--- title: TiSR in Multi-Domain Research url: https://www.emergentmind.com/topics/tisr type: topic --- # TiSR in Multi-Domain Research Searching arXiv for the cited TiSR-related papers to ground the article in current records. TiSR, also written as TISR in some papers, is not a single canonical concept in the arXiv literature. The acronym is used for at least five distinct research objects across biomedical vision, symbolic regression, super-resolution, and wireless communications: **Textual Inversion and Self-supervised Refinement** for radiology report generation [2405.20607]; **thermodynamics-informed symbolic regression** as a Julia-based framework for equations of state [2309.02805]; the **TiSR** symbolic-regression package as benchmarked under FastSRB [2508.14481]; **Thermal Image Super-Resolution** as a reconstruction task [2206.12046]; **twin-image super-resolution** in multi-image satellite super-resolution [2602.21513]; and **Time Index Modulation-Driven Standalone RIS** for symbiotic radio [2407.00763]. This suggests that domain-level disambiguation is necessary whenever the acronym appears without expansion. ## 1. Scope and nomenclature The capitalization pattern correlates with field usage. In radiology report generation, the acronym appears as **TISR**, expanding to **Textual Inversion and Self-supervised Refinement** [2405.20607]. In symbolic regression, it appears as **TiSR**, expanding to **thermodynamics-informed symbolic regression** and denoting both a framework and a Julia package [2309.02805]. In computer vision, **TISR** may denote either **Thermal Image Super-Resolution** as a problem setting [2206.12046] or **twin-image super-resolution** as a specific multi-image super-resolution scenario [2602.21513]. In wireless communications, **TiSR** denotes **Time Index Modulation-Driven Standalone RIS mechanism for symbiotic radio** [2407.00763]. These usages are methodologically unrelated. Some refer to a trainable model wrapped around an encoder–decoder pipeline, some to a genetic-programming engine, some to an inverse problem, and some to a communications mechanism. A plausible implication is that bibliographic retrieval based only on the acronym is inherently noisy unless constrained by field, title expansion, or arXiv identifier. ## 2. Textual Inversion and Self-supervised Refinement in radiology report generation In radiology report generation, TISR is built on top of the standard encoder–decoder paradigm and is intended to address two shortcomings attributed to mainstream approaches: overlooking the modality gap and ignoring report content constraints [2405.20607]. Let $\mathcal{I}\in\mathbb{R}^{B\times M\times D}$ denote visual features extracted by an image encoder and $\mathcal{T}\in\mathbb{R}^{B\times N\times D}$ text embeddings produced by the decoder’s autoregressive loop, with $B$ the batch size, $M$ image patches, $N$ maximum report length, and $D$ embedding dimension. The decoder predicts each next word via $$ \mathcal{O}_n = f_d(\mathcal{I},\,\mathcal{T}_{n-1}),\qquad \mathcal{R}_n = \mathrm{softmax}(f_l(\mathcal{O}_n)). $$ The first component, **textual inversion**, learns a lightweight MLP that maps image features into pseudo-words in the same embedding space as the text decoder: $$ P_1 = \mathrm{Dropout}(\mathrm{GELU}(f_l(\mathcal{I}))), $$ $$ \mathcal{P} = f_l\bigl(\mathrm{Dropout}(\mathrm{GELU}(f_l(P_1)))\bigr)\in\mathbb{R}^{B\times M\times D}. $$ These pseudo-words are then processed by attention in the same space as ordinary word tokens. The stated purpose is to eliminate the cross-modal feature gap by representing images as pseudo words. The second component, **self-supervised refinement**, applies cross-modal interaction and contrastive alignment to refine the pseudo-words without extra annotations. The interaction stage is $$ \mathcal{P}'=\mathrm{softmax}\!\Bigl(\tfrac{\mathcal{P}\,\mathcal{T}^\top}{\sqrt D}\Bigr)\,\mathcal{T},\qquad \mathcal{T}'=\mathrm{softmax}\!