Daily Papers

PTQTP decomposes LLM weight matrices into two ternary (trit) planes with two free per-group scales. Tying the scales to a fixed ratio of three collapses the decomposition into a single uniform nine-level quantizer, a known balanced-ternary identity. To our knowledge, at the time of writing, this work is the first to impose that identity as a constraint inside PTQTP's solver. The two trit planes then fold losslessly into one 4-bit code plane that we make the persistent serving representation: disk bytes, expert-cache bytes, and kernel input are the same 4.0625-bits/weight blocks, consumed in one integer dot pass. For this conjunction (ratio-3 nine-level code, CPU-SIMD kernels, SSD expert streaming, identical persistent bytes) we likewise found no precedent. We apply this to the routed experts of DeepSeek-V4-Flash-0731, a 284B-A13B mixture-of-experts model, quantizing in one shot from the released MXFP4 expert weights and streaming experts from SSD on a 64 GB laptop. Against a 4.5-bit Q4_K baseline, measured one process per fixture with an expert-lossless anchor arm as reference control, the tied model matches the official serving API on 5/5 fixtures at step 0 (Q4_K: 4/5) and 12/14 captured continuation steps (11/14), scores 86 vs. 84 on a 100-item MMLU subset, decodes 6.7% faster in decode phase, and ships 9% smaller files: no detected fidelity difference at these small evaluation sizes, and every fixture-level difference between the arms traces to a single measured near-tie cell. The tied fit nevertheless shows higher weight-reconstruction error and worse perplexity, a measured dissociation between proxy metrics and reference fidelity. A cumulative trunk-ternarization ladder and bitwise-pinned aarch64/x86-64 kernels complete the report. All code, formats, and evaluation artifacts are open source in the fucina inference stack.

Matrix multiplication optimization remains a fundamental challenge in computational mathematics. This work introduces a novel approach that discovers matrix multiplication schemes in the ternary field (Z_T), where coefficients are restricted to {-1, 0, 1} to minimize naive additive complexity. The core of the method is a GPU-accelerated meta flip graph algorithm that maintains ternary safety through specialized arithmetic operations and sign symmetry breaking. Key results include new best ranks for the formats 4 times 5 times 12, 5 times 6 times 10, and 6 times 7 times 9, the independent discovery of 32 schemes in Z_T that match known optimal ranks (including 8 previously known only with rational coefficients), and 30 rank improvements in the binary field. The analysis of 164 known schemes shows that 92 can be implemented in Z_T, while 72 could not be found in the ternary field with current methods, defining the current boundaries of this approach. All software, results, and discovered schemes are provided as open-source.

BalancedBio is a theoretically grounded framework for parameter-efficient biomedical reasoning, addressing multi-capability integration in domain-specific AI alignment. It establishes the Biomedical Multi-Capability Convergence Theorem, proving orthogonal gradient spaces are essential to prevent capability interference for safe deployment. Key innovations include: (1) Medical Knowledge Grounded Synthetic Generation (MKGSG), extending Source2Synth with clinical workflow constraints and medical ontology validation for factual accuracy and safety; and (2) Capability Aware Group Relative Policy Optimization, deriving optimal hybrid reward weighting to maintain orthogonality in RL, using a reward model with rule-based and model-based scores adapted to biomedical tasks. Mathematical analysis proves Pareto-optimal convergence, preserving performance across capabilities. It achieves state-of-the-art results in its parameter class: domain expertise (80.95% BIOMED-MMLU, +15.32% over baseline), reasoning (61.94%, +7.75%), instruction following (67.95%, +6.44%), and integration (86.7%, +18.5%). Theoretical safety guarantees include bounds on capability preservation and clinical accuracy. Real-world deployment yields 78% cost reduction, 23% improved diagnostic accuracy, and 89% clinician acceptance. This work provides a principled methodology for biomedical AI alignment, enabling efficient reasoning with essential safety and reliability, with the 0.5B model version to be released.

An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary (Z_2), modular ternary (Z_3) and integer ternary (Z_T = {-1,0,1}) -- and implements both fixed-dimension and meta-dimensional search operators. Using efficient bit-level encoding of coefficient vectors and OpenMP parallelism, the tools enable large-scale exploration on commodity hardware. The study covers 680 schemes ranging from (2 times 2 times 2) to (16 times 16 times 16), with 276 schemes now in Z_T coefficients and 117 in integer coefficients. With this framework, the multiplicative complexity (rank) is improved for 79 matrix multiplication schemes. Notably, a new 4 times 4 times 10 scheme requiring only 115 multiplications is discovered, achieving ωapprox 2.80478 and beating Strassen's exponent for this specific size. Additionally, 93 schemes are rediscovered in ternary coefficients that were previously known only over rationals or integers, and 68 schemes in integer coefficients that previously required fractions. All tools and discovered schemes are made publicly available to enable reproducible research.

Ternary and binary neural networks enable multiplication-free computation and promise multiple orders of magnitude efficiency gains over full-precision networks if implemented on specialized hardware. However, since both the parameter and the output space are highly discretized, such networks have proven very difficult to optimize. The difficulties are compounded for the class of transformer text generation models due to the sensitivity of the attention operation to quantization and the noise-compounding effects of autoregressive decoding in the high-cardinality output space. We approach the problem with a mix of statistics-based quantization for the weights and elastic quantization of the activations and demonstrate the first ternary and binary transformer models on the downstream tasks of summarization and machine translation. Our ternary BART base achieves an R1 score of 41 on the CNN/DailyMail benchmark, which is merely 3.9 points behind the full model while being 16x more efficient. Our binary model, while less accurate, achieves a highly non-trivial score of 35.6. For machine translation, we achieved BLEU scores of 21.7 and 17.6 on the WMT16 En-Ro benchmark, compared with a full precision mBART model score of 26.8. We also compare our approach in the 8-bit activation setting, where our ternary and even binary weight models can match or outperform the best existing 8-bit weight models in the literature. Our code and models are available at: https://github.com/facebookresearch/Ternary_Binary_Transformer

