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Jonathan Cohen

Publications and source records attributed to Jonathan Cohen.

At least 19 recordsLinked to original sources
arXiv2026

From Cycle Space to Cycle Manifold: Limits and Achievability of Blind False Data Injection Attacks

A false data injection attack (FDIA) can change the estimated grid state while evading a residual-based bad data detector (BDD). Existing blind attacks learn a low-rank measurement subspace, but this algebraic view does not state the physical grid constraints that make an attack stealthy or the minimum information needed to recover the complete attack space. Under the connected direct-current (DC) branch-flow model, we show that the residual-sensitive subspace of the noiseless orthogonal test is exactly the weighted cycle space. Its orthogonal complement is therefore the complete stealthy attack space, making weighted cycle-space knowledge both necessary and sufficient for complete blind FDIA. This space identifies the topology only up to 2-isomorphism and the relative cycle-edge parameters only up to one scale per biconnected component; bridge parameters are neither identified nor required. We then formulate a computationally unconstrained benchmark and a tractable measurement-only reconstruction method. Experiments on IEEE systems compare BDD bypass rate at a 95% nominal-acceptance threshold against state impact. As a compact alternating-current (AC) extension, we characterize feasible branch P/Q measurements by a cycle manifold and demonstrate topology-assisted manifold fitting and measurement generation on a graphics processing unit (GPU). In the lossless fixed-voltage small-angle limit, the normal space of the active-power slice reduces to the DC weighted cycle space.

cs.CR↗
arXiv2026

Compact and Infinite-Order Error Analysis for Null-Space SVD Estimation

We study null-space estimation from a noisy matrix. For a simple left null space, we first derive an exact compact expression for the error of the smallest left singular vector. We then give an all-order series for the SVD vector and projector, followed by compact and consistently truncated series forms for the fixed-realization empirical risk and conditional population generalization risk. The recursion extends to a multiple-dimensional null space by following the complete invariant subspace. The convergence radius is not inferred from an error plot: it is computed independently from the nearest complex exceptional point that joins a retained eigenvalue branch to its complement. A reduced-nullity experiment shows that moving this spectral boundary can increase the radius, although the improvement is not monotone in the retained nullity. For individually ordered null directions under Gaussian training with \(\tau\geq m\), we prove that the Wishart splitting matrix \(W\) gives a strict second-order empirical ranking. Gaussian averaging equalizes the leading generalization risks at both small and very large noise, while a column-swap theorem proves strict expected generalization ranking for an isotropic signal subspace. For unequal spikes, an exact population-overlap criterion and a simultaneous \(99\%\) Monte Carlo confidence certificate explain the observed intermediate ranking. A sixth-order risk correction improves the lower-crossover estimate in the reported experiment. This equal--ranked--equal phenomenon is a finite-sample diagnostic related to spectral mixing, but its tolerance crossings, the exceptional-point radius, and the asymptotic BBP threshold are three distinct quantities.

math.ST↗
arXiv2026

Physically Consistent Null Space Alignment for Detection of Low-Magnitude False Data Injection Attacks

False data injection attacks (FDIAs) introducing small measurement perturbations can still cause large deviations in power system state estimation when the injected signals align with the pseudo-null space of the system model. Existing model- and data-driven detectors may fail to identify such low-magnitude but high-impact attacks because residual tests ignore changes hidden in the pseudo-null space, while subspace learning methods capture correlation patterns without enforcing physical consistency. This paper proposes Physically Consistent Null Space Alignment (PCNSA), a framework that detects stealthy FDIAs by preserving, through preprocessing, the geometric correspondence between the physical null space and the measurement-derived pseudo-null space. The key point is a Pseudo-null Space Conserved data Preprocessing (PSCP) step that re-expresses measurements in the physical coordinate frame before subspace extraction. We prove that PSCP preserves the separation between row space and its orthogonal complement, a property that conventional per-feature standardization violates. This keeps the singular value decomposition (SVD)-derived pseudo-null subspace aligned with the physical residual space without explicit knowledge of H. Experiments on IEEE 14-, 30-, 57-, and 118-bus systems confirm this principle in practice: stealthy attacks that evade XTM, LSTM, AE and Isolation Forest baselines appear as clear deviations in the aligned subspace, yielding higher F1-score and detection accuracy while remaining robust under partial observability and realistic PMU noise.

