AI-generated summaries
Today's ML research,
without the noise.
Daily summaries of the latest machine learning papers from arXiv, processed every 8 hours.
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Learning Large-Scale Modular Addition with an Auxiliary Modulus
Theory
Efficient ML
- Introduces a covariate-shift-free method for learning modular addition.
- Utilizes an auxiliary modulus to reduce training difficulty while preserving input distribution.
- Demonstrates improved scalability and sample efficiency over previous methods.
- Achieves high accuracy even with smaller training datasets compared to sparse methods.
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Learning Large-Scale Modular Addition with an Auxiliary Modulus
Summary
This paper addresses the challenges of learning modular addition, a task known for its input sensitivity and difficulty in scaling with increasing summands and modulus. The authors critique a previous method that increased zeros in training sequences to reduce training difficulty, which inadvertently caused covariate shift between training and testing distributions. To overcome this, they propose a covariate-shift-free approach that introduces an auxiliary modulus during training. This method reduces wrap-around frequency and maintains consistent input distributions across training and testing phases. The authors demonstrate that their method achieves superior scalability and sample efficiency, outperforming the previous sparse method in various scenarios, including cases with large input lengths and moduli. Their experiments show that even with smaller datasets, their approach yields significantly higher accuracy compared to the sparse method, which struggles under similar conditions.
Methodology
The authors propose a new learning method that incorporates an auxiliary loss of modular addition with an enlarged modulus during training. This approach reduces the wrap-around frequency and problem difficulty while ensuring that the input distribution remains consistent between training and testing phases. They conduct both theoretical analyses and empirical experiments to validate their method's effectiveness.
Results
The proposed method achieves a Ï„-accuracy of 97.0% at Ï„ = 0.05 with 100K samples for N = 64 and q = 974269, significantly outperforming the sparse method, which only achieves 9.5% accuracy with the same sample size and 93.9% with 1M samples. The results indicate that the new method is more effective in learning modular addition tasks, especially in large-scale scenarios.
Implications
This research has potential implications for applications in cryptography, particularly in post-quantum cryptography, where efficient learning of modular arithmetic is crucial. The findings may also influence future research on learning complex symbolic tasks and improve methodologies for training deep learning models on sensitive input distributions.
The Position Curse: LLMs Struggle to Locate the Last Few Items in a List
NLP
Large Language Models
- Identified the 'Position Curse' in LLMs, where they struggle with backward retrieval of items in lists.
- Developed POSBENCH, a dataset aimed at improving position-based retrieval through post-training.
- Demonstrated that LoRA fine-tuning can enhance retrieval performance but does not reach saturation.
- Introduced PYINDEX, a benchmark for assessing position-based retrieval in code understanding.
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The Position Curse: LLMs Struggle to Locate the Last Few Items in a List
Summary
This paper investigates a specific limitation of modern large language models (LLMs), termed the 'Position Curse', which refers to their struggle in accurately retrieving the last few items in a list. Despite their high accuracy in locating relevant information within extensive contexts, LLMs like Claude Opus 4.6 frequently misidentify items near the end of short sequences. The authors evaluated the models' performance on two types of queries: retrieving an item based on its position and determining the position of a given item. The study found that backward retrieval consistently lags behind forward retrieval across various models. To address this issue, the authors developed POSBENCH, a position-focused training dataset, and applied low-rank adaptation (LoRA) fine-tuning, which improved retrieval capabilities but did not achieve saturation performance. They also introduced PYINDEX, a benchmark for evaluating position-based retrieval in code understanding, demonstrating that improvements generalize to this new task. The findings highlight the need for enhanced position-based retrieval capabilities in LLMs, particularly as they are increasingly utilized for coding tasks that require precise indexing.
Methodology
The authors conducted systematic evaluations of LLMs on position-based retrieval tasks, using both forward and backward queries. They created the POSBENCH dataset for targeted training and applied LoRA fine-tuning to assess improvements in retrieval capabilities. Additionally, they designed the PYINDEX benchmark to evaluate the generalization of these improvements in code understanding tasks.
Results
The study found that LLMs, including Claude Opus 4.6, exhibited significant difficulties in backward retrieval tasks, with performance consistently lower than that of forward retrieval. Fine-tuning with LoRA yielded improvements in both retrieval directions, but overall performance remained below saturation levels. The results from PYINDEX indicated that the enhancements from fine-tuning generalized to code understanding tasks.
Implications
The findings suggest that position-based retrieval is a critical capability that needs to be addressed in the design and training of LLMs, especially as they are increasingly used in coding environments where precise indexing is essential. This could lead to advancements in model architectures and training objectives that prioritize position-based tasks.
Bilevel Graph Structure Learning, Revisited: Inner-Channel Origins of the Reported Gain
Graph Learning
Optimization
Theory
- Inner-loop training dynamics contribute significantly to performance gains in bilevel GSL, often more than graph rewiring.
- The frozen-Ï• control allows for a clearer understanding of the contributions to performance gains by isolating training dynamics from graph modifications.
- Empirical results show that the inner channel accounts for 78-101% of gains in spatio-temporal flow forecasting and 37-44% in node classification.
- Three independent diagnostics validate the findings, providing a robust framework for future evaluations of bilevel GSL.
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Bilevel Graph Structure Learning, Revisited: Inner-Channel Origins of the Reported Gain
Summary
This paper revisits bilevel graph structure learning (GSL), a method that optimizes both model parameters and graph structures to enhance the performance of graph neural networks (GNNs). The authors challenge the common attribution of performance gains solely to graph rewiring, suggesting that inner-loop training dynamics play a significant role. They introduce a novel control mechanism called frozen-ϕ, which freezes the graph structure while maintaining the inner-loop training schedule. This allows for a clearer decomposition of the performance gains into contributions from inner-loop dynamics and graph modification. Through experiments on spatio-temporal flow forecasting and node classification, the authors demonstrate that the inner channel accounts for a substantial portion of the performance gains—78-101% for flow forecasting and 37-44% for node classification. The paper also introduces three independent diagnostics to support their findings and proposes frozen-ϕ as a standardized diagnostic tool for evaluating bilevel GSL. Overall, the work emphasizes the need to reassess how gains in bilevel GSL are attributed, highlighting the importance of inner-loop training dynamics.
Methodology
The authors introduced the frozen-Ï• control, which freezes the graph structure while retaining the inner-loop training schedule. This method allows for the isolation of the effects of inner-loop training dynamics from graph modifications. They conducted experiments on two tasks: spatio-temporal flow forecasting and node classification, using various diagnostics to corroborate their findings.