Ternary weight quantization (e.g., BitNet b1.58) offers a promising path to mitigate the memory bandwidth bottleneck in Large Language Model (LLM) inference. However, conventional compute platforms lack native support for ternary-weight arithmetic, often relying on inefficient dequantization. Lookup table (LUT)-based hardware architectures provide an effective alternative by replacing multiplications with conditional additions, but their design space remains largely unexplored. Existing designs rely on heuristic parameter selection, lacking a systematic understanding of the architectural trade-offs. This work addresses this gap by formalizing the design space of ternary LUT-based accelerators and presenting an open-source hardware generator coupled with an analytical cost model, validated against synthesis in TSMC 16nm technology. By spanning the full architectural space, this framework not only enables rapid design space exploration but also establishes a common footing for fair cross-design evaluation, which was previously hindered by inconsistent instantiations across published accelerators. Using this framework, we challenge several assumptions and design choices in recent literature. We demonstrate that the optimal architecture is fundamentally governed by the activation data type: while LUT-based reuse offers significant gains for high-cost arithmetic (e.g., FP16), it yields diminishing returns for small integer types. Furthermore, we show that maximizing core size consistently improves area density compared to highly tiled approaches. Our optimized designs achieve a 2.2x area reduction compared to multiplier-based baselines. Moreover, by benchmarking state-of-the-art implementations against our model, we reveal that correcting suboptimal parameters yields up to a 1.2x area improvement.

Distributed applications need identifiers that satisfy storage efficiency, chronological sortability, origin metadata embedding, zero-lookup verifiability, confidentiality for external consumers, and multi-century addressability. Based on our literature survey, no existing scheme provides all six of these identifier properties within a unified system. This paper introduces Source Known Identifiers (SKIDs), a three-tier identity system that projects a single entity identity across trust boundaries, addressing all six properties. The first tier, Source Known ID (SKID), is a 64-bit signed integer embedding a timestamp with a 250-millisecond precision, application topology, and a per-entity-type sequence counter. It serves as the database primary key, providing compact storage (8 bytes) and natural B-tree ordering for optimized database indexing. The second tier, Source Known Entity ID (SKEID), extends the SKID into a 128-bit Universally Unique Identifier (UUID) compatible value by adding an entity type discriminator, an epoch selector, and a BLAKE3 keyed message authentication code (MAC). SKEIDs enable zero-lookup verification of identifier origin, integrity, and entity type within trusted environments, with a big-endian byte layout that preserves chronological ordering in lexicographic UUID string comparisons. The third tier, Secure SKEID, encrypts the entire SKEID using AES-256 symmetric encryption as a single-block pseudorandom permutation, producing ciphertext indistinguishable from random bytes while remaining compatible with standard UUID data-type parsers in string representation. Deterministic bidirectional transformations connect all three tiers.

The deployment of Large Language Models (LLMs) on resource-constrained edge devices is increasingly hindered by prohibitive memory and computational requirements. While ternary quantization offers a compelling solution by reducing weights to {-1, 0, +1}, current implementations suffer from a fundamental misalignment with commodity hardware. Most existing methods must choose between 2-bit aligned packing, which incurs significant bit wastage, or 1.67-bit irregular packing, which degrades inference speed. To resolve this tension, we propose Sherry, a hardware-efficient ternary quantization framework. Sherry introduces a 3:4 fine-grained sparsity that achieves a regularized 1.25-bit width by packing blocks of four weights into five bits, restoring power-of-two alignment. Furthermore, we identify weight trapping issue in sparse ternary training, which leads to representational collapse. To address this, Sherry introduces Arenas, an annealing residual synapse mechanism that maintains representational diversity during training. Empirical evaluations on LLaMA-3.2 across five benchmarks demonstrate that Sherry matches state-of-the-art ternary performance while significantly reducing model size. Notably, on an Intel i7-14700HX CPU, our 1B model achieves zero accuracy loss compared to SOTA baselines while providing 25% bit savings and 10% speed up. The code is available at https://github.com/Tencent/AngelSlim .

Deploying Large Language Models (LLMs) on resource-constrained edge devices faces critical bottlenecks in memory bandwidth and power consumption. While ternary quantization (e.g., BitNet b1.58) significantly reduces model size, its direct deployment on general-purpose hardware is hindered by workload imbalance, bandwidth-bound decoding, and strict data dependencies. To address these challenges, we propose VitaLLM, a hardware-software co-designed accelerator tailored for efficient ternary LLM inference. We introduce a heterogeneous Dual-Core Compute Strategy that synergizes specialized TINT-Cores for massive ternary projections with a unified BoothFlex-Core for mixed-precision attention, ensuring high utilization across both compute-bound prefill and bandwidth-bound decode stages. Furthermore, we develop a Leading One Prediction (LOP) mechanism to prune redundant Key-Value (KV) cache fetches and a Dependency-Aware Scheduling framework to hide the latency of nonlinear operations. Implemented in TSMC 16nm technology, VitaLLM achieves a decoding throughput of 70.70 tokens/s within an ultra-compact area of 0.223 mm^2 and a power consumption of 65.97 mW. The design delivers a superior Figure of Merit (FOM) of 17.4 TOPS/mm^2/W, significantly outperforming state-of-the-art accelerators. Finally, we explore an extended bit-serial design (BoothFlex-BS) to demonstrate the architecture's adaptability for precision-agile inference.

Deep learning has transformed AI applications but faces critical security challenges, including adversarial attacks, data poisoning, model theft, and privacy leakage. This survey examines these vulnerabilities, detailing their mechanisms and impact on model integrity and confidentiality. Practical implementations, including adversarial examples, label flipping, and backdoor attacks, are explored alongside defenses such as adversarial training, differential privacy, and federated learning, highlighting their strengths and limitations. Advanced methods like contrastive and self-supervised learning are presented for enhancing robustness. The survey concludes with future directions, emphasizing automated defenses, zero-trust architectures, and the security challenges of large AI models. A balanced approach to performance and security is essential for developing reliable deep learning systems.

