and +37.5% with one and 16 clicks per present class, respectively.

Federated learning typically aggregates client updates using fixed or heuristic weighting rules, which can be suboptimal when clients have heterogeneous data and varying contributions to the global model. We propose a framework that refines client aggregation weights using Conditional Random Fields (CRFs). Our method defines unary potentials for individual clients and pairwise potentials for all client pairs, allowing the server to model both client-specific reliability and interactions between clients. The resulting CRF inference produces aggregation weights that enable better convergence of the global training objective. Experiments show that, under non-IID heterogeneity, our approach consistently improves performance over well-established federated learning baselines.

Sentence-level AI-generated text detection (S-AGTD) for hybrid documents, where humans and LLMs co-author one text, faces two gaps: existing methods classify each sentence in isolation, discarding inter-sentence dependencies, and existing benchmarks omit the newest generation of generators. We construct MOSAIC, a benchmark of 16,000 hybrid documents over PubMed and XSum, generated by DeepSeek-V3.2 and Kimi K2 under stringent quality controls including a perplexity-consistency filter absent from prior benchmarks. We recast S-AGTD as structured prediction over the document sentence sequence and instantiate it as SenFlow, integrating graph-based inter-sentence propagation with linear-chain CRF decoding in a single document-level pass over a sentence graph. SenFlow reaches state-of-the-art performance on MOSAIC, with a +4.15 pp average Macro-F1 margin on cross-domain transfer, the hardest of three protocols of increasing difficulty. We further find that even after the perplexity filter equalizes overt cues, AI insertions retain a generator-dependent sentence-length gap that sentence-level detectors still exploit. Code and data: https://github.com/luojingkun22/SenFlow

Sequence labelling, a core task of Natural Language Processing (NLP), consists in assigning each token of an input sentence a label. From a Machine Learning point of view, sequence labelling is often cast as a Linear-Chain Conditional Random Field (CRF) parametrised by a neural network. While this approach gives good empirical results, CRFs assume a finite decision span (eg label bigrams) which can limit their expressivity and hurt performance when long-range dependencies are required. We show we can leverage diffusion to train a CRF conditioned on an entire label sequence, with the caveat that the condition is on a noisy version of labels. We show experimentally that this method, in conjunction with approximate CRF inference, improves label accuracy with a 16.5% error reduction for POS-tagging.

MedER refers to the identification of medical entities. It is crucial for extracting structured clinical information from unstructured medical text. Many existing systems rely on transformer-based models, which are computationally expensive and difficult to deploy in resource-constrained environments. Furthermore, earlier works often use relaxed evaluation metrics that artificially inflate performance by rewarding correct prediction of dominant "Outside" (O) tokens. In this paper, we propose a lightweight Medical Entity Recognition (MedER) framework for the Bangla language. We establish a rigorous baseline using a 12-layer BanglaBERT model combined with a Conditional Random Field (CRF) layer for exact-boundary entity detection. To address deployment constraints, we compress this teacher model into a 4-layer student network through Knowledge Distillation (KD), where the student learns from the teacher's pre-CRF soft emission logits. Finally, we apply INT8 dynamic quantization to further reduce model size and inference cost. Our final quantized student achieves an 8.6x CPU speedup while requiring nearly 48 percent less storage than the CRF teacher model.

LLM-powered coding agents spend the majority of their token budget reading repository files, yet much of the retrieved code is irrelevant to the task at hand. Existing learned pruners compress this context with a single-objective sequence labeler, collapsing all facets of code relevance into one score and one transition matrix. We show that this formulation creates a modeling bottleneck: a single CRF transition prior must serve heterogeneous retention patterns, including contiguous semantic spans and sparse structural support lines. We propose LaMR (Latent Multi-Rubric), a structured pruning framework that decomposes code relevance into two interpretable quality dimensions, semantic evidence and dependency support, each modeled by a dedicated CRF with dimension-specific transition dynamics. A mixture-of-experts gating network dynamically weights the per-rubric emissions conditioned on the query, and a final CRF layer on the fused emissions produces the aggregate keep-or-prune decision. To supervise each dimension without additional annotation cost, we derive multi-rubric labels from the existing training corpus via AST-based program analysis, simultaneously denoising the teacher's binary labels. By effectively filtering distracting noise, LaMR frequently matches or even outperforms unpruned full-context baselines. Experiments on four benchmarks (SWE-Bench Verified, SWE-QA, LCC, LongCodeQA) show that LaMR wins 12 of 16 head-to-head multi-turn comparisons. It saves up to 31% more tokens on multi-turn agent tasks and improves Exact Match by up to +3.5 on single-turn tasks, while performance is frequently enhanced by denoising the context, and any remaining drops are marginal.