cs.LG↗
arXiv2026

Cycle-Space Informed Detection of Autoencoded Blind False Data Injection Attacks on Power Systems

The rapid growth of AI-driven data centers and large-scale energy storage systems is increasing the reliance of power system operation on real-time measurement data and automated decision-making. However, many existing detection methods rely on statistical or data-driven analysis of measurements and can fail when attackers exploit the same data structure to craft stealthy perturbations. To illustrate this limitation, we demonstrate a blind False Data Injection Attack (FDIA) in which an Autoencoder learns the measurement manifold and generates perturbations aligned with the Jacobian null space, thereby allowing the attack to evade both residual-based baddata detectors and time-series anomaly detectors. To mitigate data-driven FDIAs which exploit the null space, we propose a topology-informed Cycle-Space Detector (CSD) that leverages the Cycle-Space of the network to impose structural constraints that enhance null space estimation. In addition, we prove that by using the Minimum Cycle Basis (MCB), the proposed CSD achieves the optimal generalization error for attack detection. By exploiting topology-derived cycle constraints rather than relying solely on numerical null space estimation, the proposed method does not require precise line parameters and improves the separation between normal and attacked measurements. Simulation results on IEEE 14-, 30-, 57-, and 118-bus systems demonstrate that the proposed method effectively detects data-driven FDIAs under realistic measurement noise.

cs.LG↗
arXiv2026

Learning graph topology from metapopulation epidemic encoder-decoder

Metapopulation epidemic models are a valuable tool for studying large-scale outbreaks. With the limited availability of epidemic tracing data, it is challenging to infer the essential constituents of these models, namely, the epidemic parameters and the relevant mobility network between subpopulations. Either one of these constituents can be estimated while assuming the other; however, the problem of their joint inference has not yet been solved. Here, we propose two encoder-decoder deep learning architectures that infer metapopulation mobility graphs from time-series data, with and without the assumption of epidemic model parameters. Evaluation across diverse random and empirical mobility networks shows that the proposed approach outperforms the state-of-the-art topology inference. Further, we show that topology inference improves dramatically with data on additional pathogens. Our study establishes a robust framework for simultaneously inferring epidemic parameters and topology, addressing a persistent gap in modeling disease propagation.

cs.LG↗
arXiv2025

NVIDIA Nemotron Nano 2: An Accurate and Efficient Hybrid Mamba-Transformer Reasoning Model

We introduce Nemotron-Nano-9B-v2, a hybrid Mamba-Transformer language model designed to increase throughput for reasoning workloads while achieving state-of-the-art accuracy compared to similarly-sized models. Nemotron-Nano-9B-v2 builds on the Nemotron-H architecture, in which the majority of the self-attention layers in the common Transformer architecture are replaced with Mamba-2 layers, to achieve improved inference speed when generating the long thinking traces needed for reasoning. We create Nemotron-Nano-9B-v2 by first pre-training a 12-billion-parameter model (Nemotron-Nano-12B-v2-Base) on 20 trillion tokens using an FP8 training recipe. After aligning Nemotron-Nano-12B-v2-Base, we employ the Minitron strategy to compress and distill the model with the goal of enabling inference on up to 128k tokens on a single NVIDIA A10G GPU (22GiB of memory, bfloat16 precision). Compared to existing similarly-sized models (e.g., Qwen3-8B), we show that Nemotron-Nano-9B-v2 achieves on-par or better accuracy on reasoning benchmarks while achieving up to 6x higher inference throughput in reasoning settings like 8k input and 16k output tokens. We are releasing Nemotron-Nano-9B-v2, Nemotron-Nano12B-v2-Base, and Nemotron-Nano-9B-v2-Base checkpoints along with the majority of our pre- and post-training datasets on Hugging Face.

cs.CL↗
arXiv2025

Causal Head Gating: A Framework for Interpreting Roles of Attention Heads in Transformers