Quantization techniques are essential for the deployment of Large Language Models (LLMs) on edge devices. However, prevailing methods often rely on mixed-precision multiplication that lacks efficient hardware support, making it not feasible. Ternary weight quantization addresses this by constraining weights to {-1, 0, 1}, replacing expensive multiplications with hardware-efficient additions. However, such aggressive compression leads to significant accuracy degradation, even after costly quantization-aware training with massive data. We identify the core issue as deadzone trapping: a large number of weights are trapped at the deadzone boundary. This occurs because these weights receive only noisy, uninformative gradients, preventing stable escape from the deadzone and severely impeding model capacity and optimization. To address this issue, we propose Tequila, a trapping-free quantization optimization method that reactivates deadzone-trapped weights by repurposing them as dynamic biases. This allows the repurposed weights to provide a continuous signal in the forward pass and, critically, receive direct, meaningful gradient signals during backpropagation, thereby enhancing model capacity and optimization with nearly zero inference overhead. Extensive evaluations demonstrate that Tequila outperforms state-of-the-art (SOTA) ternary quantization methods across five benchmarks. Specifically, on the ARC benchmark, it achieves >4% accuracy gain over the SOTA baseline, nearly matching full-precision performance (within <1% gap) with a 3.0x inference speedup. Consequently, Tequila offers a highly practical and efficient implementation for the deployment of advanced LLMs in resource-constrained environments. The code is available at https://github.com/Tencent/AngelSlim.

We present a vector-based method to balance chemical reactions. The algorithm builds candidates in a deterministic way, removes duplicates, and always prints coefficients in the lowest whole-number form. For redox cases, electrons and protons/hydroxide are treated explicitly, so both mass and charge are balanced. We also outline the basic principles of the vector formulation of stoichiometry, interpreting reactions as integer vectors in composition space, this geometric view supports compact visualizations of reagent-product interactions and helps surface distinct reaction families. The method enumerates valid balances for arbitrary user-specified species lists without special-case balancing rules or symbolic tricks, and it provides a clean foundation for developing new algorithmic variants (e.g., alternative objectives or constraints). On representative examples (neutralization, double displacement, decomposition, classical redox, small multicomponent sets) and a negative control, the method produced correct integer balances. When multiple balances exist, we report a canonical one - minimizing the total coefficient sum with a simple tie-breaker - without claiming global optimality beyond the solutions the search enumerates. The procedure applies per reaction and extends to reaction networks via consistent per-reaction application. We do not report runtimes, broader benchmarking and code/data release are planned.

This paper presents a new state-of-the-art algorithm for exact 3times3 matrix multiplication over general non-commutative rings, achieving a rank-23 scheme with only 58 scalar additions. This improves the previous best additive complexity of 60 additions without a change of basis. The result was discovered through an automated search combining ternary-restricted flip-graph exploration with greedy intersection reduction for common subexpression elimination. The resulting scheme uses only coefficients from {-1, 0, 1}, ensuring both efficiency and portability across arbitrary fields. The total scalar operation count is reduced from 83 to 81.

This thesis is divided into three parts. The first part deals with cylindric plane partitions. The second with lambda-determinants and the third with commutators in semi-circular systems. For more detailed abstract please see inside. Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions. A generating series for the enumeration of cylindric plane partitions was recently given by Borodin. The first result of section one is a new bijective proof of Borodin's identity which makes use of Fomin's growth diagram framework for generalized RSK correspondences. The second result is a (q,t)-analog of Borodin's identity which extends previous work by Okada in the reverse plane partition case. The third result is an explicit combinatorial interpretation of the Macdonald weight occurring in the (q,t)-analog using the non-intersecting lattice path model for cylindric plane partitions. Alternating sign matrices were discovered by Robbins and Rumsey whilst studying λ-determinants. In the second part of this thesis we prove a multi-parameter generalization of the λ-determinant, generalizing a recent result by di Francesco. Like the original λ-determinant, our formula exhibits the Laurent phenomenon. Semicircular systems were first introduced by Voiculescu as a part of his study of von Neumann algebras. In the third part of this thesis we study certain commutator subalgebras of the semicircular system. We find a projection matrix with an interesting self-similar structure. Making use of our projection formula we given an alternative, elementary proof that the semicircular system is a factor.

If h is a ring-valued function on a simplicial complex G we can define two matrices L and g, where the matrix entries are the h energy of homoclinic intersections. We know that the sum over all h values on G is equal to the sum of the Green matrix entries g(x,y). We also have already seen that that the determinants of L or g are both the product of the h(x). In the case where h(x) is the parity of dimension, the sum of the energy values was the standard Euler characteristic and the determinant was a unit. If h(x) was the unit in the ring then L,g are integral quadratic forms which are isospectral and inverse matrices of each other. We prove here that the quadratic energy expression summing over all pairs h(x)^* h(y) of intersecting sets is a signed sum of squares of Green function entries. The quadratic energy expression is Wu characteristic in the case when h is dimension parity. For general h, the quadratic energy expression resembles an Ising Heisenberg type interaction. The conjugate of g is the inverse of L if h takes unit values in a normed ring or in the group of unitary operators in an operator algebra.

The advent of 1-bit large language models (LLMs), led by BitNet b1.58, has spurred interest in ternary LLMs. Despite this, research and practical applications focusing on efficient edge inference for ternary LLMs remain scarce. To bridge this gap, we introduce Bitnet.cpp, an inference system optimized for BitNet b1.58 and ternary LLMs. Given that mixed-precision matrix multiplication (mpGEMM) constitutes the bulk of inference time in ternary LLMs, Bitnet.cpp incorporates a novel mpGEMM library to facilitate sub-2-bits-per-weight, efficient and lossless inference. The library features two core solutions: Ternary Lookup Table (TL), which addresses spatial inefficiencies of previous bit-wise methods, and Int2 with a Scale (I2_S), which ensures lossless edge inference, both enabling high-speed inference. Our experiments show that Bitnet.cpp achieves up to a 6.25x increase in speed over full-precision baselines and up to 2.32x over low-bit baselines, setting new benchmarks in the field. Additionally, we expand TL to element-wise lookup table (ELUT) for low-bit LLMs in the appendix, presenting both theoretical and empirical evidence of its considerable potential. Bitnet.cpp is publicly available at https://github.com/microsoft/BitNet/tree/paper , offering a sophisticated solution for the efficient and practical deployment of edge LLMs.