Results
The study found that the inner channel of training dynamics accounted for 78-101% of the performance gain in spatio-temporal flow forecasting and 37-44% in node classification. The results were supported by three independent diagnostics, confirming the significant role of inner-loop training in the performance of bilevel GSL.
Implications
The findings suggest that researchers and practitioners should reconsider the attribution of performance gains in bilevel GSL, focusing more on inner-loop dynamics. This could lead to improved methodologies in graph learning and better understanding of the mechanisms behind performance enhancements in GNNs.
GameGen-Verifier: Parallel Keypoint-Based Verification for LLM-Generated Games via Runtime State Injection
Large Language Models
Generative Models
Reinforcement Learning
- GameGen-Verifier reformulates game verification from open-ended exploration to state-grounded checks of specification-derived keypoints.
- The approach enables parallelizable and localized verification, reducing reliance on unreliable gameplay.
- GGV-HARNESS provides a robust framework for managing verification processes at scale.
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GameGen-Verifier: Parallel Keypoint-Based Verification for LLM-Generated Games via Runtime State Injection
Summary
The paper introduces GameGen-Verifier, a novel automated verification paradigm designed to address the challenges of verifying games generated by large language models (LLMs). Traditional verification methods, particularly Agent-as-a-Verifier (AaaV), struggle with the complexities of game mechanics, leading to time-consuming and coverage-limited evaluations. GameGen-Verifier overcomes these limitations by decomposing game specifications into verifiable keypoints, which represent critical behaviors necessary for game correctness. Each keypoint is associated with a state-grounded verification unit that directly injects specific game states into the runtime, executes bounded interactions, and assesses outcomes against expected results. The authors implemented GGV-HARNESS, a scalable verification harness that manages concurrency, runtime isolation, and fault recovery. The effectiveness of GameGen-Verifier was validated using the VERIGAME dataset, which includes 100 games across various genres, achieving an impressive accuracy of 92.2% compared to human judgments, significantly outperforming the AaaV baseline with a 58.8% accuracy while also reducing verification time by up to 16.6 times.
Methodology
The authors developed GameGen-Verifier by identifying critical behaviors in game specifications and creating verifiable keypoints. Each keypoint is linked to a verification unit that injects specific game states into the runtime for bounded interaction execution. The GGV-HARNESS framework supports this process with concurrency management and fault recovery mechanisms.
Results
GameGen-Verifier achieved up to 92.2% accuracy against human judgments and 95.4% F1 score on the VERIGAME dataset, significantly outperforming the AaaV baseline (58.8% accuracy) while reducing wall-clock time by up to 16.6 times.
Implications
The proposed verification paradigm has the potential to enhance the reliability of LLM-generated games, facilitating the development of more complex and interactive gaming experiences. It also lays the groundwork for scalable verification processes in other domains of automated content generation.
The E$Δ$-MHC-Geo Transformer: Adaptive Geodesic Operations with Guaranteed Orthogonality
Theory
Optimization
Efficient ML
- Introduces a Data-Dependent Cayley rotation with unconditional orthogonality for all inputs.
- Combines Cayley rotation and Householder reflection through a learned gate for enhanced adaptability.
- Implements a midpoint-collapse regularizer to encourage effective operator selection.
- Demonstrates superior performance in stability and loss metrics compared to existing architectures.
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The E$Δ$-MHC-Geo Transformer: Adaptive Geodesic Operations with Guaranteed Orthogonality
Summary
This paper introduces the E∆-MHC-Geo Transformer, a novel architecture that integrates Manifold-Constrained Hyper-Connections (mHC), Deep Delta Learning (DDL), and the Cayley transform to achieve input-adaptive, unconditionally orthogonal residual connections. The architecture addresses limitations in existing methods by utilizing a Data-Dependent Cayley rotation that maintains orthogonality for all inputs and parameters. A hybrid approach combines Cayley rotation with Householder reflection, facilitated by a learned operator-selection gate, which allows the model to access both components of the orthogonal group. The proposed midpoint-collapse regularizer encourages binary gate decisions, enhancing the model's ability to switch between operators effectively. Experimental results demonstrate that E∆-MHC-Geo outperforms four baseline architectures, including the concurrent JPmHC, in terms of stability, near-π rotation loss, and norm preservation, while requiring fewer layers. The findings validate the theoretical predictions regarding the architecture's performance and highlight its potential for improved gradient flow in deep learning models.
Methodology
The E∆-MHC-Geo Transformer employs a Data-Dependent Cayley rotation to ensure orthogonality across all inputs and parameters. It integrates a hybrid mechanism that combines Cayley rotation with Householder reflection, controlled by a learned gate that selects the appropriate operator based on input characteristics. A midpoint-collapse regularizer is introduced to promote binary decisions in the gate, facilitating transitions between different orthogonal components.
Results
The E∆-MHC-Geo architecture achieved the best long-horizon stability (1.9× improvement over JPmHC), the best near-π rotation loss (4.5× improvement over JPmHC), and maintained strong norm preservation with a mean deviation of 0.001. It also demonstrated a high negation cosine alignment of 0.96 in diagnostic probes, all while utilizing 33% fewer layers compared to the baselines.
Implications
The findings suggest that the E∆-MHC-Geo Transformer could significantly enhance the training and performance of deep learning models, particularly in applications requiring stable gradient flow and adaptability to varying input conditions. This architecture may be particularly beneficial in fields such as reinforcement learning and generative models, where maintaining orthogonality and stability is crucial.
On the Invariance and Generality of Neural Scaling Laws
Theory
NLP
Time Series
- Introduces a framework for generalizable Neural Scaling Laws based on information theory.
- Distinguishes between bijective and non-bijective transformations and their effects on scaling laws.
- Introduces the concept of information resolution to quantify the preservation of task-relevant information.
- Validates the framework across language, vision, and speech domains.
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On the Invariance and Generality of Neural Scaling Laws
Summary
This paper addresses the challenge of developing generalizable Neural Scaling Laws (NSLs) that can be applied across different domains without the need for extensive computational resources. NSLs describe the predictable relationship between model performance and the resources used during training, such as model parameters and dataset size. The authors propose a framework grounded in information theory to understand how scaling properties change across different data transformations. They distinguish between bijective transformations, which preserve information and maintain scaling laws, and non-bijective transformations, which degrade information and alter scaling behavior. The framework introduces a new parameter, the information resolution, which quantifies the amount of task-relevant information preserved after a transformation. The authors validate their approach across various domains, including language, vision, and speech, demonstrating its effectiveness in predicting scaling behavior for language models trained on electronic health records and time-series classification under noise. This work provides a systematic method for practitioners to anticipate scaling behavior in new domains without incurring the costs of extensive model training.
