TOSense: Multidisciplinary Sensing

• TOSense is a multidisciplinary framework that optimizes signal detection by managing tradeoffs in sensing time and data transmission in cognitive radio networks.
• It enables semantic extraction from Terms of Service documents using vector encodings and clustering, improving legal transparency through automated Q&A pipelines.
• TOSense also includes non-Hermitian topological sensors and coupled cavity designs, achieving exponential sensitivity amplification for high-precision physical measurements.

TOSense encompasses multiple lines of research and technological innovation involving advanced sensing and decision mechanisms across fields such as cognitive radio networks, legal document analysis, quantum and gravitational wave detection, and non-Hermitian topological physics. The term frequently denotes, depending on context, either algorithms optimizing channel access through sensing, tools for semantic extraction and answering of Terms of Service (ToS) documents, sensors exploiting topological amplification, or optical measurement innovations in physical experiments.

1. TOSense in Cognitive Radio Networks

TOSense, as formulated in "To Sense or Not To Sense" (Shafie, 2012), refers to a class of protocols and analytical frameworks in cognitive radio, where secondary users (SUs) optimize the tradeoff between spectrum sensing and data transmission. The core issue is that, in a fixed-length time slot $T$, the time $\tau$ allocated to sensing the primary channel (to detect primary user [PU] activity) improves estimation reliability (lowering misdetection [$P_{MD}$] and false alarm [$P_{FA}$] rates) but reduces actual data transmission time ($T-\tau$).

Key elements include:

• Randomized Channel Access: The SU transmits with probability $a_s$ when the channel is declared idle and with probability $b_s$ (introduced in enhanced schemes) even when declared busy, mitigating adverse $P_{FA}$ and $P_{MD}$ effects.
• Variable Sensing Duration: $\tau$ is optimized rather than fixed, jointly with probabilities $(a_s, b_s)$, maximizing stable throughput for both primary and secondary queues, as formulated in throughput optimization problems such as

$$\max_{\tau} \lambda_s = \overline{P}_{s,sd}\,\overline{P}_{FA}\left(1 - \frac{\lambda_p}{\overline{P}_{p,pd}\,\overline{P}_{MD}}\right)$$

with constraints on $\lambda_p$ ensuring primary queue stability.

• Analytical Tradeoff and Queue Stability: Results demonstrate scenarios where minimal sensing or even omitting sensing results in superior SU throughput, depending on $(P_{MD},P_{FA})$ pairs and the PU arrival rate. Queue stability is established via Loynes’s theorem: $\lambda_i < \mu_i$ for $i\in\{\mathrm{p},\mathrm{s}\}$.

Significance: These schemes yield expanded stability regions, improved QoS guarantees, and strategic flexibility in SU access policies, critical in interference-limited spectrum environments.

2. TOSense in Semantic Analysis of Terms of Service Documents

In the context of legal document analysis, TOSense denotes a Chrome extension facilitating natural language Q&A for Terms of Service (ToS) documents by integrating automated web crawling, semantic retrieval, and lightweight LLM pipelines (Chen et al., 1 Aug 2025).

Core components:

• tos-crawl: An automated crawler that exhaustively extracts ToS content by simulating user behavior (expanding hidden sections, handling multi-page structures) and performs preprocessing (language filtering, deduplication).
• Semantic Retrieval Pipeline: Employs MiniLM for vector encoding of user queries and document sentences, using cosine similarity:

$$\mathrm{Similarity} = \frac{\vec{v}_q \cdot \vec{v}_d}{\|\vec{v}_q\|\|\vec{v}_d\|}$$

to locate relevant clauses. A BART encoder subsequently verifies answer relevance, outputting a score $b \in [0,1]$, compared to threshold $T$ (set at $0.3$).

• Question Answering Evaluation Pipeline (QEP): Avoids manual annotation by using k-means clustering on MiniLM representations to assign topics to statements; T5-based question generation tests retrieval, and accuracy is determined by cluster agreement: $C(a_i)=C(d_i)$.

Metrics and Performance:

• Accuracy: Up to $44.5\%$ on Microsoft ToS, stable across cluster granularity.
• Latency: $<3$ seconds per query-response on 2 vCPU/8GB RAM/no GPU.
• CPU/memory: $91-93\%$ utilization, $<38\%$ RAM.
• Identified limitations include model expressiveness for nuanced ToS content and crawler robustness on SPA architectures.

Planned enhancements focus on computer vision-based crawling, instruction-tuned LLMs, and user studies to assess impact on informed consent and behavioral shifts.

3. Non-Hermitian Topological Sensors (NTOS) and TOSense

TOSense also refers to non-Hermitian topological sensors as studied in (Budich et al., 2020). These devices are defined by the exponential amplification of sensitivity in response to perturbations of boundary conditions, a consequence of the non-Hermitian (NH) biorthogonal structure:

• Mechanism: In a 1D NH chain (e.g., a lattice with open boundaries and inter-end coupling $\Gamma$), the energy shift of the topological boundary mode due to $\Gamma$ is

$$S = \frac{\partial E_0}{\partial \Gamma} = \kappa \exp(\alpha N)$$

with $N$ the system size; $\alpha$ encapsulates localization asymmetry of right/left eigenvectors, leading to exponentially vanishing overlap.

