Evaluating the Efficacy of Neratinib on Live Cell HER2 Signaling Transduction Analysis Positive Triple Negative Breast

Inclusion Criteria: * The patient must have consented to participate and must have signed and dated an appropriate IRB-approved consent form that conforms to federal and i institutional guidelines for the pre-entry research core biopsy for CELx HSF testing and for initiating chemotherapy * Patients must be female. * Patients must be ≥ 18 years old. * Patient must have an ECOG performance status of 0 or 1 * The diagnosis of invasive adenocarcinoma of the breast must have been made by core needle biopsy. * The primary breast tumor must be palpable and measure ≥ 1.0 cm on physical exam. * The regional lymph nodes can be cN0 or cN1 * The tumor size can be T1c or T2 * Ipsilateral axillary lymph nodes must be evaluated by imaging (mammogram, ultrasound, and/or MRI) within 6 weeks prior to initiating chemotherapy. If suspicious or abnormal, FNA or core biopsy is recommended, also within 6 weeks prior to initiating chemotherapy. Findings of these evaluations will be used to determine the nodal status prior to initiating chemotherapy. * Nodal status - negative * Imaging of the axilla is negative; * Imaging is suspicious or abnormal but the FNA or core biopsy of the questionable node(s) on imaging is negative; * Nodal status - positive * FNA or core biopsy of the node(s) is cytologically or histologically suspicious or positive. * Imaging is suspicious or abnormal but FNA or core biopsy was not performed. * Tumor specimen obtained at the time of diagnosis must have estrogen (ER) and progesterone (PR) receptors \< 10%. * Tumor specimen obtained at the time of diagnosis must have been determined to be HER2-negative as follows: * Immunohistochemistry (IHC) 0-1+; or * IHC 2+ and ISH non-amplified with a ratio of HER2 to CEP17 \< 2.0, and if reported, average HER2 gene copy number \< 4 signals/cells; or * ISH non-amplified with a ratio of HER2 to CEP17 \< 2.0, and if reported, average HER2 gene copy number \< 4 signals/cells. * Blood counts performed within 6 weeks prior to initiating chemotherapy must meet the following criteria: * Absolute neutrophil count (ANC) must be ≥ 1200/mm3; * platelet count must be ≥ 100,000/mm3; and * hemoglobin must be ≥ 10 g/dL. * The following criteria for evidence of adequate hepatic function performed within 6 weeks prior to initiating chemotherapy must be met: * total bilirubin must be ≤ upper limit of normal (ULN) for the lab unless the patient has a bilirubin elevation \> ULN to 1.5 x ULN due to Gilbert's disease or similar syndrome involving slow conjugation of bilirubin; and * alkaline phosphatase must be ≤ 2.5 x ULN for the lab; and * AST must be ≤ 1.5 x ULN for the lab. * Alkaline phosphatase and AST may not both be \> the ULN. For example, if the alkaline phosphatase is \> the ULN but ≤ 2.5 x ULN, the AST must be ≤ the ULN. If the AST is \> the ULN but ≤ 1.5 x ULN, the alkaline phosphatase must be ≤ ULN. Note: If ALT is performed instead of AST (per institution's standard practice), the ALT value must be ≤ 1.5 x ULN; if both were performed, the AST must be ≤ 1.5 x ULN. * Patients with AST or alkaline phosphatase \> ULN are eligible for inclusion in the study if liver imaging (CT, MRI, PET-CT, or PET scan) performed within 6 weeks prior to initiating chemotherapy does not demonstrate metastatic disease and the requirements in criterion 4.2.13 are met. * Patients with alkaline phosphatase that is \> ULN but ≤ 2.5 x ULN or unexplained bone pain are eligible for inclusion in the study if a bone scan, PET-CT scan, or PET scan performed within 6 weeks prior to initiating chemotherapy does not demonstrate metastatic disease. * Serum creatinine performed within 6 weeks prior to initiating chemotherapy must be ≤ 1.5 x ULN for the lab. * The left ventricular ejection fraction (LVEF) assessment by echocardiogram or MUGA scan performed within 90 days prior to initiating chemotherapy must be ≥ 50% regardless of the facility's lower limit of normal (LLN). * Patients with reproductive potential must agree to use an effective non-hormonal method of contraception during therapy, and for at least 7 months after the last dose of study therapy. * Patients are candidates for weekly paclitaxel and carboplatin chemotherapy as determined by treating physician. * Patients with multifocal breast cancer are included as long as none of the tumors are HER2 positive by IHC or FISH and targeted lesion meets current inclusion criteria. * Conditions for patient eligibility (Study Enrollment) A