Methodology
The authors develop a theoretical framework that characterizes the sensitivity of NSLs to data transformations using information theory. They analyze the effects of bijective and non-bijective transformations on scaling laws and introduce the information resolution metric to quantify the preservation of task-relevant information. Experiments are conducted across multiple domains to validate the framework's predictions.
Results
The proposed framework accurately predicts scaling behavior across different domains, recovering data-scaling exponents to within 3% error. The authors successfully demonstrate its application in predicting scaling for language models trained on electronic health records and in time-series classification under varying noise levels.
Implications
This work has significant implications for resource allocation in machine learning, allowing practitioners to predict model performance in new domains without extensive computational resources. It enhances the understanding of how data transformations affect model training and performance, potentially leading to more efficient model development and deployment strategies.
Actor-Critic Algorithm for Dynamic Expectile and CVaR
Reinforcement Learning
Optimization
Theory
- Introduces a surrogate policy gradient method for dynamic risk optimization without transition perturbation.
- Develops model-free value learning methods for expectile and CVaR using elicitability.
- Presents an off-policy actor-critic algorithm tailored for dynamic risk measures.
- Empirical results show superior performance in learning risk-averse policies compared to existing approaches.
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Actor-Critic Algorithm for Dynamic Expectile and CVaR
Summary
This paper addresses the challenges of optimizing dynamic risk using stochastic policies in reinforcement learning (RL). The authors propose a novel surrogate policy gradient method that avoids transition perturbation, facilitating policy updates. They focus on two coherent risk measures, expectile and conditional value-at-risk (CVaR), and develop model-free value learning techniques that leverage elicitability. The paper introduces an off-policy actor-critic algorithm inspired by Expected SARSA and Expected Policy Gradient, marking a significant advancement in risk-averse RL. Empirical evaluations demonstrate that the proposed algorithm effectively learns risk-averse policies in various domains, outperforming existing methods.
Methodology
The authors propose a surrogate policy gradient approach that updates stochastic policies without perturbing transition probabilities. They derive value learning rules based on stochastic optimization and develop an off-policy actor-critic algorithm that integrates concepts from Expected SARSA and Expected Policy Gradient.
Results
The empirical results indicate that the proposed algorithm successfully learns risk-averse policies in environments characterized by risk-averse behavior, consistently outperforming traditional methods that either simplify policy updates or rely on model-based approaches.
Implications
This work has significant implications for risk-sensitive decision-making in various fields, including finance and operations research, where managing risk dynamically is crucial. The proposed methods can be applied to enhance the performance of RL agents in risk-averse scenarios.
A Hierarchical Ensemble Pipeline for Anomaly Detection in ESA Satellite Telemetry
Time Series
- Introduction of a hierarchical ensemble pipeline for anomaly detection in satellite telemetry.
- Integration of shapelet-based and statistical feature extraction techniques.
- Use of a two-level masking strategy to enhance model diversity and prevent information leakage.
- Demonstrated strong generalization capabilities on the ESA-ADB dataset.
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A Hierarchical Ensemble Pipeline for Anomaly Detection in ESA Satellite Telemetry
Summary
This paper presents a novel hierarchical ensemble pipeline designed for anomaly detection in multivariate telemetry data from the European Space Agency (ESA). The proposed method integrates shapelet-based and statistical feature extraction, along with per-channel modeling, intra-channel stacking, and a final cross-channel aggregation. The pipeline is rigorously trained and validated using time-series cross-validation and a two-level masking strategy to mitigate information leakage. The evaluation is conducted on the ESA Anomaly Detection Benchmark (ESA-ADB), which provides a comprehensive dataset with over 700 million timestamped records across multiple telemetry channels. The results indicate that the hierarchical modeling approach significantly enhances the detection of subtle anomalies in realistic satellite telemetry, achieving top-tier performance in the challenge. This work underscores the importance of robust, precise, and interpretable methods in the context of satellite operations, where timely anomaly detection is critical to prevent operational disruptions.
Methodology
The methodology involves a hierarchical ensemble approach that combines statistical segmentation, shapelet-based encoding, and multi-level anomaly detection. The pipeline processes telemetry data through distinct stages, allowing for diverse representation and robust anomaly detection. A two-level masking strategy is employed during training to ensure model diversity and prevent information leakage, while time-series cross-validation is used for validation.
Results
The proposed pipeline achieved top-tier results on the ESA Anomaly Detection Benchmark, demonstrating effective generalization to realistic satellite telemetry anomalies. The evaluation metrics emphasized precision, highlighting the model's ability to accurately localize and detect anomalies amidst a low anomaly density.
Implications
The findings suggest that hierarchical ensemble methods can significantly improve anomaly detection in complex, high-dimensional telemetry data, which is crucial for maintaining satellite operations. This approach could be applied to other domains requiring real-time monitoring and anomaly detection in time-series data.
On the Divergence of Differential Temporal Difference Learning without Local Clocks
Reinforcement Learning
Theory
- Differential TD learning can diverge with a global clock while converging with a local clock in average-reward RL.
- The correspondence between local and global clocks in convergence analysis breaks down in average-reward settings.
- The choice of learning rates has a more pronounced effect on convergence in average-reward RL compared to discounted RL.
- This work closes an open problem regarding the convergence of differential TD algorithms with global clocks.
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On the Divergence of Differential Temporal Difference Learning without Local Clocks
Summary
This paper investigates the role of learning rates in reinforcement learning (RL), specifically contrasting global and local clocks in the context of temporal difference (TD) learning. The authors establish that while convergence properties in discounted RL are preserved across both types of clocks, this correspondence fails in average-reward RL. They present a counterexample demonstrating that differential TD learning can converge with a local clock but diverge with a global clock. This finding highlights the significant impact of learning rate choices on the convergence of RL algorithms in average-reward settings, addressing an open problem in the literature and emphasizing the need for careful consideration of learning rates in practical applications.
Methodology
The authors construct a counterexample to demonstrate the divergence of differential TD learning with a global clock. They analyze the convergence properties of RL algorithms under both local and global clocks, utilizing theoretical frameworks from previous works in the field.
Results
The main result is the identification of a scenario where differential TD learning diverges with a global clock, despite being convergent with a local clock. This result is significant as it challenges the previously held assumption that convergence properties in discounted RL apply similarly in average-reward RL.
Implications
The findings have important implications for the design and implementation of RL algorithms, particularly in average-reward scenarios. Practitioners may need to adopt more nuanced approaches to learning rate selection to ensure convergence and optimal performance of RL systems.
RateQuant: Optimal Mixed-Precision KV Cache Quantization via Rate-Distortion Theory
NLP
Large Language Models
Efficient ML
- Introduces RATEQUANT for optimal mixed-precision KV cache quantization.