\Bigl(\tfrac{\mathcal{T}\,\mathcal{P}^\top}{\sqrt D}\Bigr)\,\mathcal{P}, $$ followed by fusion $$ \mathcal{P}'' = \mathrm{MLP}\bigl([\mathcal{P}',\,\mathcal{T}']\bigr)\in\mathbb{R}^{B\times S\times D},\qquad S=M+N. $$ A score matrix $S_{ij}=\cos(\mathcal{I}'_i,\mathcal{O}'_j)$ is formed over the batch, and the refinement objective is a symmetric cross-entropy loss $\mathcal{L}_{sr}$. The full training objective is $$ \mathcal{L} = \mathcal{L}_{rrg} + \mathcal{L}_{sr}. $$ Architecturally, TISR is described as **orthogonal to most existing methods** and **plug-and-play**. No change is required to the base encoder or decoder; the framework adds the inversion MLP and the contrastive head. The authors apply it to **R2Gen**, **R2GenCMN**, and **VLCI**, with preprocessing following each baseline’s existing pipeline. Experiments are conducted on **IU X-ray** with **7 470 images, 3 955 reports**, split **7:1:2 [official]**, and **MIMIC-CXR** with **377 110 images, 227 835 reports**, using official train/val/test splits. Metrics include **BLEU-1…4, METEOR, ROUGE-L**, and **Clinical Efficacy: precision, recall, F1 via CheXbert label extraction**. The reported gains are consistent across baselines and datasets. On **IU-Xray with R2Gen**, BLEU-1 improves from **0.443 to 0.470**, BLEU-4 from **0.168 to 0.187**, METEOR from **0.175 to 0.194**, and ROUGE-L from **0.355 to 0.369**. On **MIMIC-CXR with R2Gen**, BLEU-1 improves from **0.350 to 0.358**, BLEU-4 from **0.103 to 0.106**, CE-Precision from **0.424 to 0.467**, CE-Recall from **0.254 to 0.302**, and CE-F1 from **0.317 to 0.367**. The paper reports no formal $p$-values. Qualitative attention maps indicate improved focus on clinically relevant lung regions and fewer hallucinated findings, including an example where the baseline misses **atelectasis** and hallucinates **consolidation**, while the TISR-enhanced model highlights and mentions the true finding. ## 3. Thermodynamics-informed symbolic regression for equations of state In symbolic regression, TiSR denotes a **Julia-based, genetic-programming-driven framework specifically engineered to accelerate and partly automate the discovery of analytical equations of state from often noisy, scattered thermodynamic data** [2309.02805]. Its core search loop combines a **modified NSGA-II** multi-objective selector, an **island-model** population structure on a **static ring topology**, and a **grammar-checking layer** to forbid physically meaningless subexpressions such as $\exp(\log(x))$ or parameters in exponents. The per-generation workflow includes random initialization or seed injection, mutation and subtree crossover, individual instantiation, **Levenberg–Marquardt** parameter identification, singularity checks, complexity and residual evaluation, periodic migration, and hybrid selection by Pareto sorting followed by tournament filling. The objective layer is explicitly multi-objective. For data $\{(\mathbf{x}_i,y_i)\}_{i=1}^N$ and model $f(\mathbf{x};\boldsymbol\theta)$, TiSR defines raw residuals $r_i=y_i-\hat y_i$ and optionally processed residuals $\tilde r_i=\mathcal{P}(r_i,y_i)$. The default parameter-estimation objective is the weighted mean square error $$ J(\boldsymbol\theta)=\mathrm{ms\_processed\_e}=\frac{1}{N}\sum_{i=1}^N w_i(\tilde r_i)^2, $$ while selectable optimization targets include $\mathrm{mse}$, $\mathrm{mae}$, $\max|r|$, relative-error metrics, total node count $\mathrm{compl}$, $\mathrm{recursive\_compl}$, and $\mathrm{n\_params}$. Parameter fitting uses LM with **early stopping** by splitting data into fit and validation sets and aborting when validation residual increases for $k_{\rm sto}$ consecutive LM iterations. TiSR incorporates pre- and post-processing machinery intended for EOS development. Before regression, inputs may be normalized or Z-scaled, outputs transformed, and a **pre_residual_processing!** hook supplied to enforce known functional structure. The paper gives the example of fitting $g(T,\rho)$ when one knows $Z=\exp(g(T,\rho))$. Post-processing includes a **drastic_simplify!** mutation, symbolic simplification with **SymbolicUtils.jl**, and a planned $\ell_1$-regularized fitting step. Built-in thermodynamic supports include protected evaluation of $x^y$, $\log x$, and division, **factor variables**, and support for **Helmholtz energy formulation**; full thermodynamic consistency enforcement is explicitly described as not yet built in. The default function set is $$ \{+,-,\times,\!