patient cannot be considered eligible for this study unless all of the following conditions are met: * The patient must have consented to participate and must have signed and dated an appropriate IRB-approved consent form that conforms to federal and institutional guidelines for the FACT-2 study treatment. * Tumor determined to have abnormal HER2-driven signaling activity based on the CELx HSF test. Exclusion Criteria: * T3 or T4 tumors including inflammatory breast cancer. * FNA alone to diagnose the breast cancer. * Excisional biopsy or lumpectomy performed prior to initiating chemotherapy. * Surgical axillary staging procedure prior to initiating chemotherapy. Pre- neoadjuvant therapy sentinel node biopsy is not permitted. (FNA or core biopsy is acceptable.) * Definitive clinical or radiologic evidence of metastatic disease. Required imaging studies must have been performed within 6 weeks prior to initiating chemotherapy. * Synchronous bilateral invasive breast cancer. (Patients with synchronous and/or previous contralateral DCIS or LCIS are eligible.) * Any previous history of ipsilateral invasive breast cancer or ipsilateral DCIS. (Patients with synchronous or previous ipsilateral LCIS are eligible.) * Previous therapy with anthracycline, taxanes, trastuzumab, or other HER2 targeted therapies for any malignancy. * Any sex hormonal therapy, e.g., birth control pills, ovarian hormone replacement therapy, etc. (These patients are eligible if this therapy is discontinued prior to initiating chemotherapy.) * History of non-breast malignancies (except for in situ cancers treated only by local excision and basal cell and squamous cell carcinomas of the skin) within 2 years prior to initiating chemotherapy. * Cardiac disease (history of and/or active disease) that would preclude the use of the drugs included in the treatment regimens. This includes but is not confined to: * Active cardiac disease: * angina pectoris that requires the use of anti-anginal medication; * ventricular arrhythmias except for benign premature ventricular contractions; * supraventricular and nodal arrhythmias requiring a pacemaker or not controlled with medication; * conduction abnormality requiring a pacemaker; * valvular disease with documented compromise in cardiac function; and * symptomatic pericarditis. * History of cardiac disease: * myocardial infarction documented by elevated cardiac enzymes or persistent regional wall abnormalities on assessment of left ventricular (LV) function; * history of documented congestive heart failure (CHF); and * documented cardiomyopathy. * Uncontrolled hypertension defined as sustained systolic BP \> 150 mmHg or diastolic BP \> 90 mmHg. (Patients with initial BP elevations are eligible prior to initiating chemotherapy if initiation or adjustment of BP medication lowers pressure.) * Active hepatitis B or hepatitis C with abnormal liver function tests. * Intrinsic lung disease resulting in dyspnea. * Poorly controlled diabetes mellitus. * Active infection or chronic infection requiring chronic suppressive antibiotics. * Patients known to be HIV positive. * Nervous system disorder (paresthesia, peripheral motor neuropathy, or peripheral sensory neuropathy) ≥ grade 2, per the CTCAE v4.0. * Malabsorption syndrome, ulcerative colitis, resection of the stomach or small bowel, or other disease significantly affecting gastrointestinal function. * Other non-malignant systemic disease that would preclude treatment with any of the treatment regimens or would prevent required follow-up. * Conditions that would prohibit administration of corticosteroids. * Chronic daily treatment with corticosteroids with a dose of ≥ 10 mg/day methylprednisolone equivalent (excluding inhaled steroids). * Known hypersensitivity to any of the study drugs or any of the ingredients or excipients of these drugs (e.g., Cremophor® EL), including sensitivity to benzyl alcohol. * Pregnancy or lactation at the initiation of chemotherapy. (Note: Pregnancy testing must be performed within 2 weeks prior to initiating chemotherapy according to institutional standards for women of childbearing potential). * Psychiatric or addictive disorders or other conditions that, in the opinion of the investigator, would preclude the patient from meeting the study requirements. * Evidence after a clinical examination that the subject's tumor is progressing after treatment with one week of paclitaxel and before a CELx HSF test result is available. * For participation in adherence monitoring: no access to the web via smart phone, tablet or computer