- Addresses distortion model mismatch, a critical failure mode in existing quantization methods.
- Implements a rate-distortion optimization framework for effective bit allocation.
- Achieves a 70% reduction in perplexity for KIVI and improves QuaRot performance.
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RateQuant: Optimal Mixed-Precision KV Cache Quantization via Rate-Distortion Theory
Summary
The paper presents RATEQUANT, a novel framework for optimizing mixed-precision quantization of key-value (KV) caches in large language models (LLMs). Traditional quantization methods apply uniform bit-widths across all attention heads, disregarding the varying importance of these heads. RATEQUANT addresses this limitation by leveraging rate-distortion theory to allocate bits more effectively based on the sensitivity of each head. The authors identify a critical issue known as distortion model mismatch, where different quantizers exhibit distinct distortion-rate curves, leading to suboptimal performance when applying one quantizer's model to another. To overcome this, RATEQUANT calibrates a per-quantizer distortion model from a small calibration dataset and employs a reverse waterfilling algorithm to determine the optimal bit allocation. The framework also separates the bit budget for keys and values, enhancing performance further. Empirical results demonstrate that RATEQUANT significantly reduces perplexity in various models while maintaining low calibration overhead and zero runtime cost during inference.
Methodology
RATEQUANT employs a rate-distortion optimization framework, fitting a per-quantizer distortion model from calibration data. It uses reverse waterfilling to solve the bit allocation problem in closed form and separates the bit budgets for keys and values to optimize performance further.
Results
The calibrated RATEQUANT reduces KIVI's perplexity from 49.3 to 14.9 (a 70% reduction) at an average of 2.5 bits. It also improves QuaRot by 6.6 perplexity points and recovers 66% of quantization-induced degradation in TURBOQUANT at 4.0 bits, all with negligible calibration time and no runtime overhead.
Implications
The findings suggest that RATEQUANT can enhance the efficiency of large language models by optimizing memory usage without sacrificing performance, making it applicable in scenarios where resource constraints are critical. This approach could lead to more scalable LLM deployments in real-world applications.
Latent Order Bandits
Reinforcement Learning
Theory
Efficient ML
- Introduction of Latent Order Bandits (LOB) to improve personalization in bandit algorithms.
- LOB requires only a partial order of action preferences, allowing for variability in reward distributions.
- Development of a UCB algorithm (lobUCB) and a Thompson sampling algorithm (lobTS) tailored for LOB.
- Empirical results show competitive performance against traditional latent bandits, especially in cases of differing reward scales.
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Latent Order Bandits
Summary
The paper introduces Latent Order Bandits (LOB), a novel approach to bandit algorithms that addresses the inefficiencies in personalization by relaxing the assumptions of traditional latent bandits. Unlike existing methods that require a full distribution of rewards based on latent states, LOB only requires prior knowledge of a partial order of action preferences within each state. This flexibility allows for variations in reward distributions among instances sharing the same latent state, making it applicable in scenarios like user preferences in streaming services. The authors propose an upper-confidence bound (UCB) algorithm and a Thompson sampling variant for LOB, demonstrating their effectiveness through empirical experiments. The results indicate that these algorithms perform comparably to traditional latent bandits when reward parameters are shared and outperform them when instances have differing reward scales. The findings suggest that LOB can significantly reduce exploration times while maintaining robust performance in personalized recommendation systems.
Methodology
The authors propose a UCB algorithm (lobUCB) and a heuristic Thompson sampling algorithm (lobTS) that leverage knowledge of possible state orders to optimize action selection. They also provide theoretical bounds on regret and conduct empirical evaluations to compare the performance of LOB against traditional latent bandit algorithms.
Results
The experiments demonstrate that both lobUCB and lobTS algorithms perform comparably to fully specified latent bandits when reward parameters are shared, and they outperform them when instances with the same latent state exhibit different reward scales. The algorithms also show resilience to model misspecification, degrading gracefully under such conditions.
Implications
The findings suggest that LOB can be effectively applied in various personalized recommendation systems, such as streaming services, where user preferences may vary significantly. This approach can lead to improved user experiences by reducing exploration times and enhancing the accuracy of recommendations.
Modulated learning for private and distributed regression with just a single sample per client device
Federated Learning
Theory
Efficient ML
- Introduces a method for federated learning with clients having only one data sample.
- Utilizes a cosine-modulated transformation and Gaussian noise for privacy preservation.
- Achieves unbiased gradient estimation that matches centralized gradient updates.
- Establishes asymptotic normality for valid statistical inference on regression coefficients.
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Modulated learning for private and distributed regression with just a single sample per client device
Summary
This paper addresses the challenge of federated learning in scenarios where each client device holds only a single data sample. Traditional federated learning methods become ineffective under these conditions, as local updates derived from a single data point are unreliable, especially when privacy-preserving noise is added. The authors propose a novel approach that involves a cosine-modulated, contractive transformation of the client's data, followed by a Gaussian perturbation to ensure privacy. The transformed data is then processed to create an intermediate representation that allows the server to estimate an unbiased gradient update, which aligns with the non-private centralized gradient while maintaining data privacy. This method diverges from conventional federated learning, which typically communicates model coefficients, instead focusing on sharing transformed data samples. The authors also derive the covariance of the stochastic gradient updates and establish the asymptotic normality of their model estimator, enabling valid inference on regression coefficients within the distributed framework. The paper includes a detailed analysis of variance, convergence, and design trade-offs, along with experimental results supporting the proposed method.
Methodology
The proposed methodology involves a two-step process: first, a cosine-modulated, contractive transformation is applied to the client's single data sample, followed by the addition of Gaussian noise to ensure privacy. The transformed data is then processed to create an intermediate representation that allows the server to recover an unbiased gradient estimator, facilitating effective model training without compromising individual privacy.
Results
The results indicate that the proposed method successfully enables collaborative learning from clients with minimal data, yielding unbiased gradient updates that align with traditional centralized methods. The theoretical analysis confirms the asymptotic normality of the estimator, allowing for valid inference on regression coefficients, and experimental results demonstrate the practical effectiveness of the approach.
Implications
This work has significant implications for real-world applications where data privacy is crucial, such as mobile health monitoring, fitness tracking, and other scenarios involving personal data. It enables effective machine learning in environments with limited data availability while ensuring privacy, potentially broadening the scope of federated learning applications.
PerCaM-Health: Personalized Dynamic Causal Graphs for Healthcare Reasoning
Graph Learning
Time Series
Interpretability
- Introduces a framework for learning personalized dynamic causal graphs from longitudinal health data.
- Bridges the gap between cohort-level models and patient-specific causal discovery.
- Utilizes a knowledge-guided population temporal graph adapted with patient-specific evidence.