The optimal bit-width for achieving the best trade-off between quantized model size and accuracy has been a subject of ongoing debate. While some advocate for 4-bit quantization, others propose that 1.58-bit offers superior results. However, the lack of a cohesive framework for different bits has left such conclusions relatively tenuous. We present ParetoQ, the first unified framework that facilitates rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings. Our findings reveal a notable learning transition between 2 and 3 bits: For 3-bits and above, the fine-tuned models stay close to their original pre-trained distributions, whereas for learning 2-bit networks or below, the representations change drastically. By optimizing training schemes and refining quantization functions, ParetoQ surpasses all previous methods tailored to specific bit widths. Remarkably, our ParetoQ ternary 600M-parameter model even outperforms the previous SoTA ternary 3B-parameter model in accuracy, using only one-fifth of the parameters. Extensive experimentation shows that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off and generally exceeds 4-bit and binary quantization. Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.

Bias has been a constant in face recognition models. Over the years, researchers have looked at it from both the model and the data point of view. However, their approach to mitigation of data bias was limited and lacked insight on the real nature of the problem. Here, in this document, we propose to revise our use of ethnicity labels as a continuous variable instead of a discrete value per identity. We validate our formulation both experimentally and theoretically, showcasing that not all identities from one ethnicity contribute equally to the balance of the dataset; thus, having the same number of identities per ethnicity does not represent a balanced dataset. We further show that models trained on datasets balanced in the continuous space consistently outperform models trained on data balanced in the discrete space. We trained more than 65 different models, and created more than 20 subsets of the original datasets.

This paper presents a parallel random-search method for reducing additive complexity in fast matrix multiplication. The approach replaces expensive exact evaluation with fast heuristic scoring, including the new Greedy-Intersections strategy. The method runs many independent common subexpression elimination processes in parallel, exploring the search space through random pair substitutions and diverse selection strategies while sharing promising partial solutions. Tested on 164 ternary-coefficient schemes, the method achieves lower addition counts than the state-of-the-art Greedy-Potential on 103 schemes, matches it on 59, and is outperformed on 2. For most schemes, it gives equal or better results while being much faster, making it practical for algorithm exploration. All software and results are open source.

Digital identity is unsolved: after many years of research there is still no trusted communication over the Internet. To provide identity within the context of mutual distrust, this paper presents a blockchain-based digital identity solution. Without depending upon a single trusted third party, the proposed solution achieves passport-level legally valid identity. This solution for making identities Self-Sovereign, builds on a generic provable claim model for which attestations of truth from third parties need to be collected. The claim model is then shown to be both blockchain structure and proof method agnostic. Four different implementations in support of these two claim model properties are shown to offer sub-second performance for claim creation and claim verification. Through the properties of Self-Sovereign Identity, legally valid status and acceptable performance, our solution is considered to be fit for adoption by the general public.

In the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal') relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is similarly harmless. We show that this is far from being the case, and there can be quite a big jump in complexity, even from decidable to the highly undecidable. Our undecidable logics can also be viewed as new fragments of first- order logic where adding equality changes a decidable fragment to undecidable. We prove our results by a novel application of counter machine problems. While our formalism apparently cannot force reliable counter machine computations directly, the presence of a unique diagonal in the models makes it possible to encode both lossy and insertion-error computations, for the same sequence of instructions. We show that, given such a pair of faulty computations, it is then possible to reconstruct a reliable run from them.

This paper explores the intersection of identity, individuality, and reality through competing frameworks, including classical metaphysics, quantum mechanics, and computational theories. Traditional metaphysical notions of fixed identity are challenged by advancements in cloning, teletransportation, and digital replication, which reveal the fluid and relational nature of individuality. Quantum mechanics further complicates these notions, emphasizing the indistinguishability and contextuality of fundamental particles. Computational approaches, such as the Ruliad and Constructor Theory, offer expansive views of emergent realities but often lack practical constraints for observer relevance. Algorithmic idealism is introduced as a unifying framework, proposing that reality is an emergent construct governed by computational rules prioritizing coherence, sufficiency, and observer-dependent experiences. By redefining identity as an informational construct and reality as a process shaped by algorithmic transitions, algorithmic idealism resolves foundational paradoxes and offers a superior lens for understanding existence in an increasingly digital and interconnected world. The framework bridges gaps between competing theories, providing a coherent and pragmatic model for addressing ethical, metaphysical, and technological challenges.

The great advancements of generative adversarial networks and face recognition models in computer vision have made it possible to swap identities on images from single sources. Although a lot of studies seems to have proposed almost satisfactory solutions, we notice previous methods still suffer from an identity-attribute entanglement that causes undesired attributes swapping because widely used identity encoders, eg, ArcFace, have some crucial attribute biases owing to their pretraining on face recognition tasks. To address this issue, we design BlendFace, a novel identity encoder for face-swapping. The key idea behind BlendFace is training face recognition models on blended images whose attributes are replaced with those of another mitigates inter-personal biases such as hairsyles. BlendFace feeds disentangled identity features into generators and guides generators properly as an identity loss function. Extensive experiments demonstrate that BlendFace improves the identity-attribute disentanglement in face-swapping models, maintaining a comparable quantitative performance to previous methods.

Large language models (LLMs) have transformed natural-language processing, yet their scale makes real-world deployment costly. Post-training quantization reduces memory and computation but often degrades accuracy, while quantization-aware training can recover performance at the cost of extra training. Pushing quantization to the ternary (2-bit) regime yields even larger savings but is notoriously unstable. Building on recent work showing that a bias-free, RMS-normalized Transformer with straight-through estimation can reach 1.58-bit precision, we demonstrate that simply inserting RMS normalization before every linear projection and applying a gradual, layer-wise quantization schedule stably fine-tunes full-precision checkpoints into ternary LLMs. Our approach matches or surpasses more elaborate knowledge-distillation pipelines on standard language-modeling benchmarks without adding model complexity. These results indicate that careful normalization alone can close much of the accuracy gap between ternary and full-precision LLMs, making ultra-low-bit inference practical.