/\,,\;x^y,\;\exp,\;\log,\;\sin,\;\cos,\;\tanh\}, $$ and arbitrary Julia-level functions may be registered with protected-domain guards. In the case-study discussion, TiSR is reported to have been used in **Frotscher et al. (2023)** to rediscover simplified virial expansions and polynomial fits to experimental PVT data with **population size 200–300 per island**, **3–5 islands**, **500–2000 generations**, and **run time on 8 cores of approximately 1–3 h for moderate data sets $(N\sim100)$**. One reported model is $$ Z(\rho,T)=1+\bigl(a_0+a_1/T+a_2/T^2\bigr)\rho+(b_0+b_1/T)\rho^2, $$ with **RMSE $\approx 10^{-3}$** and **max relative error $<1\%$**, using **5–7 parameters** and **recursive complexity $<30$**. The framework is described as not ready for end users yet, and the roadmap includes constrained fitting, singularity prevention in two-phase regions, direct Helmholtz EOS discovery, regularization, tighter coupling to REFPROP/CoolProp, and a GUI front-end. ## 4. TiSR as benchmarked under FastSRB The paper **“Fast Symbolic Regression Benchmarking”** does not introduce TiSR as a new algorithm; instead, it uses the existing **TiSR Julia package (“\tisr,” Martinek et al. 2023)** as one of two off-the-shelf symbolic-regression toolkits in the **FastSRB** framework [2508.14481]. For this benchmark, TiSR is configured as a **classic tree-based genetic-programming engine** with the common function set $$ \{ +, -, *, /, \mathrm{pow}, \mathrm{neg}, \exp, \log, \sqrt, \mathrm{pow2}, \mathrm{pow3}, \sin, \cos, \tanh \}. $$ Tree-structure restrictions prohibit nesting of $\{\log,\exp\}$ with each other or themselves and likewise for $\{\sin,\cos,\tanh\}$; in TiSR, the **pow** operator may only raise to a constant exponent. Other GP parameters remain at package defaults. FastSRB’s central intervention is an early-termination callback. TiSR natively supports a user callback, which the authors attach by editing **commit 5b541b3**. Internally, approximately every **15 s** the search loop invokes the callback on all members of the current hall of fame. A run is eligible for early termination only if the relative-error measure $$ \delta(e)=\frac{\|y_{\mathrm{orig}}-y_{\mathrm{pred}}\|}{\|y_{\mathrm{orig}}\|+o}, \qquad o=10^{-100}, $$ satisfies $\delta(e)\le 1\times10^{-6}\%$ and the candidate’s tree size $c(e)$ does not exceed $1.2\times c_{\mathrm{ref}}$. If these filters pass, the expression is simplified with **Sympy**, constants are rounded to **five significant digits**, and the result is compared against a curated set of functionally equivalent ground-truth forms. A match signals immediate termination; near-misses are logged for future inclusion. The benchmark comprises **120 Feynman-derived SRSD tasks**, each run **5× for 30 min max**, with **200 train / 200 test points**, **no multiprocessing**, on an **8-core AMD Ryzen 7 PRO machine**. TiSR’s rediscovery rates under FastSRB are reported as **100.0 %** on the easy category, **78.0 %** on medium, **42.6 %** on hard, and **69.4 %** overall. Time savings from early termination are reported as **63 % less CPU time (approximately 184 h saved)**. For comparison, **SymbolicRegression.jl** rises from **26.7 %** to **44.7 %** rediscovery and saves **41.2 %** CPU time. The paper attributes TiSR’s stronger rediscovery rate primarily to the new benchmarking methodology—acceptance of equivalent forms plus early stopping—rather than to any intrinsic superiority of TiSR’s core GP operators. Caveats include three dropped problems (**B4, B11, III.9.52**) due to recurrent Sympy failures, a fairness assumption that discovered expressions would survive to normal termination, variable maximum expression complexity, and the evolving nature of the curated list of acceptable forms. ## 5. Thermal Image Super-Resolution In computer vision, TISR also denotes **Thermal Image Super-Resolution**, a task motivated by the lower native resolution, higher noise, and wider temperature-to-radiance nonlinearity of thermal sensors [2206.12046]. In the **PBVS-2022 Challenge**, the goal is to reconstruct either a **$\times4$** or **$\times2$** higher-resolution thermal image from a given low-resolution input while maintaining both **PSNR/SSIM** and perceptual or clinical utility. Yan et al. address this problem with **BN-CSNT**, a **Bilateral Network with Channel Splitting Network and Transformer**. BN-CSNT uses two parallel branches. The **context branch** applies channel splitting and **$K=8$ Swin-Based Blocks** to capture long-range contextual cues; the **spatial branch** uses a shallow transformer with **two Swin Basic Layers** to preserve fine local detail. The context branch is coupled with an **Attention Refinement Module (ARM)**, implemented in squeeze-and-excitation style: $$ s = \sigma(W_2\,\mathrm{ReLU}(W_1\,g(x))),\qquad g(x)=\frac1{HW}\sum_{i,j} x_{i,j,:},\qquad R=x\odot s. $$ The two branches are merged by a **Feature Fusion Module (FFM)**, followed by pixel-shuffle upsampling and a final convolution. Training uses an $\ell_1$ loss for **Track-1 ($\times4$ SR on Flir data)** and for the first phase of **Track-2 ($\times2$ Axis$\to$Axis)**; the second phase of Track-2 adds an **LSGAN** objective and an **SSIM** loss, yielding $$ L_G=L_{\ell_1}+\alpha L_{SSIM}+\beta L_{GAN}. $$ The reported training hyperparameters are **Adam** with $\beta_1=0.9$, $\beta_2=0.999$, initial learning rate **$1\times10^{-4}$** decayed by half every **200 epochs**, **batch size 16** with **$64\times64$** crops, **1000** total epochs, and augmentation by random horizontal/vertical flips and rotation. Final single-model challenge results are **PSNR = 33.64, SSIM = 0.9263** for **Track-1 ($\times4$)** and **PSNR = 21.08, SSIM = 0.7803** for **Track-2 ($\times2$)**. Compared to prior TiSR methods on the same challenge benchmark, including **CSN** with approximately **32.5 dB / 0.918** and **SwinIR-based SR** with approximately **33.2 dB / 0.923** on $\times4$, BN-CSNT yields a **+0.4 dB PSNR gain** and **+0.003 SSIM gain**. The paper attributes this to the bilateral design, channel splitting, ARM-based reweighting, and lightweight fusion of long-range and local features. ## 6. Twin-image super-resolution in remote sensing A different super-resolution usage appears in remote sensing, where TISR denotes **twin-image super-resolution**, described as the most challenging **multi-image super-resolution (MISR)** scenario because the high-resolution image must be recovered from a low-resolution image and its **subpixel-shift counterpart** [2602.21513]. The observation model is $$ y_1=D(x),\qquad y_2=D(Sx), $$ where $x\in\mathbb{R}^{MN}$ is the unknown HR image, $D$ is a blur-plus-downsampling operator, and $S$ is a fixed half-pixel shift on the HR grid. The reconstruction objective is the convex problem $$ \min_x \frac12\|y_1-Dx\|_2^2+\frac12\|y_2-DSx\|_2^2+\lambda R(x), $$ with convex self-similarity prior $$ R(x)=\frac12\sum_{(i,j)\in K}\alpha_{ij}\|P_i x-P_j x\|_2^2. $$ The paper solves this formulation with **COSUP**, a **convex self-similarity unfolding supermode super-resolution** algorithm. The derivation proceeds through **ADMM** by introducing an auxiliary variable $z\approx x$ and alternating between a proximal step for $R$ and a closed-form $x$-update involving $(H^\top H + cI)^{-1}$. In the network realization, the shift operator is embedded as a parameter-free pixel shift layer; the proximal map is approximated by **Model 1**, a **residual-in-residual CNN** whose inner blocks are **Swin-Transformer layers** and which is pretrained under the self-similarity loss $$ L_{SS}(G)=\|G(x)-x\|_1+\frac{\lambda}{2}\sum_{(i,j)\in K}\alpha_{ij}\|P_i[G(x)]-P_j[G(x)]\|_2^2. $$ The data-fidelity step is implemented as **Model 2**, which uses the **Woodbury identity** to reduce the inverse to a **$2mn\times2mn$** matrix $\Phi$ realized as a tiny **symmetric fully-connected** layer. The unfolding uses **$K=3$** stages; Model 1 has **4 Swin blocks** with **embedding dimension 96** and **window 8**; the parameter $c$ is learned. Training uses HR panchromatic patches from **GeoEye-1 (0.58 m)**, **CBERS-4A (2 m)**, and **PlanetScope (3 m)**, converted to panchromatic via **NTSC weights** and sliced into **$512\times512$** patches. Twin LR pairs are synthesized by Gaussian blur, $2\times$ downsampling, and half-pixel shift. The prox network is pretrained with **Adam**, learning rate **$5\times10^{-4}\to10^{-7}$** halved on plateau, **110 epochs**, **batch size 6**; then the entire unfolding model is trained with $\ell_1$ loss on the final stage output, with **$c$ initialized to 2**. Inference speed is approximately **50 ms per $512\times512$ LR pair on RTX 3090**. On **100 LR-pair samples** from **SPOT-5 THR mode**, the official CNES supermode product gives average **NIQE 4.85** and **PI 3.49**, whereas COSUP gives **NIQE 3.99** and **PI 2.76**. The reported qualitative outcome is better preservation of sharp edges and fine textures with less over-smoothing and ringing. ## 7. Time Index Modulation-Driven Standalone RIS for symbiotic radio In wireless communications, TiSR denotes a **Time Index Modulation-Driven Standalone RIS mechanism for symbiotic radio** [2407.00763]. The system comprises a **single-antenna primary transmitter (PTx)**, an **$M_R$-antenna primary receiver (PRx)**, a standalone **RIS** with **$N=N_1+N_2+N_3$** unit cells, and a passive **energy harvester (EH)**. Group 1 unit cells assist PTx transmission by phase shifts, Group 2 are perfect absorbers for wireless energy harvesting to power the RIS, and Group 3 reflect while conveying RIS information using **$J=2$** discrete phase shifts per RIS symbol. All links follow a **Rician fading model with path loss**. The PTx uses **time index modulation (TIM)** across a block of **$K$** slots with **$L