- Enables patient-level counterfactual queries for healthcare interventions.
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PerCaM-Health: Personalized Dynamic Causal Graphs for Healthcare Reasoning
Summary
The paper introduces PerCaM-Health, a novel framework designed to learn personalized dynamic causal graphs from longitudinal health data, addressing the limitations of existing temporal causal discovery methods. Traditional cohort-level models provide stable but non-personalized structures, while per-patient discovery struggles with short, noisy, and irregular trajectories. PerCaM-Health bridges this gap by first constructing a knowledge-guided population temporal graph and then adapting it using patient-specific temporal evidence through rolling-window updates. This approach allows for the generation of interpretable graph sequences that can be used for patient-level counterfactual queries, such as estimating outcome changes under hypothetical interventions. The framework is evaluated on a semi-synthetic dynamic health benchmark, demonstrating improvements in graph recovery, dynamic edge tracking, and intervention direction accuracy compared to existing methods. The results indicate that combining personalization with temporal evolution leads to more reliable causal structures and enhances intervention reasoning in healthcare.
Methodology
The PerCaM-Health framework begins by mapping heterogeneous health data into interpretable patient-state variables. It learns a population temporal graph using techniques such as lagged prediction and sparsity, which is then adapted using patient-specific temporal evidence. The framework employs rolling-window updates to track changes over time, producing a sequence of interpretable graphs that can be audited and analyzed for causal relationships.
Results
Experiments on a semi-synthetic dynamic health benchmark reveal that PerCaM-Health significantly outperforms cohort-level, per-patient, and non-personalized temporal baselines in terms of graph recovery, dynamic edge tracking, and accuracy in predicting intervention outcomes. This indicates that the framework effectively captures the complexities of personalized healthcare reasoning.
Implications
The findings suggest that PerCaM-Health can enhance decision-making in personalized healthcare by providing clearer insights into causal relationships and enabling more accurate predictions of outcomes under various interventions. This could lead to improved treatment planning and patient management strategies.
Graph Representation Learning Augmented Model Manipulation on Federated Fine-Tuning of LLMs
Large Language Models
Federated Learning
Graph Learning
- Introduction of AugMP, a novel manipulation strategy targeting FFT-based LLMs.
- Utilization of a graph representation learning framework to synthesize malicious updates.
- Demonstrated significant degradation in model performance while maintaining benign-like characteristics.
- AugMP outperforms existing defenses by evading detection based on statistical consistency metrics.
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Graph Representation Learning Augmented Model Manipulation on Federated Fine-Tuning of LLMs
Summary
This paper addresses the vulnerabilities of Federated Fine-Tuning (FFT) of Large Language Models (LLMs) to model manipulation threats. The authors propose a novel strategy called Augmented Model manipulation (AugMP), which utilizes a graph representation learning (GRL) framework to capture feature correlations among benign LLM updates. This framework guides the generation of malicious updates that can effectively disrupt the global model's performance while maintaining a benign appearance. The AugMP strategy employs an iterative manipulation algorithm based on an augmented Lagrangian dual formulation, optimizing malicious updates to embed adversarial objectives without being easily detectable. Experimental results demonstrate that AugMP significantly reduces the accuracy of the global LLM by up to 26% and local LLM agents by up to 22%, while evading conventional defense mechanisms that rely on distance and similarity metrics. This work highlights the need for robust defenses against adversarial manipulations in federated learning settings, particularly for LLMs that are increasingly deployed across distributed environments.
Methodology
The authors developed an adversarial graph representation learning framework that constructs a feature correlation graph from benign updates. They employed a variational graph autoencoder (VGAE) to learn graph-structured representations and a graph spectral transformation (GST) module to generate malicious updates. An iterative manipulation algorithm based on augmented Lagrangian dual formulation was also introduced to optimize the malicious updates while preserving their benign-like properties.
Results
The AugMP strategy achieved a maximum reduction of 26% in global LLM accuracy and 22% in local LLM agent accuracy across multiple LLM backbones. The method maintained high statistical and geometric consistency with benign updates, allowing it to evade conventional detection methods.
Implications
The findings underscore the vulnerabilities of federated learning systems, particularly in the context of LLMs, and suggest that enhanced security measures are necessary to protect against adversarial manipulations. The proposed AugMP strategy could inform the development of more resilient federated learning frameworks.
Convergent Stochastic Training of Attention and Understanding LoRA
Theory
Optimization
Efficient ML
- Establishes trainability of attention layers and LoRA under stochastic methods without data or architecture assumptions.
- Proves that a mild regularization induces a Poincaré inequality for Gibbs measures, facilitating convergence.
- Introduces a novel SDE framework that captures the dynamics of stochastic gradient methods for training.
- Provides theoretical insights into the optimization dynamics of neural models using LoRA.
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Convergent Stochastic Training of Attention and Understanding LoRA
Summary
This paper investigates the trainability of attention mechanisms and Low Rank Adaptation (LoRA) in neural networks using stochastic methods. The authors establish a unified framework that rigorously proves the convergence of training for attention layers and LoRA parameterization without relying on assumptions about the data or architecture size. They demonstrate that a mild regularization of the empirical regression loss induces a Poincaré inequality for the corresponding Gibbs measure, leading to the conclusion that a stochastic differential equation (SDE) mimicking stochastic gradient descent (SGD) minimizes these losses. This work not only sheds light on the mathematical properties of attention mechanisms but also initiates a theoretical exploration of training dynamics for neural networks under LoRA, revealing a first-of-its-kind provably convergent training mechanism for both settings.
Methodology
The authors utilize stochastic differential equations (SDEs) to analyze the training dynamics of attention mechanisms and LoRA parameterization. They establish mathematical properties of the attention map and regression losses, proving convergence through the application of isoperimetric results related to SDE convergence.
Results
The paper shows that for both attention layers and depth-2 neural networks under LoRA, a mildly regularized regression loss is a Villani function, which implies that the corresponding Gibbs measure satisfies the Poincaré inequality. This leads to the conclusion that the continuous-time stochastic gradient dynamics, represented by an SDE, converges for any number of parameters and data.
Implications
The findings have significant implications for the training of large-scale models in machine learning, particularly in applications requiring efficient fine-tuning methods like LoRA. The theoretical insights into the convergence of training dynamics can enhance the understanding and optimization of attention mechanisms in various domains, including natural language processing and scientific machine learning.
GRAPHLCP: Structure-Aware Localized Conformal Prediction on Graphs
Graph Learning
- GRAPHLCP integrates graph topology into localized conformal prediction for GNNs.
- The framework includes a feature-aware densification step to enhance prediction reliability in sparse graphs.
- Personalized PageRank is used to model structural proximity, improving anchor sampling and calibration.