Federated learning allows collaborative workers to solve a machine learning problem while preserving data privacy. Recent studies have tackled various challenges in federated learning, but the joint optimization of communication overhead, learning reliability, and deployment efficiency is still an open problem. To this end, we propose a new scheme named federated learning via plurality vote (FedVote). In each communication round of FedVote, workers transmit binary or ternary weights to the server with low communication overhead. The model parameters are aggregated via weighted voting to enhance the resilience against Byzantine attacks. When deployed for inference, the model with binary or ternary weights is resource-friendly to edge devices. We show that our proposed method can reduce quantization error and converges faster compared with the methods directly quantizing the model updates.

As large language models (LLMs) become integral to multi-agent systems, new privacy risks emerge that extend beyond memorization, direct inference, or single-turn evaluations. In particular, seemingly innocuous responses, when composed across interactions, can cumulatively enable adversaries to recover sensitive information, a phenomenon we term compositional privacy leakage. We present the first systematic study of such compositional privacy leaks and possible mitigation methods in multi-agent LLM systems. First, we develop a framework that models how auxiliary knowledge and agent interactions jointly amplify privacy risks, even when each response is benign in isolation. Next, to mitigate this, we propose and evaluate two defense strategies: (1) Theory-of-Mind defense (ToM), where defender agents infer a questioner's intent by anticipating how their outputs may be exploited by adversaries, and (2) Collaborative Consensus Defense (CoDef), where responder agents collaborate with peers who vote based on a shared aggregated state to restrict sensitive information spread. Crucially, we balance our evaluation across compositions that expose sensitive information and compositions that yield benign inferences. Our experiments quantify how these defense strategies differ in balancing the privacy-utility trade-off. We find that while chain-of-thought alone offers limited protection to leakage (~39% sensitive blocking rate), our ToM defense substantially improves sensitive query blocking (up to 97%) but can reduce benign task success. CoDef achieves the best balance, yielding the highest Balanced Outcome (79.8%), highlighting the benefit of combining explicit reasoning with defender collaboration. Together, our results expose a new class of risks in collaborative LLM deployments and provide actionable insights for designing safeguards against compositional, context-driven privacy leakage.

Recent research, such as BitNet, is paving the way for a new era of 1-bit Large Language Models (LLMs). In this work, we introduce a 1-bit LLM variant, namely BitNet b1.58, in which every single parameter (or weight) of the LLM is ternary {-1, 0, 1}. It matches the full-precision (i.e., FP16 or BF16) Transformer LLM with the same model size and training tokens in terms of both perplexity and end-task performance, while being significantly more cost-effective in terms of latency, memory, throughput, and energy consumption. More profoundly, the 1.58-bit LLM defines a new scaling law and recipe for training new generations of LLMs that are both high-performance and cost-effective. Furthermore, it enables a new computation paradigm and opens the door for designing specific hardware optimized for 1-bit LLMs.

Ternary Vision Transformers offer substantial model compression, however state-of-the-art methods only ternarize the encoder layers, leaving patch embeddings, LayerNorm parameters, and classifier heads in full precision. In compact models targeting resource-constrained processors, such as microcontrollers, these remaining full-precision components determine the total memory footprint, severely limiting deployment efficiency and on-device feasibility. In this work, we introduce a fully ternarized Vision Transformer in which all weight matrices and normalization parameters are ternarized (FTerViT). To this end, we introduce two novel operators : TernaryBitConv2d with per-channel scaling for patch embedding and TernaryLayerNorm. FTerViT is trained using knowledge distillation, followed by a lightweight quantization-aware recovery phase. Our ternary W2A8 DeiT-III-S at 384times384 resolution achieves 82.43\% ImageNet-1K top-1 at 6.09\,MB ({sim}15times compression, -2.42\,pp vs.\ FP32), outperforming prior ternary ViTs methods up to 8 pp. Finally, we demonstrate the first implementation of ternary vision transformers on a dual cores XTensa LX7 microcontroller inside the ESP32-S3 system-on-chip. By deploying FTerViT-Small (based on DeiT-III-Small at 224times224 resolution, 5.81\,MB), we achieve 79.64\% ImageNet-1K top-1 accuracy.

Consider the following process: Take any four-digit number which has at least two distinct digits. Then, rearrange the digits of the original number in ascending and descending order, take these two numbers, and find the difference between the two. Finally, repeat this routine using the difference as the new four-digit number. In 1949, D. R. Kaprekar became the first to discover that this process, known as the Kaprekar Routine, would always yield 6174 within 7 iterations. Since this number remains unchanged after an application of the Kaprekar Routine, it became known as Kaprekar's Constant. Previous works have shown that the only base 10 Kaprekar's Constants are 495 and 6174, the 3-digit and 4-digit case. However, little attention has been given to other bases or determining which digit cases and which bases have a Kaprekar's Constant. This paper analyzes the behavior of the Kaprekar Routine in the 3-digit case, deriving an expression for all 3-digit Kaprekar Constants. In addition, the author developed a series of C++ programs to analyze the paths integers followed to their respective Kaprekar's Constant. Surprisingly, it was determined from this program that the most commonly required number of iterations required to reach Kaprekar's Constant for 3-digit integers was consistently 3, regardless of base. When loaded as a matrix, the iteration requirement data demonstrates a precise recurring relationship reminiscent of Pascal's Triangle.

Vision Transformers (ViTs) have achieved remarkable performance in various image classification tasks by leveraging the attention mechanism to process image patches as tokens. However, the high computational and memory demands of ViTs pose significant challenges for deployment in resource-constrained environments. This paper introduces ViT-1.58b, a novel 1.58-bit quantized ViT model designed to drastically reduce memory and computational overhead while preserving competitive performance. ViT-1.58b employs ternary quantization, which refines the balance between efficiency and accuracy by constraining weights to {-1, 0, 1} and quantizing activations to 8-bit precision. Our approach ensures efficient scaling in terms of both memory and computation. Experiments on CIFAR-10 and ImageNet-1k demonstrate that ViT-1.58b maintains comparable accuracy to full-precision Vit, with significant reductions in memory usage and computational costs. This paper highlights the potential of extreme quantization techniques in developing sustainable AI solutions and contributes to the broader discourse on efficient model deployment in practical applications. Our code and weights are available at https://github.com/DLYuanGod/ViT-1.58b.