The Probabilistic Transformer (PT) establishes that the Transformer's self-attention plus its feed-forward block is mathematically equivalent to Mean-Field Variational Inference (MFVI) on a Conditional Random Field (CRF). Under this equivalence the Transformer ceases to be a black-box neural network and becomes a programmable factor graph: graph topology, factor potentials, and the message-passing schedule are all explicit and inspectable primitives that can be engineered. PT was originally developed for natural language and in this report we investigate its potential for time series. We first lift PT into the Spatial-Temporal Probabilistic Transformer (ST-PT) to repair PT's missing channel axis and weak per-step semantics, and adopt ST-PT as a shared cornerstone backbone. We then identify three distinct properties that PT/ST-PT offers as a factor-graph model and derive three Research Questions, one per property, that probe how each property can be exploited in time series: RQ1. The graph topology and potentials are direct programmable primitives. Can this be used to inject symbolic time-series priors into ST-PT through structural graph modifications, especially under data scarcity and noise? RQ2. The CRF's factor matrices are the operator's potentials. Can an external condition program these factor matrices on a per-sample basis, so that conditional generation becomes structural rather than feature-level modulation of a fixed one? RQ3. Each MFVI iteration is a Bayesian posterior update on the factor graph. Can this turn the latent transition of latent-space AutoRegressive (AR) forecasting from an opaque MLP into a principled posterior update, and can a CRF teacher distill its latents into the AR student to counter cumulative error? We give one empirical study per question. Together, these three studies position ST-PT as a programmable framework for time-series modeling.

Recent advances in autonomous driving have motivated research on pedestrian intention prediction, which aims to infer future crossing decisions and actions by modeling temporal dynamics, social interactions, and environmental context. However, existing studies remain constrained by oversimplified multi-agent interaction patterns, opaque reasoning logic, and a lack of global consistency in behavioral predictions, which compromise both robustness and interpretability. In this work, we propose ESIA (Energy-based Spatiotemporal Interaction-Aware framework), a novel Conditional Random Field (CRF)-based paradigm. We cast the intention prediction task as a structured prediction problem over a unified graph-based representation, treating pedestrians and the environment as spatiotemporal nodes. To characterize their distinct roles, we assign unary potentials to nodes to capture individual intentions, and pairwise potentials to edges to encode social and environmental interactions. These potentials are integrated into a unified global energy function to ensure scene-level consistency across behavioral predictions. To further constrain inference without ground-truth supervision, we introduce structural consistency terms to penalize logical contradictions. This optimization is efficiently solved via a novel Unary-Seeded Simulated Annealing (U-SSA) algorithm, which leverages high-confidence unary priors to rapidly converge to a high-quality solution. Extensive experiments on standard benchmarks demonstrate that ESIA achieves state-of-the-art performance with improved interpretability over existing methods.

Semi-Markov Conditional Random Fields (semi-CRFs) assign labels to segments of a sequence rather than to individual positions, enabling exact inference over segment-level features and principled uncertainty estimates at their boundaries. However, existing implementations must materialize a large edge potential tensor whose size grows with sequence length, maximum segment length, and label count, becoming prohibitive for speech-scale state spaces and intractable at genomic scales where sequences can exceed 100,000 positions. This memory bottleneck has limited the adoption of exact segment-level inference for long sequences and large label sets. We identify that the core inefficiency is materializing edge potentials that can instead be evaluated on-the-fly from a compact prefix-sum array, and make several improvements. First, replacing the stored edge tensor with prefix-sum lookup reduces the memory footprint by a factor proportional to the product of segment length and label count. Second, a streaming forward-backward pass with checkpoint-boundary normalization keeps working memory sublinear in sequence length while preserving exact gradients. Third, zero-centered cumulative scores control numerical drift and induce an adaptive duration prior under label imbalance. We integrate these ideas into Flash-SemiCRF, a fused Triton kernel that enables exact semi-CRF inference on previously intractable problem sizes. Available at https://github.com/biobenkj/flash-semicrf.

We propose PPEDCRF, a calibrated selective perturbation framework that protects \emph{background-based location privacy} in released video frames against gallery-based retrieval attackers. Even after GPS metadata are stripped, an adversary can geolocate a frame by matching its background visual cues to geo-tagged reference imagery; PPEDCRF mitigates this threat by estimating location-sensitive background regions with a dynamic conditional random field (DCRF), rescaling perturbation strength with a normalized control penalty (NCP), and injecting Gaussian noise only inside the inferred regions via a DP-style calibration rule. On a controlled paired-scene retrieval benchmark with eight attacker backbones and three noise seeds, PPEDCRF reduces ResNet18 Top-1 retrieval accuracy from 0.667 to $0.361\pm0.127$ at $σ_0=8$ while preserving $36.14\,$dB PSNR -- an ${\approx}6\,$dB quality advantage over global Gaussian noise. Transfer across the eight-backbone seed-averaged benchmark is broadly supportive (23 of 24 backbone-gallery cells show negative $Δ$), while appendix-scale confirmation identifies MixVPR as a remaining adverse-transfer exception. Matched-operating-point analysis shows that PPEDCRF and global Gaussian noise converge in Top-1 privacy at equal utility, so the practical benefit is spatially concentrated perturbation that preserves higher visual quality at any given noise scale rather than stronger matched-utility privacy. Code: https://github.com/mabo1215/PPEDCRF