• Robustness: The sensitivity scaling persists under local disorder and without fine-tuning, protected by a NH topological invariant (winding number $\nu$).
• Platforms: Implementations include topological electric circuits, arrays of coupled optical ring-resonators (via chiral mode coupling), synthetic quantum materials (quantum dot/cold atom chains), and classical meta-materials.

Implications: Enables ultrahigh-precision detection (signal-to-noise ratio enhancable by device size), robust to fabrication defects and environmental perturbations, without the fragility of conventional EP (exceptional point)-based sensors.

4. TOSense in Quantum and Gravitational Sensing

In high-precision measurement scenarios, TOSense appears in proposals for advanced wavefront and angular sensors, particularly for gravitational wave detection (Oshima et al., 2022):

• Coupled Cavity Wavefront Sensor: For the TOBA (torsion bar antenna), a coupled cavity amplifies the angular signal by compensating the Gouy phase difference between first-order Hermite-Gaussian modes (HG$_{10}$) and the fundamental mode (HG$_{00}$). This is achieved using an auxiliary cavity engineered for simultaneous resonance:
  • Reflection coefficients $r_{cc1}$ account for distinct phase responses to each mode.
  • Amplification factors such as $1/(1 - r_f|r_{a0}|)(1 - r_f|r_{a1}|)$ boost sensitivity to pendulum tilt.
• Experimental Techniques: Dual-frequency Pound–Drever–Hall locking ensures stable coupled cavity operation, supporting hierarchical control of multiple loops. Performance is validated in simulation (FINESSE) and experiment: angular resolutions approaching $5 \times 10^{-16}\ \mathrm{rad}/\sqrt{\mathrm{Hz}}$ are predicted to be feasible.

Application: The enhanced sensitivity directly supports gravitational wave detection in the sub-$10$\,Hz band and enables direct detection of Newtonian noise and potential deployment in earthquake early warning systems.

5. Analytical Formulations and Tradeoffs

The unifying mathematical structure in TOSense implementations is the explicit management of tradeoffs and sensitivity amplification, often expressed through formal optimization or amplification equations:

Area	Key Equations / Metrics
Cognitive Radio	$\lambda_i < \mu_i$, $$P_{MD}^{(\tau)}=1-Q\left(\frac{1}{\sqrt{2\gamma+1}}(Q^{-1}(P_{FA})-\sqrt{\tau f_s}\,\gamma)\right)$$
Semantic QA	$\text{cosine}(v_q, v_d)$, $b \geq T$ (accept answer), $C(a_i)=C(d_i)$ (cluster match in QEP)
Topological Sensors	$S = \kappa \exp(\alpha N)$
Coupled Cavities	$r_{cc1} = \ldots$ (see above), angular sensitivity $$<5 \times 10^{-16}\ \mathrm{rad}/\sqrt{\mathrm{Hz}}$$

Each implementation rigorously confronts the limitations imposed by the physical, algorithmic, or legal domain by optimizing over parameters (e.g., sensing time, cluster size, system size, or phase-matching), balancing competing targets such as sensitivity, accuracy, and resource budget.

6. Limitations, Open Problems, and Future Directions

Current TOSense applications face limitations:

• Cognitive Radio: Sensitivity of throughput advantage to $(P_{MD}, P_{FA})$, reliance on accurate estimates, and implicit assumptions of queueing stationarity.
• Semantic QA: Lightweight transformer models limit semantic nuance, especially in legal text parsing; current cluster-based evaluation does not fully capture answer correctness for complex or multi-topic questions.
• NTOS: While NH topology yields robust amplification, experimental realization depends on precise control of asymmetric coupling and dissipation engineering.
• Coupled Cavity Sensing: Optical loss and cavity stabilization may limit the practical sensitivity; extensions to multi-mode or multi-parameter schemes remain to be explored.

Potential improvements include:

• Integration of more expressive and ToS-specialized LLMs for semantic QA
• Advanced computer vision for robust document extraction
• Materials and circuit engineering for stable and scalable NTOS fabrication
• User studies for ToS comprehension impact and behavioral change quantification

7. Synthesis and Impact

Across its diverse technical instantiations, TOSense serves as a paradigm in which the optimal extraction, amplification, or interpretation of signals—be these wireless spectrum states, legal clauses, quantum modes, or optomechanical perturbations—is achieved through principled algorithmic or physical design. The recurring theme is tradeoff management (e.g., between resource allocation and accuracy) and the leveraging of advanced mathematical machinery (transformer encodings, queuing theory, non-Hermitian topology, cavity response engineering).

Through demonstrated improvements in performance metrics (stability region, sensitivity, responsiveness) and user agency (legal transparency), TOSense systems exemplify state-of-the-art approaches to sensing and interpretation across information, physical, and legal domains.