We present Three-Phase Transformer (3PT), a residual-stream structural prior for decoder-only Transformers on a standard SwiGLU + RMSNorm + RoPE + GQA backbone. The hidden vector is partitioned into N equally-sized cyclic channels, each maintained by phase-respecting ops: a per-channel RMSNorm, a 2D Givens rotation between attention and FFN that rotates each channel by theta + i*(2*pi/N), and a head-count constraint aligning GQA heads with the partition. The architecture is a self-stabilizing equilibrium between scrambling and re-imposition, not a bolted-on module. The partition carves out a one-dimensional DC subspace orthogonal to the channels, into which we inject a fixed Gabriel's horn profile r(p) = 1/(p+1) as an absolute-position side-channel composing orthogonally with RoPE's relative-position rotation. The canonical N=3 borrows its metaphor from balanced three-phase AC, where three sinusoids 120 degrees apart sum to zero with no anti-correlated pair. At 123M parameters on WikiText-103, 3PT achieves -7.20% perplexity (-2.62% bits-per-byte) over a matched RoPE-Only baseline at +1,536 parameters (0.00124% of total), with 1.93x step-count convergence speedup (1.64x wall-clock). N behaves as a parameter-sharing knob rather than a unique optimum: at 5.5M an N-sweep over {1,2,3,4,6,8,12} is near-monotone with N=1 winning; at 123M a three-seed sweep finds N=3 and N=1 statistically indistinguishable. The load-bearing mechanism is the channel-partitioned residual stream, per-block rotation, per-phase normalization, and horn DC injection. We characterize (a) self-stabilization of the geometry without explicit enforcement, a novel instance of the conservation-law framework for neural networks; (b) a U-shaped depth profile of rotation-angle drift at 12 layers; (c) orthogonal composition with RoPE, attention, and FFN.

Text-to-image (T2I) diffusion models have made remarkable advancements, yet aligning them with diverse preferences remains a persistent challenge. Current methods often optimize single metrics or depend on narrowly curated datasets, leading to overfitting and limited generalization across key visual quality metrics. We present BalancedDPO, a novel extension of Direct Preference Optimization (DPO) that addresses these limitations by simultaneously aligning T2I diffusion models with multiple metrics, including human preference, CLIP score, and aesthetic quality. Our key novelty lies in aggregating consensus labels from diverse metrics in the preference distribution space as compared to existing reward mixing approaches, enabling robust and scalable multi-metric alignment while maintaining the simplicity of the standard DPO pipeline that we refer to as BalancedDPO. Our evaluations on the Pick-a-Pic, PartiPrompt and HPD datasets show that BalancedDPO achieves state-of-the-art results, outperforming existing approaches across all major metrics. BalancedDPO improves the average win rates by 15%, 7.1%, and 10.3% on Pick-a-pic, PartiPrompt and HPD, respectively, from the DiffusionDPO.

In this paper, we present CAT-Q, Cost-efficient and Accurate Ternary Quantization, for compressing and accelerating LLMs. Unlike existing state-of-the-art ternary quantization methods that rely on data-intensive and costly quantization-aware training to mitigate severe performance degradation, CAT-Q is a simple yet effective post-training quantization scheme that is readily applicable to LLMs with diverse architectures and model sizes. It has two key components, learnable modulation (LM) and softened ternarization (ST), which are coupled from an optimization perspective. LM leverages a composition of learnable factors to modulate the distribution of pre-trained high-precision weights and the ternary threshold, making them less sensitive to ternarization. ST further introduces a differentiable transition function to guide the ternarization process toward stable convergence. We show that, for pre-trained LLMs with 1.7B to 8B parameters, CAT-Q can efficiently quantize them into ternary models using only 512 calibration samples, while achieving superior performance than the seminal BitNet 1.58-bit v1 and v2 families (with 1.3B to 7B parameters) trained with 100B tokens, yielding about a 100,000X reduction in training tokens. Moreover, we show for the first time that CAT-Q can quantize much larger pre-trained LLMs having 14B to 235B parameters into leading ternary models within just 8 to 60 hours on 8 A100-80GB GPUs. Code is available at https://github.com/IntelChina-AI/BitTern.

Certain tasks in high-dimensional statistics become easier when the underlying distribution satisfies a local-to-global property called approximate tensorization of entropy (ATE). For example, the Glauber dynamics Markov chain of an ATE distribution mixes fast and can produce approximate samples in a small amount of time, since such a distribution satisfies a modified log-Sobolev inequality. Moreover, identity-testing for an ATE distribution requires few samples if the tester is given coordinate conditional access to the unknown distribution, as shown by Blanca, Chen, Štefankovič, and Vigoda (COLT 2023). A natural class of distributions that do not satisfy ATE consists of mixtures of (few) distributions that do satisfy ATE. We study the complexity of identity-testing and sampling for these distributions. Our main results are the following: 1. We show fast mixing of Glauber dynamics from a data-based initialization, with optimal sample complexity, for mixtures of distributions satisfying modified log-Sobolev inequalities. This extends work of Huang, Koehler, Lee, Mohanty, Rajaraman, Vuong, and Wu (STOC 2025, COLT 2025) for mixtures of distributions satisfying Poincaré inequalities. 2. Answering an open question posed by Blanca et al., we give efficient identity-testers for mixtures of ATE distributions in the coordinate-conditional sampling access model. We also give some simplifications and improvements to the original algorithm of Blanca et al.

High network communication cost for synchronizing gradients and parameters is the well-known bottleneck of distributed training. In this work, we propose TernGrad that uses ternary gradients to accelerate distributed deep learning in data parallelism. Our approach requires only three numerical levels {-1,0,1}, which can aggressively reduce the communication time. We mathematically prove the convergence of TernGrad under the assumption of a bound on gradients. Guided by the bound, we propose layer-wise ternarizing and gradient clipping to improve its convergence. Our experiments show that applying TernGrad on AlexNet does not incur any accuracy loss and can even improve accuracy. The accuracy loss of GoogLeNet induced by TernGrad is less than 2% on average. Finally, a performance model is proposed to study the scalability of TernGrad. Experiments show significant speed gains for various deep neural networks. Our source code is available.