- Extensive experiments show GRAPHLCP achieves efficient marginal and conditional coverage.
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GRAPHLCP: Structure-Aware Localized Conformal Prediction on Graphs
Summary
The paper introduces GRAPHLCP, a novel framework for applying localized conformal prediction (CP) to graph neural networks (GNNs). Traditional CP methods struggle with the unique challenges posed by graph structures, such as inter-node dependencies and the combinatorial nature of graphs, which can lead to uncertain predictions. GRAPHLCP addresses these issues by incorporating graph topology into the localization and weighting processes. The framework includes a feature-aware densification step to alleviate locality bias in sparse graphs and utilizes a Personalized PageRank-based kernel to model structural proximity. This allows for effective anchor sampling and calibration weighting that captures both local and long-range dependencies. The authors conducted extensive experiments across multiple regression and classification datasets, demonstrating that GRAPHLCP maintains marginal coverage while achieving favorable conditional coverage, thus providing reliable uncertainty quantification in GNN applications.
Methodology
GRAPHLCP employs a proximity-based localized CP framework that incorporates graph topology and inter-node dependencies. It features a densification step to enhance locality in sparse graphs and utilizes a Personalized PageRank-based kernel for modeling structural proximity. This combination allows for effective calibration weighting and anchor sampling, addressing the challenges of traditional CP methods in graph settings.
Results
The experiments conducted on seven regression and eight classification datasets demonstrated that GRAPHLCP guarantees marginal coverage with finite samples while achieving efficient approximate conditional coverage. The results indicate that GRAPHLCP outperforms existing methods, particularly in complex graph topologies, by providing more reliable uncertainty quantification.
Implications
GRAPHLCP has significant implications for applications in high-stakes domains such as drug discovery, weather prediction, and fraud detection, where reliable uncertainty quantification is crucial. The framework can enhance the trustworthiness of GNN predictions, making it a valuable tool for practitioners in these fields.
Transfer Learning Across Fast- and Full-Simulation Domains in High-Energy Physics
Theory
Efficient ML
Graph Learning
- Transfer learning can effectively bridge the gap between fast-simulated and fully simulated datasets in HEP.
- Pretrained models consistently outperform independently trained baselines across various tasks.
- Significant reduction in target-domain training data requirements, typically by a factor of two.
- Demonstrates the utility of fast simulation data in creating reusable representations.
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Transfer Learning Across Fast- and Full-Simulation Domains in High-Energy Physics
Summary
This paper investigates the application of transfer learning techniques in high-energy physics (HEP), specifically focusing on the transfer of knowledge between fast-simulated and fully simulated datasets. The authors explore three key tasks: signal-background classification, quark-gluon jet tagging, and missing transverse energy reconstruction, utilizing various neural network architectures including dense neural networks, graph neural networks, and transformers. The study demonstrates that models pretrained on fast simulation data can be effectively adapted to different simulation environments, achieving superior performance compared to models trained independently on target datasets. Notably, the pretrained models require significantly less training data from the target domain, often reducing the necessary statistics by approximately half. These findings highlight the potential of fast simulation data to generate robust representations that can be reused across different experimental setups, advocating for the publication of such pretrained models as valuable scientific resources.
Methodology
The authors employed a systematic approach to transfer learning by pretraining models on ATLAS-like fast simulation data and then adapting them to CMS-like fast simulation and fully simulated ATLAS Open Data. They utilized dense neural networks, graph neural networks, and transformer architectures to address three representative tasks in HEP.
Results
The results indicate that models pretrained on fast simulation data significantly outperform those trained independently on target datasets. The pretrained models also require less training data from the target domain, effectively reducing the data needs by about 50%. This demonstrates the effectiveness of transfer learning in enhancing model performance and efficiency in HEP analyses.
Implications
The findings suggest that fast simulation data can be leveraged to create robust models that generalize well across different experimental conditions, potentially reducing the reliance on expensive full simulations. This approach could lead to more efficient data usage in HEP and encourage the sharing of pretrained models as reusable resources in the scientific community.
When Are Experts Misrouted? Counterfactual Routing Analysis in Mixture-of-Experts Language Models
NLP
Large Language Models
Efficient ML
- Standard top-k routing in MoE models is effective for confident tokens but misaligned for fragile tokens.
- Routing decisions are evaluated based on executed routes, leading to potential suboptimal choices.
- A minimal update to the router can improve performance on difficult reasoning tasks.
- The study emphasizes the need to consider routing quality as a critical aspect of MoE training.
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When Are Experts Misrouted? Counterfactual Routing Analysis in Mixture-of-Experts Language Models
Summary
This paper investigates the routing decisions made by the standard top-k router in Mixture-of-Experts (MoE) language models, focusing on their effectiveness in assigning tokens to experts. The authors conduct a counterfactual analysis by comparing the standard routing choices against sampled equal-compute alternatives, assessing their performance based on next-token probabilities. The findings reveal that while the standard router performs well on confident tokens, it is often misaligned on fragile tokens that require more complex reasoning. This misalignment is attributed to the training process, which evaluates routing decisions based solely on executed routes, neglecting potential better alternatives. The authors demonstrate that a minimal update to the final-layer router can significantly improve performance on challenging tasks, suggesting that routing quality should be prioritized in MoE training. Overall, the study highlights the importance of effective routing in enhancing the capabilities of MoE language models.
Methodology
The authors conducted a counterfactual analysis by fixing the model and comparing the standard routing choices against sampled equal-compute alternatives. They scored each route based on the next-token probability assigned to the realized token in verified reasoning trajectories, categorizing tokens by their confidence levels.
Results
The analysis showed that the standard router was best on only 0.8% of fragile tokens, while the best sampled equal-compute route improved next-token probability by 20.4 percentage points. Updating only the final-layer router led to significant performance improvements on downstream tasks, indicating that routing misallocation contributes to high-loss predictions.
Implications
The findings suggest that improving routing decisions in MoE models could enhance their performance on complex reasoning tasks, advocating for a shift in focus towards routing quality in model training.
Convex Optimization with Nested Evolving Feasible Sets
Optimization
Theory
- Introduction of CONES framework for convex optimization with evolving feasible sets.
- Development of lazy-algorithm achieving O(T^(1−β)) and O(T^β) for regret and movement cost.
- FRUGAL algorithm achieves zero regret with O(log T) movement cost for strongly convex loss functions.
- Establishment of lower bounds for movement cost in relation to regret, proving FRUGAL's optimality.