We present causal head gating (CHG), a scalable method for interpreting the functional roles of attention heads in transformer models. CHG learns soft gates over heads and assigns them a causal taxonomy - facilitating, interfering, or irrelevant - based on their impact on task performance. Unlike prior approaches in mechanistic interpretability, which are hypothesis-driven and require prompt templates or target labels, CHG applies directly to any dataset using standard next-token prediction. We evaluate CHG across multiple large language models (LLMs) in the Llama 3 model family and diverse tasks, including syntax, commonsense, and mathematical reasoning, and show that CHG scores yield causal, not merely correlational, insight validated via ablation and causal mediation analyses. We also introduce contrastive CHG, a variant that isolates sub-circuits for specific task components. Our findings reveal that LLMs contain multiple sparse task-sufficient sub-circuits, that individual head roles depend on interactions with others (low modularity), and that instruction following and in-context learning rely on separable mechanisms.

cs.AI↗
arXiv2025

Understanding Task Representations in Neural Networks via Bayesian Ablation

Neural networks are powerful tools for cognitive modeling due to their flexibility and emergent properties. However, interpreting their learned representations remains challenging due to their sub-symbolic semantics. In this work, we introduce a novel probabilistic framework for interpreting latent task representations in neural networks. Inspired by Bayesian inference, our approach defines a distribution over representational units to infer their causal contributions to task performance. Using ideas from information theory, we propose a suite of tools and metrics to illuminate key model properties, including representational distributedness, manifold complexity, and polysemanticity.

cs.LG↗
arXiv2025

Nemotron-H: A Family of Accurate and Efficient Hybrid Mamba-Transformer Models

As inference-time scaling becomes critical for enhanced reasoning capabilities, it is increasingly becoming important to build models that are efficient to infer. We introduce Nemotron-H, a family of 8B and 56B/47B hybrid Mamba-Transformer models designed to reduce inference cost for a given accuracy level. To achieve this goal, we replace the majority of self-attention layers in the common Transformer model architecture with Mamba layers that perform constant computation and require constant memory per generated token. We show that Nemotron-H models offer either better or on-par accuracy compared to other similarly-sized state-of-the-art open-sourced Transformer models (e.g., Qwen-2.5-7B/72B and Llama-3.1-8B/70B), while being up to 3$\times$ faster at inference. To further increase inference speed and reduce the memory required at inference time, we created Nemotron-H-47B-Base from the 56B model using a new compression via pruning and distillation technique called MiniPuzzle. Nemotron-H-47B-Base achieves similar accuracy to the 56B model, but is 20% faster to infer. In addition, we introduce an FP8-based training recipe and show that it can achieve on par results with BF16-based training. This recipe is used to train the 56B model. We are releasing Nemotron-H base model checkpoints with support in Hugging Face and NeMo.

cs.CL↗
arXiv2025

Emergent Symbolic Mechanisms Support Abstract Reasoning in Large Language Models

Many recent studies have found evidence for emergent reasoning capabilities in large language models (LLMs), but debate persists concerning the robustness of these capabilities, and the extent to which they depend on structured reasoning mechanisms. To shed light on these issues, we study the internal mechanisms that support abstract reasoning in LLMs. We identify an emergent symbolic architecture that implements abstract reasoning via a series of three computations. In early layers, symbol abstraction heads convert input tokens to abstract variables based on the relations between those tokens. In intermediate layers, symbolic induction heads perform sequence induction over these abstract variables. Finally, in later layers, retrieval heads predict the next token by retrieving the value associated with the predicted abstract variable. These results point toward a resolution of the longstanding debate between symbolic and neural network approaches, suggesting that emergent reasoning in neural networks depends on the emergence of symbolic mechanisms.

cs.CL↗
arXiv2024

Siegel Vectors for Nongeneric Depth Zero Supercuspidals of $GSp(4)$

Let $F$ be a non-archimedean local field of characteristic zero. If $F$ has even residual characteristic, we assume $F/\mathbb{Q}_2$ is unramified. Let $V$ be a depth zero, irreducible, nongeneric supercuspidal representation of $GSp(4, F)$. We calculate the dimensions of the spaces of Siegel-invariant vectors in $V$ of level $\mathfrak{p}^n$ for all $n\geq0$.