Current artificial intelligence systems exhibit a fundamental architectural limitation: they resolve ambiguity prematurely. This premature semantic collapse--collapsing multiple valid interpretations into single outputs--stems from classical identity assumptions in neural architectures. We propose Non-Resolution Reasoning (NRR), a framework treating ambiguity retention as a valid reasoning mode. NRR introduces three principles: (1) Non-Identity (A neq A)--the same symbol refers to different entities across contexts; (2) Approximate Identity (A approx A)--entities share partial structural overlap without being identical; (3) Non-Resolution--conflicting interpretations coexist without forced convergence. We formalize these through Multi-Vector Embeddings for context-dependent representation, Non-Collapsing Attention for parallel interpretation retention, and Contextual Identity Tracking (CIT) for maintaining A neq A across inference. We illustrate NRR through case studies in paradox handling, creative generation, and context-dependent reasoning. Functional verification in a synthetic two-turn disambiguation task shows NRR-lite maintains high entropy (H = 0.91 bits, near-maximum 1.0) at ambiguous turns while standard architectures collapse early (H = 0.15 bits), preserving interpretive flexibility until context arrives. NRR challenges the assumption that meaning must collapse to be useful. The question is not whether AI should resolve ambiguity, but when, how, and under whose control.

We present ITQ3_S (Interleaved Ternary Quantization -- Specialized), a novel 3-bit weight quantization format for LLMs integrating TurboQuant (TQ), a rotation-domain strategy based on the Fast Walsh-Hadamard Transform (FWHT). Conventional 3-bit methods suffer precision loss from heavy-tailed weight distributions and inter-channel outliers. ITQ3_S pre-rotates the weight space via FWHT before quantization, spreading outlier energy across the vector and inducing a near-Gaussian distribution amenable to uniform ternary coding. We derive a rigorous dequantization procedure fusing a 256-point Inverse FWHT into the CUDA shared-memory loading stage, ensuring reconstruction error is bounded exclusively by the ternary quantization grid with no additional error from the transform inversion. For any weight vector w in R^{256}, the reconstruction satisfies |mathbf{w} - w|_2 leq ε_q, strictly smaller than uniform 3-bit baselines that do not exploit rotation-induced distribution normalization. TurboQuant lacks a native CUDA kernel, precluding direct deployment; naively composing TQ with existing weight quantizers introduces domain mismatch errors that accumulate across layers, degrading quality below standard 3-bit baselines. ITQ3_S resolves this by co-designing the FWHT rotation and quantization kernel as a unified pipeline grounded in the IQ3_S weight format, with the inverse transform fused into the CUDA MMQ kernel. Empirically, on the NVIDIA RTX 5090 (Blackwell), ITQ3_S achieves perplexity competitive with FP16 while delivering throughput exceeding 1.5x that of 4-bit alternatives via optimized DP4A and Tensor Core scheduling. Our results establish ITQ3_S as a practical, mathematically grounded solution for high-fidelity LLM deployment on consumer hardware.

White balance (WB) algorithms in many commercial cameras assume single and uniform illumination, leading to undesirable results when multiple lighting sources with different chromaticities exist in the scene. Prior research on multi-illuminant WB typically predicts illumination at the pixel level without fully grasping the scene's actual lighting conditions, including the number and color of light sources. This often results in unnatural outcomes lacking in overall consistency. To handle this problem, we present a deep white balancing model that leverages the slot attention, where each slot is in charge of representing individual illuminants. This design enables the model to generate chromaticities and weight maps for individual illuminants, which are then fused to compose the final illumination map. Furthermore, we propose the centroid-matching loss, which regulates the activation of each slot based on the color range, thereby enhancing the model to separate illumination more effectively. Our method achieves the state-of-the-art performance on both single- and multi-illuminant WB benchmarks, and also offers additional information such as the number of illuminants in the scene and their chromaticity. This capability allows for illumination editing, an application not feasible with prior methods.

We propose ScaleQ-1.58, a scalable ternary post-training quantization (PTQ) framework for reasoning LLMs. Its core insight stems from an empirical finding: although modern LLMs are typically trained to exhibit chain-of-thought reasoning capabilities, in the PTQ regime, even the latest CAT-Q method based on learning-based differentiable ternarization still leads to performance collapse on challenging mathematics and coding tasks when using conventional calibration schemes that ignore the model's reasoning process. Driven by this finding, we introduce a simple calibration approach, Attend to Your Own Thoughts (AYOT), where reasoning traces and final answers generated by the pre-trained high-precision target LLM on a proper set of calibration samples are used as the context input during the ternarization process, along with the corresponding questions. ScaleQ-1.58 is formed by simply integrating AYOT with CAT-Q, which demonstrates several scaling properties: (1) with only 4M calibration tokens, Qwen3-1.7B ternarized by ScaleQ-1.58 reaches over 90.52% of the performance of the prior best BitNet b1.58 2B4T averaged over 4 mathematics and coding tasks, and our ternary Qwen3-4B shows an absolute gain of 8.97%, while requiring 1,000,000x fewer calibration tokens for quantization; (2) ScaleQ-1.58 generalizes well to both dense and MoE architectures, with performance improving as model scale increases (up to 235B parameters); (3) ScaleQ-1.58 demonstrates strong generalization across tasks of varying difficulty levels, including mathematics, coding and scientific logic reasoning, as well as commonsense reasoning and basic language generation; (4) its performance continues to improve as the number of calibration tokens increases. Notably, AYOT also exhibits strong generalization ability across other quantization bit-widths. Code will be available at https://github.com/IntelChina-AI/BitTern.

Post-training quantization (PTQ) of large language models (LLMs) to extremely low bit-widths remains challenging due to the fundamental trade-off between computational efficiency and model expressiveness. While existing ultra-low-bit PTQ methods rely on binary approximations or complex compensation mechanisms, they suffer from either limited representational capacity or computational overhead that undermines their efficiency gains. We introduce PTQ to Trit-Planes (PTQTP), the first ternary-weight PTQ framework that decomposes weight matrices into structured ternary {-1, 0, 1} trit-planes using 2x1.58-bit representation. PTQTP achieves multiplication-free inference, identical to 1-bit quantization, while maintaining superior expressiveness through its novel structured decomposition. Our approach provides: (1) a theoretically grounded progressive approximation algorithm ensuring global weight consistency; (2) model-agnostic deployment across diverse modern LLMs without architectural modifications; and (3) uniform ternary operations that eliminate the need for mixed-precision or compensation schemes. Comprehensive experiments across LLaMA3.x and Qwen3 model families (0.6B-70B parameters) demonstrate that PTQTP significantly outperforms existing low-bit PTQ methods, achieving 82.4% mathematical reasoning retention versus 0% for competing approaches. PTQTP approaches and sometimes surpasses 1.58-bit quantization-aware training performance while requiring only single-hour quantization compared to 10-14 GPU days for training-based methods. These results establish PTQTP as a practical solution for efficient LLM deployment in resource-constrained environments.