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Convex Optimization with Nested Evolving Feasible Sets
Summary
This paper introduces Convex Optimization with Nested Evolving Feasible Sets (CONES), where the objective function remains fixed while the feasible region evolves over time as a nested sequence of convex sets. The authors aim to develop online algorithms that minimize both the regret against a static optimal benchmark and the total movement cost while ensuring feasibility at all times. They propose a lazy-algorithm that achieves O(T^(1−β)) and O(T^β) for regret and movement cost, respectively, for any β in (0, 1]. Additionally, they introduce the FRUGAL algorithm, which achieves zero regret and a movement cost of O(log T) when the loss function is strongly convex or α-sharp. The paper also establishes that any online algorithm with sub-linear regret incurs a movement cost of at least Ω(log T), demonstrating the optimality of the FRUGAL algorithm. This work generalizes classical constrained convex optimization by allowing the feasible region to change, reflecting real-world scenarios where constraints may tighten over time.
Methodology
The authors propose two algorithms: a lazy-algorithm for general convex loss functions and a FRUGAL algorithm for strongly convex or α-sharp loss functions. They analyze the performance of these algorithms in terms of regret and movement cost, comparing them against a static optimal benchmark. The analysis includes deriving upper and lower bounds for the performance metrics.
Results
The lazy-algorithm achieves regret and movement costs of O(T^(1−β)) and O(T^β) respectively, while the FRUGAL algorithm achieves zero regret and a movement cost of O(log T). The paper also proves that any online algorithm with sub-linear regret must incur a movement cost of at least Ω(log T), confirming the optimality of the FRUGAL algorithm.
Implications
The CONES framework has significant implications for various fields such as operations research, control, and machine learning, where decision-making under evolving constraints is critical. The results can be applied to real-time optimization problems where constraints may change dynamically.
Beyond Distribution Estimation: Simplex Anchored Structural Inference Towards Universal Semi-Supervised Learning
Theory
Graph Learning
Computer Vision
- Introduction of Universal Semi-supervised Learning (UniSSL) to address challenges with unlabeled data distributions.
- Development of Simplex Anchored Graph-state Equipartition (SAGE) to leverage inter-sample relations for representation learning.
- Utilization of a simplex equiangular tight frame to improve representation separation.
- Implementation of a weighting strategy to enhance the quality of pseudo-labels.
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Beyond Distribution Estimation: Simplex Anchored Structural Inference Towards Universal Semi-Supervised Learning
Summary
This paper addresses the challenges of semi-supervised learning (SSL) in scenarios with scarce labeled data and unknown distributions of unlabeled data, introducing the concept of Universal Semi-supervised Learning (UniSSL). Traditional SSL methods often rely on the assumption of uniform unlabeled data distributions or require sufficient labeled data for estimation, leading to erroneous pseudo-labels and representation confusion. The authors propose a novel approach called Simplex Anchored Graph-state Equipartition (SAGE), which focuses on representation-level structural inference to bypass the need for distribution estimation. SAGE captures high-order inter-sample dependencies to establish structural consensus for representation learning. Additionally, the method employs a simplex equiangular tight frame to enhance inter-class representation separation and introduces a weighting strategy to prioritize reliable pseudo-labels while isolating potentially erroneous ones. The proposed method demonstrates significant improvements over existing state-of-the-art techniques, achieving an average accuracy gain of 8.52% across five standard benchmarks.
Methodology
The authors propose SAGE, which captures high-order inter-sample dependencies to create a structural consensus for representation learning. This method avoids direct distribution estimation by focusing on representation-level inference. A simplex equiangular tight frame is used to guide the separation of inter-class representations, while a weighting strategy prioritizes reliable pseudo-labels and isolates erroneous ones.
Results
SAGE consistently outperforms state-of-the-art methods across five standard benchmarks, achieving an average accuracy improvement of 8.52%. The method effectively mitigates representation confusion and enhances the quality of pseudo-labels compared to existing approaches.
Implications
The findings suggest that focusing on representation-level structural inference can significantly improve semi-supervised learning performance in real-world scenarios with limited labeled data and unknown unlabeled data distributions. This approach could be beneficial in various applications, including medical diagnosis and other fields where labeled data is scarce.
Less Random, More Private: What is the Optimal Subsampling Scheme for DP-SGD?
Theory
Efficient ML
Federated Learning
- Balanced Iteration Subsampling (BIS) outperforms Poisson subsampling in terms of privacy amplification.
- BIS is optimal at both low and high noise levels, addressing participation variance effectively.
- A near-exact Monte Carlo accountant for BIS is introduced, improving privacy evaluation accuracy.
- Empirical results show a significant reduction in required noise multipliers with BIS.
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Less Random, More Private: What is the Optimal Subsampling Scheme for DP-SGD?
Summary
This paper investigates the optimal subsampling scheme for differentially private stochastic gradient descent (DP-SGD), challenging the prevalent use of Poisson subsampling. The authors demonstrate that the randomness inherent in Poisson subsampling leads to significant participation variance, which negatively impacts privacy amplification. They introduce Balanced Iteration Subsampling (BIS), a structured approach where each sample participates in a fixed number of iterations, thus eliminating participation variance. The authors prove that BIS achieves superior privacy amplification compared to Poisson subsampling at both low and high noise levels. To facilitate practical application, they develop a near-exact Monte Carlo accountant for BIS, which efficiently evaluates privacy guarantees without the analytical slack of previous methods. Empirical evaluations across various DP-SGD configurations reveal that BIS consistently outperforms Poisson subsampling, particularly in low-noise scenarios, reducing the required noise multiplier by up to 9.6%. This work overturns the assumption that increased randomness leads to better privacy amplification, highlighting the benefits of structured participation in DP-SGD.
Methodology
The authors analyze the privacy amplification of different subsampling schemes theoretically and empirically. They prove the optimality of BIS through rigorous mathematical analysis and develop a near-exact Monte Carlo accountant that leverages dynamic programming and screening bounds to efficiently compute privacy guarantees.
Results
The study shows that BIS consistently provides stronger privacy amplification than Poisson subsampling, particularly in low-noise regimes, achieving up to a 9.6% reduction in the required noise multiplier. In high-noise scenarios, BIS matches the performance of Poisson subsampling.
Implications
The findings suggest that structured sampling methods like BIS can enhance privacy in differentially private machine learning applications, particularly in scenarios where utility is critical. This could lead to more effective implementations of DP-SGD in real-world applications, such as federated learning and privacy-preserving data analysis.
Causal-Aware Foundation-Model for Bilevel Optimization in Discrete Choice Settings
Optimization
- Introduction of C3PO network for bi-level decision-making in discrete-choice settings.
- Integration of imitation learning, multi-task learning, and in-context learning for effective pricing strategies.
- Demonstrated strong performance in simulated and real-world datasets.
- C3PO consistently improves pricing KPIs, especially with higher customer price sensitivity.