math.RT↗
arXiv2024

Siegel $\mathfrak{p}^2$ Vectors for Representations of $GSp(4)$

Let $F$ be a $p$-adic field and $(\pi, V)$ an irreducible complex representation of $G=GSp(4, F)$ with trivial central character. Let ${\rm Si}(\mathfrak{p}^2)\subset G$ denote the Siegel congruence subgroup of level $\mathfrak{p}^2$ and $u\in N_G({\rm Si}(\mathfrak{p}^2))$ the Atkin-Lehner element. We compute the dimension of the space of ${\rm Si}(\mathfrak{p}^2)$-fixed vectors in $V$ as well as the signatures of the involutions $\pi(u)$ acting on these spaces.

math.RT↗
arXiv2024

Nemotron-4 340B Technical Report

We release the Nemotron-4 340B model family, including Nemotron-4-340B-Base, Nemotron-4-340B-Instruct, and Nemotron-4-340B-Reward. Our models are open access under the NVIDIA Open Model License Agreement, a permissive model license that allows distribution, modification, and use of the models and its outputs. These models perform competitively to open access models on a wide range of evaluation benchmarks, and were sized to fit on a single DGX H100 with 8 GPUs when deployed in FP8 precision. We believe that the community can benefit from these models in various research studies and commercial applications, especially for generating synthetic data to train smaller language models. Notably, over 98% of data used in our model alignment process is synthetically generated, showcasing the effectiveness of these models in generating synthetic data. To further support open research and facilitate model development, we are also open-sourcing the synthetic data generation pipeline used in our model alignment process.

cs.CL↗
arXiv2024

Nemotron-4 15B Technical Report

We introduce Nemotron-4 15B, a 15-billion-parameter large multilingual language model trained on 8 trillion text tokens. Nemotron-4 15B demonstrates strong performance when assessed on English, multilingual, and coding tasks: it outperforms all existing similarly-sized open models on 4 out of 7 downstream evaluation areas and achieves competitive performance to the leading open models in the remaining ones. Specifically, Nemotron-4 15B exhibits the best multilingual capabilities of all similarly-sized models, even outperforming models over four times larger and those explicitly specialized for multilingual tasks.

cs.CL↗
arXiv2023

NeMo Guardrails: A Toolkit for Controllable and Safe LLM Applications with Programmable Rails

NeMo Guardrails is an open-source toolkit for easily adding programmable guardrails to LLM-based conversational systems. Guardrails (or rails for short) are a specific way of controlling the output of an LLM, such as not talking about topics considered harmful, following a predefined dialogue path, using a particular language style, and more. There are several mechanisms that allow LLM providers and developers to add guardrails that are embedded into a specific model at training, e.g. using model alignment. Differently, using a runtime inspired from dialogue management, NeMo Guardrails allows developers to add programmable rails to LLM applications - these are user-defined, independent of the underlying LLM, and interpretable. Our initial results show that the proposed approach can be used with several LLM providers to develop controllable and safe LLM applications using programmable rails.

cs.CL↗
arXiv2023

Klingen Vectors for Depth Zero Supercuspidals of $GSp(4)$

Let $F$ be a non-archimedean local field of characteristic zero and $(\pi, V)$ a depth zero, irreducible, supercuspidal representation of $GSp(4, F)$. We calculate the dimensions of the spaces of Klingen-invariant vectors in $V$ of level $\mathfrak{p}^n$ for all $n\geq 0 $.

math.RT↗
arXiv2023

Beyond Transformers for Function Learning

The ability to learn and predict simple functions is a key aspect of human intelligence. Recent works have started to explore this ability using transformer architectures, however it remains unclear whether this is sufficient to recapitulate the extrapolation abilities of people in this domain. Here, we propose to address this gap by augmenting the transformer architecture with two simple inductive learning biases, that are directly adapted from recent models of abstract reasoning in cognitive science. The results we report demonstrate that these biases are helpful in the context of large neural network models, as well as shed light on the types of inductive learning biases that may contribute to human abilities in extrapolation.

cs.LG↗