Identity-preserving video generation offers powerful tools for creative expression, allowing users to customize videos featuring their beloved characters. However, prevailing methods are typically designed and optimized for a single identity reference. This underlying assumption restricts creative flexibility by inadequately accommodating diverse real-world input formats. Relying on a single source also constitutes an ill-posed scenario, causing an inherently ambiguous setting that makes it difficult for the model to faithfully reproduce an identity across novel contexts. To address these issues, we present AnyID, an ultra-fidelity identity-preservation video generation framework that features two core contributions. First, we introduce a scalable omni-referenced architecture that effectively unifies heterogeneous identity inputs (e.g., faces, portraits, and videos) into a cohesive representation. Second, we propose a primary-referenced generation paradigm, which designates one reference as a canonical anchor and uses a novel differential prompt to enable precise, attribute-level controllability. We conduct training on a large-scale, meticulously curated dataset to ensure robustness and high fidelity, and then perform a final fine-tuning stage using reinforcement learning. This process leverages a preference dataset constructed from human evaluations, where annotators performed pairwise comparisons of videos based on two key criteria: identity fidelity and prompt controllability. Extensive evaluations validate that AnyID achieves ultra-high identity fidelity as well as superior attribute-level controllability across different task settings.

Conditional image generation enhances text-to-image synthesis with structural, spatial, or stylistic priors, but current methods face challenges in handling conflicts between sources. These include 1) input-level conflicts, where the conditioning image contradicts the text prompt, and 2) model-bias conflicts, where generative biases disrupt alignment even when conditions match the text. Addressing these conflicts requires nuanced solutions, which standard supervised fine-tuning struggles to provide. Preference-based optimization techniques like Direct Preference Optimization (DPO) show promise but are limited by gradient entanglement between text and condition signals and lack disentangled training data for multi-constraint tasks. To overcome this, we propose a bidirectionally decoupled DPO framework (BideDPO). Our method creates two disentangled preference pairs-one for the condition and one for the text-to reduce gradient entanglement. The influence of pairs is managed using an Adaptive Loss Balancing strategy for balanced optimization. We introduce an automated data pipeline to sample model outputs and generate conflict-aware data. This process is embedded in an iterative optimization strategy that refines both the model and the data. We construct a DualAlign benchmark to evaluate conflict resolution between text and condition. Experiments show BideDPO significantly improves text success rates (e.g., +35%) and condition adherence. We also validate our approach using the COCO dataset. Project Pages: https://limuloo.github.io/BideDPO/.

We propose Zero-Error Horizon (ZEH) for trustworthy LLMs, which represents the maximum range that a model can solve without any errors. While ZEH itself is simple, we demonstrate that evaluating the ZEH of state-of-the-art LLMs yields abundant insights. For example, by evaluating the ZEH of GPT-5.2, we found that GPT-5.2 cannot even compute the parity of a short string like 11000, and GPT-5.2 cannot determine whether the parentheses in ((((()))))) are balanced. This is surprising given the excellent capabilities of GPT-5.2. The fact that LLMs make mistakes on such simple problems serves as an important lesson when applying LLMs to safety-critical domains. By applying ZEH to Qwen2.5 and conducting detailed analysis, we found that while ZEH correlates with accuracy, the detailed behaviors differ, and ZEH provides clues about the emergence of algorithmic capabilities. Finally, while computing ZEH incurs significant computational cost, we discuss how to mitigate this cost by achieving up to one order of magnitude speedup using tree structures and online softmax.

We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92\%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50\% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

The activation function plays a crucial role in model optimisation, yet the optimal choice remains unclear. For example, the Sigmoid activation is the de-facto activation in balanced classification tasks, however, in imbalanced classification, it proves inappropriate due to bias towards frequent classes. In this work, we delve deeper in this phenomenon by performing a comprehensive statistical analysis in the classification and intermediate layers of both balanced and imbalanced networks and we empirically show that aligning the activation function with the data distribution, enhances the performance in both balanced and imbalanced tasks. To this end, we propose the Adaptive Parametric Activation (APA) function, a novel and versatile activation function that unifies most common activation functions under a single formula. APA can be applied in both intermediate layers and attention layers, significantly outperforming the state-of-the-art on several imbalanced benchmarks such as ImageNet-LT, iNaturalist2018, Places-LT, CIFAR100-LT and LVIS and balanced benchmarks such as ImageNet1K, COCO and V3DET. The code is available at https://github.com/kostas1515/AGLU.

We give explicit low-rank bilinear non-commutative schemes for multiplying structured n times n matrices with 2 leq n leq 5, which serve as building blocks for recursive algorithms with improved multiplicative factors in asymptotic complexity. Our schemes are discovered over F_2 or F_3 and lifted to Z or Q. Using a flip graph search over tensor decompositions, we derive schemes for general, upper-triangular, lower-triangular, symmetric, and skew-symmetric inputs, as well as products of a structured matrix with its transpose. In particular, we obtain 4 times 4 rank-34 schemes: (i) multiplying a general matrix by its transpose using 10 recursive calls, improving the factor from 26/41 (0.634) to 8/13 (0.615); and (ii) multiplying an upper-triangular matrix by a general matrix using 12 recursive calls, improving the factor from 8/13 (0.615) to 22/37 (0.595). Additionally, using F_3 flip graphs, we discover schemes over Q that fundamentally require the inverse of 2, including a 2 times 2 symmetric-symmetric multiplication of rank 5 and a 3 times 3 skew-symmetric-general multiplication of rank 14 (improving upon AlphaTensor's 15).