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Causal-Aware Foundation-Model for Bilevel Optimization in Discrete Choice Settings
Summary
This paper presents a novel causal-aware foundation-model framework aimed at optimizing decision-making in discrete-choice environments. The authors introduce the Constrained Triple-Head Price Optimization (C3PO) network, which addresses a bi-level decision problem where a service provider selects an optimal assortment while heterogeneous users make personalized choices based on their preferences. C3PO integrates various learning techniques, including imitation learning for price setting, multi-task learning for revenue responses, and in-context learning for price elasticity, to generate effective pricing recommendations while adhering to business constraints. The model is trained using simulated data derived from classical discrete choice models and is evaluated in various choice environments without access to the underlying preference structure. The results indicate that C3PO significantly improves pricing key performance indicators (KPIs), particularly as customer price sensitivity increases. The framework is successfully applied in real-world scenarios, such as healthcare and airline pricing, demonstrating substantial gains across multiple products and markets.
Methodology
The authors developed the C3PO network, which combines imitation learning, multi-task learning, and in-context learning to optimize pricing decisions in discrete-choice environments. The model is trained on synthetic datasets generated from established discrete choice models and evaluated in diverse choice scenarios without prior knowledge of customer preferences.
Results
C3PO showed consistent improvements in pricing KPIs across simulated and real-world datasets. The model's effectiveness increased with customer price sensitivity, leading to substantial gains in pricing strategies for applications in healthcare, tender pricing, and airline ancillary pricing.
Implications
The proposed framework can enhance decision-making processes in various industries by providing a universal model for optimal pricing and assortment strategies. Its adaptability to different contexts suggests potential applications in product design, marketing, and other areas requiring complex decision-making.
ProteinJEPA: Latent prediction complements protein language models
NLP
Generative Models
Theory
- Introduction of masked-position MLM+JEPA as a superior training recipe for protein language models.
- Demonstrated that this hybrid approach outperforms MLM-only methods in several downstream tasks.
- Identified critical factors for success, including the retention of MLM objectives and targeted latent predictions.
- Provided a comprehensive evaluation across multiple models and tasks, showcasing the versatility of the proposed method.
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ProteinJEPA: Latent prediction complements protein language models
Summary
This paper investigates the integration of latent-space prediction with traditional masked language modeling (MLM) in protein language models. The authors propose a novel approach, termed masked-position MLM+JEPA, which predicts latent targets only at masked positions while retaining the MLM cross-entropy loss. Through a controlled comparison across various protein sequence encoders, the study demonstrates that this hybrid approach can outperform traditional MLM-only methods on a suite of 16 downstream tasks, achieving notable wins in tasks related to stability, fitness, and structural retrieval. The results indicate that while all-position MLM+JEPA matches MLM-only performance, it fails to replicate the gains observed with the masked-position variant. The findings suggest that combining MLM with JEPA can enhance the performance of protein language models, particularly in continued training scenarios, while also highlighting the importance of task-specific adaptations in model architecture.
Methodology
The authors conducted a controlled comparison of different training recipes for protein language models, including MLM-only, masked-position MLM+JEPA, all-position MLM+JEPA, and JEPA-only. They evaluated these methods on a suite of 16 tasks, utilizing pretrained and random-initialized protein sequence encoders with parameter sizes ranging from 35M to 150M. The masked-position MLM+JEPA approach involved predicting latent targets at masked positions while retaining the MLM cross-entropy loss, using a two-layer SwiGLU predictor with a Sketched Isotropic Gaussian Regularizer (SIGReg).
Results
The results showed that the masked-position MLM+JEPA approach achieved 10 wins, 3 losses, and 3 ties against MLM-only on pretrained ESM2-35M, and 11 wins, 2 losses, and 3 ties on ESM2-150M. Gains were observed across multiple tasks, particularly in stability, β-lactamase fitness, and SCOPe-40 fold retrieval. However, the all-position MLM+JEPA did not replicate the masked-position gains, and JEPA-only configurations performed poorly in most experiments.
Implications
The findings suggest that integrating latent prediction with traditional MLM can significantly enhance the performance of protein language models, particularly in tasks requiring structural and functional understanding of proteins. This approach may lead to improved methodologies in protein sequence analysis and related bioinformatics applications, potentially aiding in drug discovery and protein engineering.
Geometric Kolmogorov–Arnold Network (GeoKAN)
Theory
Optimization
Efficient ML
- GeoKAN introduces a geometry-aware approach to KAN models, enhancing function approximation capabilities.
- The model learns a diagonal Riemannian metric that adapts the input space for better representation.
- Three main variants of GeoKAN are developed, each tailored for different applications in function approximation and physics-informed learning.
- GeoKAN reallocates representational resolution dynamically, improving performance in regions with sharp variations.
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Geometric Kolmogorov–Arnold Network (GeoKAN)
Summary
The paper introduces Geometric Kolmogorov–Arnold Networks (GeoKANs), a novel family of geometry-aware models that enhance the traditional Kolmogorov–Arnold Network (KAN) framework by learning a diagonal Riemannian metric to adapt the input space. This adaptation allows GeoKAN to perform function approximation in learned, geometry-adapted coordinates rather than fixed Euclidean coordinates, addressing limitations in handling non-uniform target functions. The authors develop three main variants of GeoKAN: GeoKAN-NNMetric, GeoKAN-γ, and LM-KAN, with the latter further divided into basis-specific versions. These models are designed to allocate representational capacity dynamically, stretching regions with rapid variations and compressing smoother areas, making them particularly effective for scientific machine learning and differential equations. The paper evaluates GeoKAN's performance through supervised function-approximation benchmarks and physics-informed learning scenarios, demonstrating its advantages over standard neural networks and existing KAN models. The results indicate that GeoKAN can effectively capture complex solutions in differential equations, showcasing its potential for applications in scientific computing and machine learning.
Methodology
The authors propose a framework where the input space is warped using a learned metric before applying basis expansion and feature mixing. They develop three main variants of GeoKAN, each with different metric parameterizations and feature constructions. The models are evaluated through curve-fitting benchmarks and physics-informed learning scenarios, comparing their performance against traditional neural networks and existing KAN models.
Results
GeoKAN models demonstrated superior approximation capabilities in curve-fitting benchmarks, particularly for functions with oscillatory and multiscale structures. In physics-informed learning, the LM-KAN variant outperformed previous PIKAN models, effectively capturing solutions to differential equations with sharp gradients and localized features.
Implications
GeoKAN has significant implications for scientific machine learning, particularly in fields requiring accurate solutions to complex differential equations. Its ability to adaptively allocate representational capacity makes it a promising tool for various applications in computational physics, engineering, and beyond.